The Pitfalls of "Regression to the Mean" analysis (1 Viewer)

[Sigmund Bloom]

I am getting tired of seeing someone's quality play actually held against them and cited as a reason to not pursue them in fantasy drafts. If a player has been mediocre for their whole career and there are no other indicators that this is the "new" version of that player, sure, regression to the mean is a good way to say that past results are no guarantee of future performance. However, this type of analysis is being misused in my opinion to stand for the idea that ALL players regress to the mean , when we observe the opposite - in fact, if that were true then fantasy football would be about avoiding players that play at an exceptional level! In this case, the player in question in Hakeem Nicks and I was responding to the idea that Nicks high YPC and TD% is a reason for "concern". I am interested in the pool's thoughts not so much on Nicks, but on the way "regression to the mean" analysis is being used in fantasy football today:

In a nutshell, it stands for the idea that "Average players in the league will tend to put up league average numbers". So when a player has numbers high above the league average for a season, but other evidence tells us that he is average, we should proceed with caution when importing too much meaning into their performance in the previous season. However, numbers high above the league average can actually be an indicator in the exact opposite direction, that the player really is a rare talent that is most definitely "above average" - especially when that is all that is contained in their track record, such as with Nicks, or Michael Turner when he was a backup RB. "Regression to the mean" should only be applied to be players whose talent is close to the mean. If it is applied to all players equally as if every player in the NFL is average, that will cause many breakout players to be missed. The numbers of young players who excel in limited opportunity will be taken as an indicator to stay away, when actually it should be an indicator to push your chips in! Finding breakout players before the breakout is one of the most crucial skills in fantasy football, and I think "regression to the mean" can short circuit that effort when it is misapplied.

 

[baconisgood]

I am getting tired of seeing someone's quality play actually held against them and cited as a reason to not pursue them in fantasy drafts. If a player has been mediocre for their whole careers and there are no other indicators that this is the "new" version of that player, sure regression to the mean is a good way to say that past results are no guarantee of future performance. However, this type of analysis is being misused in my opinion to stand for the idea that ALL players regress to the mean , when we observe the opposite - in fact, if that were true then fantasy football would be about avoiding players that play at an exceptional level! In this case, the player in question in Hakeem Nicks and I was responding to the Nicks high YPC and TD% being cited a reason for "concern". I am interested in the pool's thoughts not so much on Nicks, but on the way "regression to the mean" analysis is being used in fantasy football today:

In a nutshell, it stands for the idea that "Average players in the league will tend to put up league average numbers". So when a player has numbers high above the league average for a season, but other evidence tells us that he is average, we should proceed with caution when importing too much meaning into their performance in the previous season. However, numbers high above the league average can actually be an indicator in the exact opposite direction, that the player really is a rare talent that is most definitely "above average" - especially when that is all that is contained in their track record, such as with Nicks, or Michael Turner when he was a backup RB. "Regression to the mean" should only be applied to be players whose talent is close to the mean. If it is applied to all players equally as if every player in the NFL is average, that will cause many breakout players to be missed. The numbers of young players who excel in limited opportunity will be taken as an indicator to stay away, when actually it should be an indicator to push your chips in! Finding breakout players before the breakout is one of the most crucial skills in fantasy football, and I think "regression to the mean" can short circuit that effort when it is misapplied.

Regression to the mean doesn't just apply to average players, individual players have their own 'mean'. Chris Johnson, for example, should not be expected to have 2,500 yards from scrimmage next season, but he also shouldn't be expected to produce what an average starting back should produce. When used correctly "regression to the mean" for individual players means looking at what NFL players have done historically and trying to determine how far off someone's performance is from the typical NFL performance. Should elite players have a higher level? Yes. Does that mean that elite players can't massively overplay their own expectations and suffer from regression to the mean? No.

 

[BuckeyeArt]

I agree. It seems like people constantly use this when the player has no history. In those cases, they are regressing to the league mean, which makes no sense at all.

It seems to me that "regression to the mean" is just a lazy way to account for fundamental factors like injuries, schedule strength, and personnel additions or losses.

 

[PewterFan]

I think you have to look at each player individually. In 2002 Marc Boerigter, WR for Kansas City caught 8 touchdowns on 20 catches.

Because he was an average WR (at best) no one should've expected him to continue at that rate the following year. He just had one of those weird and lucky seasons where almost 50% of his catches were for scores. He didn't do anything after that.

Anyone who've seen Nicks play know that he's a special talent and should be a WR1 for years to come.

 

[Sigmund Bloom]

I think you have to look at each player individually.

Definitely a takeaway point, and it goes hand-in-hand with BuckeyeArt's point about it being lazy analysis - making the case that a player is average or below average, and that therefore, it is foolish to expect above average numbers to continue is the compelling way to use regression to the mean analysis, as opposed to just stating it as a conclusion - "player X's numbers were above average last year, therefore, we should be worried that his numbers will be average this year" - that is the analysis that I see as unhelpful at best, and destructive at worst - mistaking a positive indicator for a negative one.

 

[Matt Waldman]

I think you have to look at each player individually.

Definitely a takeaway point, and it goes hand-in-hand with BuckeyeArt's point about it being lazy analysis - making the case that a player is average or below average, and that therefore, it is foolish to expect above average numbers to continue is the compelling way to use regression to the mean analysis, as opposed to just stating it as a conclusion - "player X's numbers were above average last year, therefore, we should be worried that his numbers will be average this year" - that is the analysis that I see as unhelpful at best, and destructive at worst - mistaking a positive indicator for a negative one.

I agree. Eli Manning is a concrete example. To say Manning will regress to the mean because he had his best season with his best collection of talent that is still developing is a mistake. Could he go back to being a 3300-yard passer this year? Sure, but I would bet his receiving corps and offensive line were decimated in the process.

 

[Chase Stuart]

Here's something I wrote about the topic:

http://www.pro-football-reference.com/blog/?p=370

 

[Sigmund Bloom]

Here's something I wrote about the topic:

http://www.pro-football-reference.com/blog/?p=370

I think your study stands for a different proposition (The more exceptional the level of production is over an entire season, the more unlikely it is to be reproduced), than what I am talking about which is based more on averages (when a player has more big plays/scores/gains more on an average play than the league average in a limited opportunity, then he is likely to perform like an average player when the opportunity gets larger).Also, while the study is useful for showing that when you lump all players together, bet on regression to the mean, as Ive said on many occasions, fantasy football is not about being able to identify the players that adhere to the rule, it is about correctly identifying the players that are likely to be the exceptions to the rule. As was said above, we should look at each player on an case-by-case basis. Nothing in any study of rookie RBs growth in year N+1 was going to indicate Chris Johnson or Ray Rice's meteoric rise last year, in fact, those studies would strongly indicate that what Rice and Johnson did last year was basically impossible - and yet, they did it, and carried many fantasy teams to championships in the process.

 

[Pictus Cat]

I think you can start from either side, but both are important tools. Predict on observation, but double check the regression to the mean to fully understand that you are the player to perform that far from the mean. The other side is predict regression to the mean, then adjust from their based on your observations. I also think it is very important to check against record performances to understand if you are so excited about a player that you are predicting him to be the GOAT.

 

[Creed Bratton]

I completely agree with Sigmund that statistical analysis like "regression to the mean" is being misused to analyze players. However, I hypothesize that it isn't being done to support the idea that ALL players regress to the mean but, as BuckeyeArt alluded to, in reference to players with less proven fantasy history. Fantasy players usually aren't downgrading guys like Hakeem Nicks because they're statistical nazis, but because they're not sure if they should believe what they see. It's a lot easier for fantasy players and experts to say "I'm going to downgrade Nicks because he's going to regress to the mean" than say "I'm going to downgrade Nicks because I'm not sure if he's for real." Nobody would ever make the same statements if Andre Johnson put up identical YPC and TD% and used regression to the mean as reason to downgrade him in a fantasy draft.

It's actually pretty similar to my pet peeve of people referring to every uncertain fantasy situation as a "committee" and then projecting touches based on how much they like a player. It's substituting odds of being "the man" with how coaches will actually distribute touches. A perfect example was the Giants receiver situation a year ago and the associated speculation. Both types of analysis substitute incorrect reasoning to stand in for our uncertainty in evaluating and ranking a player and that type of thinking is a hard thing to get away from. I know that I certainly do it in some form or other and I think the only way around it is to systematically analyze a player's talent, surrounding talent, opportunity, and risk/reward ratio all within a backdrop of statistical perspective. And that's time consuming.

By the way, Sigmund and Matt have completely sold me and I'm on board with Nicks. My main league is PPR and the only thing I'm trying to figure out is how many catches he might get considering Steve Smith is such a trusted target for Eli.

 

[JDub15]

I would agree with the above assessments. Regression to the mean does have some fantasy application but to apply the principle to Nicks is borderline ridiculous. As Bloom mentioned one of the best ways to predict breakout players is to look at those who have done a lot with limited touches who are in line for a heavier workload... i.e., Hakeem Nicks in 2010.

If we drill down further into the data though sometimes we can find some valuable information... i.e., Bloom & Cecil mentioned Thomas Jones fluky low 1 rushing touchdown in 2007 was a reason he would bounce back in 2008 (+ upgrades at o-line, fb, and qb) - which he did from 1 rushing TD to 13 rushing TDs.

 

[ZWK]

People were correct to predict regression towards the mean for Michael Turner. He averaged 5.5 yards per carry in San Diego and probably couldn't keep that up, and he didn't - he ran for only 4.5 ypc his first year in Atlanta. But he was in a new situation and role as the starter in Atlanta, which meant that his ypc were only a small part of the story. You couldn't just take his previous stats and project them forward with some modifications for things like regression to the mean. You had to take what you know about his talent and situation to make guesses about his usage pattern and his success. Atlanta had a good offense and Turner had a huge role in it - he led the league in carries, carries inside the 10 yard line, and TDs inside the 10 - and that's why he had such a great fantasy season.

It's similar with Nicks - the big question for him is how big a role he'll play in the Giants offense. When a player has great per-touch performance with a small number of touches, it's usually safe to predict some decline in their per-touch performance, but what really matters is whether they'll see a big increase in their role. The circumstances look good for Nicks, since he's a first rounder coming off his rookie season, without an established starter blocking his way. If he has the talent and gets the targets, then he should have a great year, even though it'll probably be with less than a 16.8 ypr.

 

[Matt Waldman]

Here's something I wrote about the topic:

http://www.pro-football-reference.com/blog/?p=370

I think your study stands for a different proposition (The more exceptional the level of production is over an entire season, the more unlikely it is to be reproduced), than what I am talking about which is based more on averages (when a player has more big plays/scores/gains more on an average play than the league average in a limited opportunity, then he is likely to perform like an average player when the opportunity gets larger).Also, while the study is useful for showing that when you lump all players together, bet on regression to the mean, as Ive said on many occasions, fantasy football is not about being able to identify the players that adhere to the rule, it is about correctly identifying the players that are likely to be the exceptions to the rule. As was said above, we should look at each player on an case-by-case basis. Nothing in any study of rookie RBs growth in year N+1 was going to indicate Chris Johnson or Ray Rice's meteoric rise last year, in fact, those studies would strongly indicate that what Rice and Johnson did last year was basically impossible - and yet, they did it, and carried many fantasy teams to championships in the process.

Amen on the bold section.

 

[netnalp]

I think you have to look at each player individually.

Definitely a takeaway point, and it goes hand-in-hand with BuckeyeArt's point about it being lazy analysis - making the case that a player is average or below average, and that therefore, it is foolish to expect above average numbers to continue is the compelling way to use regression to the mean analysis, as opposed to just stating it as a conclusion - "player X's numbers were above average last year, therefore, we should be worried that his numbers will be average this year" - that is the analysis that I see as unhelpful at best, and destructive at worst - mistaking a positive indicator for a negative one.

I agree. Eli Manning is a concrete example. To say Manning will regress to the mean because he had his best season with his best collection of talent that is still developing is a mistake. Could he go back to being a 3300-yard passer this year? Sure, but I would bet his receiving corps and offensive line were decimated in the process.

Eli was who I was thinking ofwhen reading the initial post.Eli could regress but it is very possible he repeats or builds on last years numbers. He used to get tunnel vision, just focusing on Plax, the new situation I think has caused him to change his game, where he spreads the ball around rather than throwing a jump ball to Burress.

 

[Ramblin Wreck]

I think you have to look at each player individually.

Definitely a takeaway point, and it goes hand-in-hand with BuckeyeArt's point about it being lazy analysis - making the case that a player is average or below average, and that therefore, it is foolish to expect above average numbers to continue is the compelling way to use regression to the mean analysis, as opposed to just stating it as a conclusion - "player X's numbers were above average last year, therefore, we should be worried that his numbers will be average this year" - that is the analysis that I see as unhelpful at best, and destructive at worst - mistaking a positive indicator for a negative one.

I agree. Eli Manning is a concrete example. To say Manning will regress to the mean because he had his best season with his best collection of talent that is still developing is a mistake. Could he go back to being a 3300-yard passer this year? Sure, but I would bet his receiving corps and offensive line were decimated in the process.

Or maybe Eli's passing stats went up because of the health, or lack thereof, in the running game last season. If Jacobs and Bradshaw are both healthy for 16 games this year, no way Eli approaches last years passing numbers.

 

[Sigmund Bloom]

I think you have to look at each player individually.

Definitely a takeaway point, and it goes hand-in-hand with BuckeyeArt's point about it being lazy analysis - making the case that a player is average or below average, and that therefore, it is foolish to expect above average numbers to continue is the compelling way to use regression to the mean analysis, as opposed to just stating it as a conclusion - "player X's numbers were above average last year, therefore, we should be worried that his numbers will be average this year" - that is the analysis that I see as unhelpful at best, and destructive at worst - mistaking a positive indicator for a negative one.

I agree. Eli Manning is a concrete example. To say Manning will regress to the mean because he had his best season with his best collection of talent that is still developing is a mistake. Could he go back to being a 3300-yard passer this year? Sure, but I would bet his receiving corps and offensive line were decimated in the process.

Or maybe Eli's passing stats went up because of the health, or lack thereof, in the running game last season. If Jacobs and Bradshaw are both healthy for 16 games this year, no way Eli approaches last years passing numbers.

Eli was playing on a bum wheel for a lot of the season - that alone can make up for any leveling of the run/pass split, not to mention steps forward by Smith/Manningham/Nicks - it would be one thing if Eli threw something like 600 passes last year that indicates a clear outlier because of run/pass split that is unsustainable. As I mentioned in the Nicks spotlight thread, the Giants were only three pass attempts per game higher in 2009 than they were in 2008. I just don't see how that can be responsible for the majority of Eli's increase in production.

 

[Sigmund Bloom]

People were correct to predict regression towards the mean for Michael Turner. He averaged 5.5 yards per carry in San Diego and probably couldn't keep that up, and he didn't - he ran for only 4.5 ypc his first year in Atlanta. But he was in a new situation and role as the starter in Atlanta, which meant that his ypc were only a small part of the story. You couldn't just take his previous stats and project them forward with some modifications for things like regression to the mean. You had to take what you know about his talent and situation to make guesses about his usage pattern and his success. Atlanta had a good offense and Turner had a huge role in it - he led the league in carries, carries inside the 10 yard line, and TDs inside the 10 - and that's why he had such a great fantasy season.It's similar with Nicks - the big question for him is how big a role he'll play in the Giants offense. When a player has great per-touch performance with a small number of touches, it's usually safe to predict some decline in their per-touch performance, but what really matters is whether they'll see a big increase in their role. The circumstances look good for Nicks, since he's a first rounder coming off his rookie season, without an established starter blocking his way. If he has the talent and gets the targets, then he should have a great year, even though it'll probably be with less than a 16.8 ypr.

This is true, and its an illustration of why "regression to the mean" will sometimes lead you down the wrong path. Nicks doesn't have to average 16.8 YPC or 1 TD every 8 catches to be a breakout player this year. 15 YPC and 1 TD/10 catches will make him this year's Sidney Rice. The important thing is that his YPC and TD% are not an indicator to be wary of his prospects, they are an indicator to be excited about them.

 

[Anthony Borbely]

This is true, and its an illustration of why "regression to the mean" will sometimes lead you down the wrong path. Nicks doesn't have to average 16.8 YPC or 1 TD every 8 catches to be a breakout player this year. 15 YPC and 1 TD/10 catches will make him this year's Sidney Rice. The important thing is that his YPC and TD% are not an indicator to be wary of his prospects, they are an indicator to be excited about them.

This pretty much summarizes my opinion of this topic. I think people are getting too locked into the specific stats instead of looking at the big picture.

 

[SSOG]

Regression to the mean doesn't just apply to average players, individual players have their own 'mean'. Chris Johnson, for example, should not be expected to have 2,500 yards from scrimmage next season, but he also shouldn't be expected to produce what an average starting back should produce. When used correctly "regression to the mean" for individual players means looking at what NFL players have done historically and trying to determine how far off someone's performance is from the typical NFL performance. Should elite players have a higher level? Yes. Does that mean that elite players can't massively overplay their own expectations and suffer from regression to the mean? No.

Agreed. Every player has his own "true mean", his actual average performance level that over a large enough sample he will approach. The problem is that football doesn't give us a large enough sample, so most players produce performances that are out of line with their "true mean" talent level. Our job as fantasy footballers is to recognize and identify that "true mean" talent level in the face of a blizzard of stats and evidence and data (that's probably providing more confusion than clarity).As a "for example"... Justin Forsett averaged 5.4 yards per carry last year in Seattle. It is my personal opinion that that figure is way, way above his own personal "true mean" talent level, that he's really more of a 4.4-ypc RB who happened to get incredibly lucky over a small sample size. As a result, when I'm projecting him this season, I'm going to project him more in the 4.4 ypc range. DeAngelo Williams, on the other hand, averaged 5.2 yards per carry. Personally, I don't think that was much of a fluke at all. I don't know if any RB's "true mean" talent level can really be above 5 yards per carry, but if any RB's is, it's DeAngelo's. As a result, I have no problem projecting DeAngelo Williams to average 5.2 ypc again this season. In both cases, I'm using "regression to the mean", but one instance involved me turning a 5.4 ypc RB into a 4.4 ypc RB, and another instance involved me turning a 5.2 ypc RB into... a 5.2 ypc RB.I'm going to disagree with Bloom's statement that the best owners are the guys who can identify the exceptions to the rule. I don't believe that *ANYONE* can predict the outlier seasons. Nobody could have predicted CJ3's 2,000 yard season. Nobody could have predicted Tom Brady throwing for 50 TDs. All an owner could have done is recognized that CJ3 and Tom Brady has a very high "true mean" talent level and then ranked them highly as a result... but there is no such thing as a player that is more likely to outperform his "true mean" than another player. I mean, it flies in the face of the whole concept of a "true mean" to suggest otherwise. The best fantasy owners are the ones who are best able to identify players' "true means", not the ones who happen to luck into a statistical fluke. Last year, those best fantasy owners would have been more likely to own Rice or CJ3 (because they recognized that both players were more talented than they were getting credit for). There might be other years where those best owners are LESS likely to get the out-of-nowhere breakout that single-handedly wins championships (for instance, I doubt many of the best owners had the Drew Bennett/Billy Volek pairing at the end of 2004 because, to be quite honest, Bennett and Volek really aren't that talented).

 

[Maurile Tremblay]

Regression to the mean is best understood in Bayesian terms, IMO, and the basic idea can be stated pretty simply.

If we expect a player to perform at Level X, and he in fact performs for a limited period at Level Y, we should update our expectations for him to be somewhere between X and Y.

So if we expected Nicks to be a 14 yards-per-catch receiver, and he averaged 16 yards per catch in 2009, we should update our estimation of his true YPC ability to be higher than 14 but lower than 16.

The idea is that his actual performance gives us new data to consider, pushing him away from our previous expectations toward his actual performance; but our previous expectations aren't to be thrown out completely based on a limited sample. So we land somewhere in between. (Exactly where in between -- whether closer to our previous expectations or to his actual performance -- depends on factors such as how big the observed sample of results is, how sure we were in our previous expectations, and so on.)

The phrase "regression to the mean" can be a bit misleading because it doesn't tell us which mean will be regressed to. The mean for all NFL players? The mean for all first-round draft picks? The mean for players with a certain size-speed combo? Or what?

The answer should be the mean for all players in the same situation (same ability, same surrounding cast, etc.) as the player in question. In the NFL, no two players are ever in the exact situation, so we muddle through by doing the best we can -- finding players who were most similar in the most relevant respects, taking everything realistically possible into account. Which is the same thing as what I meant above by our "previous expectations."

The idea of regression to the mean is applicable to football performances at least in broad terms. But football is more complicated than many of the math problems commonly subjected to statistical analysis. Regression to the mean is typically used to adjust expectations based on newly observed results. In football, though, we are not limited to observing results. We can also observe the underlying skills that contributed to those results.

(When I watch basketball players shoot free throws, for example, I can often tell you who the better shooter is after just a couple shots, even if the better shooter went 1 for 2 while the worse shooter went 2 for 2. I'm not doing statistical analysis: I'm evaluating their mechanics, which gives me more information than just their statistical results. So my subjective evaluation may trump those limited statistics. Similarly, if our previous expectations for Nicks were based on subjective evaluations that his performance has caused us to revise -- independent of his results -- then our updated expectations may not always fall between our previous expectations and our newly observed results. In other words, "regression to the mean" may not apply to every player; there may be exceptions.)

On the whole, though, regression to the mean is a valid concept that does apply, broadly, to football stats. And it applies to superstars no less than it applies to average players. Moreover, it does not penalize players for stellar performances. Just the opposite, it causes our expectations to be adjusted upwards when a player's performance is stellar (or downwards when a player's performance is disappointing).

 

[Sigmund Bloom]

I think SSOG and Maurile's points are strong and a good way to combine both approaches - players will regress to their mean, which is constantly changing to reflect their current level of play - and to determine that mean there has to be some subjective analysis, some evaluation of the player's skills.

I think where we can all agree is that exceptional stats/averages should not automatically trigger a reduction in future expectations simply because they are not in line with league averages - some subjective analysis must be to explain why a player's "true mean" is below their production levels.

 

[H8fulHuck]

The phrase "regression to the mean" can be a bit misleading because it doesn't tell us which mean will be regressed to. The mean for all NFL players? The mean for all first-round draft picks? The mean for players with a certain size-speed combo? Or what?



The answer should be the mean for all players in the same situation (same ability, same surrounding cast, etc.) as the player in question. In the NFL, no two players are ever in the exact situation, so we muddle through by doing the best we can -- finding players who were most similar in the most relevant respects, taking everything realistically possible into account. Which is the same thing as what I meant above by our "previous expectations."

You could work with the numbers until collapsing from dizziness trying to quantify the numbers. The NFL is fluid. Each team is constantly evolving and changing through the draft, injury, free agency and player development/regression. A players mean can change at any point in preseason all the way through the playoffs. Rashard Mendenhall for example, takes a hit with Willie Colon being lost for the season. To analyze why the "true mean" is often projected below a player's current production level, it is likely based upon how that player to be used in the future or a reality check after a statistically brilliant season.

I like to relate it to Doug's projections in the subscriber contest. Based on the weekly stat projections, he could predict with amazing accuracy, how likely a team's chances are to advance to the next week. On a player level it's like Brady in 2007 hitting that 1/10% chance that you get a perfect storm of events followed up in 2008 with a 2% chance of being injured for the season. No one should project him at 07 or 08 stats ever again from Brady even though it is possible. If I could only harness that power to select my players before the season starts...

 

[SSOG]

I think where we can all agree is that exceptional stats/averages should not automatically trigger a reduction in future expectations simply because they are not in line with league averages - some subjective analysis must be to explain why a player's "true mean" is below their production levels.

Agreed 100%. If Chris Johnson outperformed your projections by 1,000 yards, then that's always better than if he outperformed your projections by 400 yards, even with regression. For example, a very simplistic method of finding a player's "true mean" might be to take your estimation of their true mean last season, and to take their actual performance last season, and then to simply split the difference. In that case, if you thought Chris Johnson was a 1500 yard back and he got 1900, you'd estimate him at 1700 yards. If he went for 2500 yards, you'd estimate him at 2000. Still a substantial "regression", but a full 300 yards more than if he'd performed at a less exceptional pace.

 

[gethugefast1]

I am interested in the pool's thoughts not so much on Nicks, but on the way "regression to the mean" analysis is being used in fantasy football today:

"Regression to the Mean" is exactly my thinking towards Jamaal Charles 2nd half of '09.You cannot tell which way an individual's score will move based on the regression to the mean phenomenon. Even though the group's average will move toward the population's, some individuals in the group are likely to move in the other direction.

________________________________________________________________________________

http://bleacherreport.com/articles/400714-...yards-per-carry

 

[ookook]

Regression to the mean occurs because of sampling error and the imperfect relationship between performance of one season and the performance in the next, all else being equal.

That is, in a bivariate regression equation where the only predictor variable is last season's performance, you would tend to be off if you predicted them to do the same (all else being equal, which is the key).

What would be a better prediction? Well, if there is a mean for that player from several seasons, it will tend to be closer to that mean because the correlation is not 1.00 (or -1.00).

Or as Maurile points out, on average it will fall between their extreme score from their most recent season and the mean of the others.

By how much? This depends on some things such as correlation between seasons' fantasy points for that position, the variance of players playing that position, and the variance of that player's past fantasy performance, the distance between the extreme score and the position mean, and the distance between the extreme score and the individual player's mean.

Now, lots of this we do not have on hand. Hopefully Chase can point us to something that helps for the mean and SD of FBG fantasy points by postion and the correlation between seasons by position for starters. I played with this some about 8 years ago, but do not have it in front of me.

So what can we eyeball quickly? Three of these I think: (a) variance of that player's past fantasy performance (lots of spread vs. little dispersion), (b) the distance between the extreme score and the position mean (presumably of other starters at same position), and © the distance between the extreme score and the individual player's mean.

The larger any of these are, the more likely will be regression to the means (of the position and of the player) will happen.

We usually only are attending to top performers, so their extreme score tend to be distal from the mean of other starters at that psoitions.

So someone who has a great season, their best, but is really just a little better than their tightly clustered past seasons, no reason to predict much drop-off. But someone who has a great season, their best, and it is a lot better than their widely dispersed past performance one should be prepared for a decline.

If the situation is similar.

That is the problem with bivariate reression: It ignores every single other possible predictor. It is overly simplistic and a "mispecified model". It is an omitted variable bias in prediction and seems to be what drives Bloom's sentiment. And he is right: ignoring every other variable that could have accounted for the banner season besides sampling error will often lead you astray. After all, even if the correlation between seasons is .70, half of the variance is not explained and would be if we could account for every meaningful variable.

So if something changed that can explain why the past season was a marked improvement, and that situation has not changed, then one should not explect a decline. The values on these omitted variables have not changed and will tend to compensate for the regression to the mean (the imperfect relationship between the single predictor and the criterion) when the predicted performance is estimated.

Of course, many fantasy owners might be biased in assessing which parts of the situation might have changed to create the banner season and whether these have changed (or whether other variables have changed they are not paying attention to).

Be that is it may, the takeaway is that unless you can posit the factors that accounted for the extreme score and unless they have stayed the same, regression to the means will be likely. If you were right and if nothing else changed to delteriously affect their future performance that you missed.

If that player has no past mean, you only have the position mean to go by, which is a relatively bad predictor of an individual's performance.

 

[kurtrudder]

I think you have to look at each player individually.

Definitely a takeaway point, and it goes hand-in-hand with BuckeyeArt's point about it being lazy analysis - making the case that a player is average or below average, and that therefore, it is foolish to expect above average numbers to continue is the compelling way to use regression to the mean analysis, as opposed to just stating it as a conclusion - "player X's numbers were above average last year, therefore, we should be worried that his numbers will be average this year" - that is the analysis that I see as unhelpful at best, and destructive at worst - mistaking a positive indicator for a negative one.

I agree. Eli Manning is a concrete example. To say Manning will regress to the mean because he had his best season with his best collection of talent that is still developing is a mistake. Could he go back to being a 3300-yard passer this year? Sure, but I would bet his receiving corps and offensive line were decimated in the process.

Or maybe Eli's passing stats went up because of the health, or lack thereof, in the running game last season. If Jacobs and Bradshaw are both healthy for 16 games this year, no way Eli approaches last years passing numbers.

Eli was playing on a bum wheel for a lot of the season - that alone can make up for any leveling of the run/pass split, not to mention steps forward by Smith/Manningham/Nicks - it would be one thing if Eli threw something like 600 passes last year that indicates a clear outlier because of run/pass split that is unsustainable. As I mentioned in the Nicks spotlight thread, the Giants were only three pass attempts per game higher in 2009 than they were in 2008. I just don't see how that can be responsible for the majority of Eli's increase in production.

Not to rag on Pasquino too much but when I read him say "regression to the mean" in the Eli Manning faceoff the other day, I had to vomit in my mouth. Matt in the article had outlined it fairly clearly for me why 2009 wasn't an outlier season. Sig's points above add even more weight to what Matt said in that faceoff, in fact I think he might not have mentioned Eli playing much of 2009 with that foot injury.

 

[Kenny Powers]

Good thread and has given me more to think about when starting up my projections in the next month

 

[SSOG]

Not to rag on Pasquino too much but when I read him say "regression to the mean" in the Eli Manning faceoff the other day, I had to vomit in my mouth. Matt in the article had outlined it fairly clearly for me why 2009 wasn't an outlier season. Sig's points above add even more weight to what Matt said in that faceoff, in fact I think he might not have mentioned Eli playing much of 2009 with that foot injury.

I think regression to the mean is still a perfectly valid concern for Eli Manning. He had a career season last year. Despite all the perfectly logical reasons to think he's capable of sustaining that production, the simple fact is that he had his career season in the most QB-friendly season the NFL has ever seen. He broke the 4,000 yard passing barrier in the season where more people broke the 4,000 yard barrier than any other year in history. While his raw point total was an outlier, his rank among his peers was 100% business as usual. In 2006-2008, Eli Manning ranked 10th, 13th, and 13th. In 2009, he ranked 10th. In other words, Eli Manning had another Eli Manning year.It's possible that this league-wide passing explosion was a fluke that is going to return to prior levels, and that Eli Manning will return with it. It's possible that this league-wide passing explosion is a trend that will remain in effect, and that all of Eli Manning's peers will sustain their career numbers right along with him. Either way, the fact that Eli Manning has ranked 10th-13th in each of the last 4 seasons remains more relevant, in my mind, than the fact that he had 4,000 yards passing last year. His position among his peers has remained relatively static for half a decade now.

Last year's QB numbers kind of remind me of the 1995 WR numbers. For those who aren't familiar with the 1995 season... that's the year that Isaac Bruce had 119/1781/15 (the second highest receiving-yardage total in NFL history)... and didn't even make the pro bowl. He missed out because Michael Irvin had 111/1603/10, Herman Moore had 123/1686/13, Cris Carter had 122/1371/17, and Jerry Rice had 122/1848/15. Last year's #1 WR (Andre Johnson) would have ranked SEVENTH in 1995- he would have been a below-average WR1!

Anyway, what does 1995 have to do with Eli Manning? Well, with the benefit of hindsight we are able to see that 1995 was a 1-year fluke. After the 1995 season, it would have been easy to claim that the NFL was entering a new era of WR dominance and those numbers would remain high for years to come... but that simply wasn't the case. Isaac Bruce, Cris Carter, Tim Brown, Herman Moore, Jerry Rice, and Michael Irvin played for a combined 93 seasons. They made 43 combined pro bowls. Two of them are already HoFers, two more are very likely to make it in the next couple of years, and the other two are among the very best WRs in the "just-shy-of-HoF-caliber" group. Despite that, EVERY SINGLE ONE OF THEM set a career high for fantasy points in 1995. Even middle-of-the-road guys like Anthony Miller (59/1079/14) and Carl Pickens (99/1234/17) were producing like uberstuds in 1995. In hindsight, it turns out that something about the 1995 season just created a perfect storm for production that none of those elite receivers would ever again match, and all of those reasons we had to believe it was sustainable, that "regression to the mean" was a ludicrous suggestion... all those reasons wound up being wrong.

It's very possible that 2009 was to QBs what 1995 was to WRs. It's possible that 15 years from now we'll be talking to over-optimistic fantasy owners about the time that the NFL saw 9 players pass for 4200+ yards, and even saw Eli Manning get in on the action and chip in 4k yards of his own.

At the end of the day, I'm reminded of the saying "A rising tide lifts all ships". Eli's stats last year were aberrationally high... but so where the league's as a whole. It's possible that something about 2009 just created the perfect environment for QBs to flourish, and that 2010 will return us to business as usual... but even if it doesn't, every QB in the league benefited from the environment that led to Eli Manning passing for 4,000. Regression to the mean is a perfectly valid point to bring up with respect to Eli Manning- or, really, to bring up any time a 6-year vet sees such a dramatic and unexpected jump in his production. Especially when such a jump in raw numbers results in absolutely no change whatsoever in his ranking relative to his peers.

Edit: In fact, anyone who is projecting Eli Manning's numbers to stay flat from last year, but his ranking against his peers to rise, is essentially saying that they believe in regression to the mean as it applies to every single QB in the entire NFL... except for Eli Manning.

 

[Pip's Invitation]

This ain't baseball, folks. 16 games is a much smaller sample size than 162, which makes any kind of predictions based on statistical analysis more precarious. As does the violent nature of the sport, which leads to high rates of injuries.

What really matters is talent, opportunity, and team factors/supporting cast. Don't overthink the rest of it.

 

[Hoot&HoLLer]

Could someone try to apply their line of thinking of how proper or improper use of RTM was used or not used or could have been used as described so far in this thread to have attempted to predict the year two performances on the following WRs?

Randy Moss

Eddie Royal

Marques Colston

Dwayne Bowe

Desean Jackson

Anquan Boldin

Based on that use of RTM analysis, what would hold for these soon to be 2nd year WR's:

Mike Wallace

Maclin

Crabtree

Harvin

Edited to try and better clarify what is being requested.

 

[Jason Wood]

Regression to the mean is best understood in Bayesian terms, IMO, and the basic idea can be stated pretty simply.

If we expect a player to perform at Level X, and he in fact performs for a limited period at Level Y, we should update our expectations for him to be somewhere between X and Y.

So if we expected Nicks to be a 14 yards-per-catch receiver, and he averaged 16 yards per catch in 2009, we should update our estimation of his true YPC ability to be higher than 14 but lower than 16.

The idea is that his actual performance gives us new data to consider, pushing him away from our previous expectations toward his actual performance; but our previous expectations aren't to be thrown out completely based on a limited sample. So we land somewhere in between. (Exactly where in between -- whether closer to our previous expectations or to his actual performance -- depends on factors such as how big the observed sample of results is, how sure we were in our previous expectations, and so on.)

The phrase "regression to the mean" can be a bit misleading because it doesn't tell us which mean will be regressed to. The mean for all NFL players? The mean for all first-round draft picks? The mean for players with a certain size-speed combo? Or what?

The answer should be the mean for all players in the same situation (same ability, same surrounding cast, etc.) as the player in question. In the NFL, no two players are ever in the exact situation, so we muddle through by doing the best we can -- finding players who were most similar in the most relevant respects, taking everything realistically possible into account. Which is the same thing as what I meant above by our "previous expectations."

The idea of regression to the mean is applicable to football performances at least in broad terms. But football is more complicated than many of the math problems commonly subjected to statistical analysis. Regression to the mean is typically used to adjust expectations based on newly observed results. In football, though, we are not limited to observing results. We can also observe the underlying skills that contributed to those results.

(When I watch basketball players shoot free throws, for example, I can often tell you who the better shooter is after just a couple shots, even if the better shooter went 1 for 2 while the worse shooter went 2 for 2. I'm not doing statistical analysis: I'm evaluating their mechanics, which gives me more information than just their statistical results. So my subjective evaluation may trump those limited statistics. Similarly, if our previous expectations for Nicks were based on subjective evaluations that his performance has caused us to revise -- independent of his results -- then our updated expectations may not always fall between our previous expectations and our newly observed results. In other words, "regression to the mean" may not apply to every player; there may be exceptions.)

On the whole, though, regression to the mean is a valid concept that does apply, broadly, to football stats. And it applies to superstars no less than it applies to average players. Moreover, it does not penalize players for stellar performances. Just the opposite, it causes our expectations to be adjusted upwards when a player's performance is stellar (or downwards when a player's performance is disappointing).

Regression to the mean occurs because of sampling error and the imperfect relationship between performance of one season and the performance in the next, all else being equal.

That is, in a bivariate regression equation where the only predictor variable is last season's performance, you would tend to be off if you predicted them to do the same (all else being equal, which is the key).

What would be a better prediction? Well, if there is a mean for that player from several seasons, it will tend to be closer to that mean because the correlation is not 1.00 (or -1.00).

Or as Maurile points out, on average it will fall between their extreme score from their most recent season and the mean of the others.

By how much? This depends on some things such as correlation between seasons' fantasy points for that position, the variance of players playing that position, and the variance of that player's past fantasy performance, the distance between the extreme score and the position mean, and the distance between the extreme score and the individual player's mean.

Now, lots of this we do not have on hand. Hopefully Chase can point us to something that helps for the mean and SD of FBG fantasy points by postion and the correlation between seasons by position for starters. I played with this some about 8 years ago, but do not have it in front of me.

So what can we eyeball quickly? Three of these I think: (a) variance of that player's past fantasy performance (lots of spread vs. little dispersion), (b) the distance between the extreme score and the position mean (presumably of other starters at same position), and © the distance between the extreme score and the individual player's mean.

The larger any of these are, the more likely will be regression to the means (of the position and of the player) will happen.

We usually only are attending to top performers, so their extreme score tend to be distal from the mean of other starters at that psoitions.

So someone who has a great season, their best, but is really just a little better than their tightly clustered past seasons, no reason to predict much drop-off. But someone who has a great season, their best, and it is a lot better than their widely dispersed past performance one should be prepared for a decline.

If the situation is similar.

That is the problem with bivariate reression: It ignores every single other possible predictor. It is overly simplistic and a "mispecified model". It is an omitted variable bias in prediction and seems to be what drives Bloom's sentiment. And he is right: ignoring every other variable that could have accounted for the banner season besides sampling error will often lead you astray. After all, even if the correlation between seasons is .70, half of the variance is not explained and would be if we could account for every meaningful variable.

So if something changed that can explain why the past season was a marked improvement, and that situation has not changed, then one should not explect a decline. The values on these omitted variables have not changed and will tend to compensate for the regression to the mean (the imperfect relationship between the single predictor and the criterion) when the predicted performance is estimated.

Of course, many fantasy owners might be biased in assessing which parts of the situation might have changed to create the banner season and whether these have changed (or whether other variables have changed they are not paying attention to).

Be that is it may, the takeaway is that unless you can posit the factors that accounted for the extreme score and unless they have stayed the same, regression to the means will be likely. If you were right and if nothing else changed to delteriously affect their future performance that you missed.

If that player has no past mean, you only have the position mean to go by, which is a relatively bad predictor of an individual's performance.

To Bloom's broader point, I'm curious who is making a blanket "regression to the mean" argument? I'm sure they're out there, I guess I am just conditioned not to pay them any mind.

I think it's certainly a valid COMPONENT to analyzing a player's situation. Take Peyton Manning or Tom Brady's record-setting passing seasons. We had large bodies or prior work (particularly with Manning) that were consistently below that year, which was historic against both his output AND NFL history. Yet I saw way too many people saying he would throw 40+ TDs again the following season, arguing that haircutting his TD total by 20%ish was being conservative and "accounting for a regression to the mean." Projecting Manning to throw 40+ TDs that following season was flawed logic. So in THAT case, where situation was stable, supporting cast was relatively stable, coaching was stable and the player was stable...regression to the mean is a very powerful indicator that helps people come down from unrealistic outlooks.

But to the opposite end of the spectrum, Eli, I agree that you have to look at WHY his numbers took a big jump. His receiving corps is MUCH better than it had been, and Manning is still young enough that incremental improvement in his ability to execute the offense can account for a step forward. Add to that a complete degradation of the Giants defense after the early 5 game winning streak, and the commensurate erosion of the productivity of both Jacobs (all season) and Bradshaw (the final three months), and the recipe was in place for Eli to put all the pieces together. As an Eagles fan, the last thing I want to see if Eli maintain that level of PER ATTEMPT productivity and combine that with a renewed defensive vigor and a healthy tailback tandem. But that's certainly a possible, if not most likely, outcome.

 

[kurtrudder]

Not to rag on Pasquino too much but when I read him say "regression to the mean" in the Eli Manning faceoff the other day, I had to vomit in my mouth. Matt in the article had outlined it fairly clearly for me why 2009 wasn't an outlier season. Sig's points above add even more weight to what Matt said in that faceoff, in fact I think he might not have mentioned Eli playing much of 2009 with that foot injury.

I think regression to the mean is still a perfectly valid concern for Eli Manning. He had a career season last year. Despite all the perfectly logical reasons to think he's capable of sustaining that production, the simple fact is that he had his career season in the most QB-friendly season the NFL has ever seen. He broke the 4,000 yard passing barrier in the season where more people broke the 4,000 yard barrier than any other year in history. While his raw point total was an outlier, his rank among his peers was 100% business as usual. In 2006-2008, Eli Manning ranked 10th, 13th, and 13th. In 2009, he ranked 10th. In other words, Eli Manning had another Eli Manning year.It's possible that this league-wide passing explosion was a fluke that is going to return to prior levels, and that Eli Manning will return with it. It's possible that this league-wide passing explosion is a trend that will remain in effect, and that all of Eli Manning's peers will sustain their career numbers right along with him. Either way, the fact that Eli Manning has ranked 10th-13th in each of the last 4 seasons remains more relevant, in my mind, than the fact that he had 4,000 yards passing last year. His position among his peers has remained relatively static for half a decade now.

Last year's QB numbers kind of remind me of the 1995 WR numbers. For those who aren't familiar with the 1995 season... that's the year that Isaac Bruce had 119/1781/15 (the second highest receiving-yardage total in NFL history)... and didn't even make the pro bowl. He missed out because Michael Irvin had 111/1603/10, Herman Moore had 123/1686/13, Cris Carter had 122/1371/17, and Jerry Rice had 122/1848/15. Last year's #1 WR (Andre Johnson) would have ranked SEVENTH in 1995- he would have been a below-average WR1!

Anyway, what does 1995 have to do with Eli Manning? Well, with the benefit of hindsight we are able to see that 1995 was a 1-year fluke. After the 1995 season, it would have been easy to claim that the NFL was entering a new era of WR dominance and those numbers would remain high for years to come... but that simply wasn't the case. Isaac Bruce, Cris Carter, Tim Brown, Herman Moore, Jerry Rice, and Michael Irvin played for a combined 93 seasons. They made 43 combined pro bowls. Two of them are already HoFers, two more are very likely to make it in the next couple of years, and the other two are among the very best WRs in the "just-shy-of-HoF-caliber" group. Despite that, EVERY SINGLE ONE OF THEM set a career high for fantasy points in 1995. Even middle-of-the-road guys like Anthony Miller (59/1079/14) and Carl Pickens (99/1234/17) were producing like uberstuds in 1995. In hindsight, it turns out that something about the 1995 season just created a perfect storm for production that none of those elite receivers would ever again match, and all of those reasons we had to believe it was sustainable, that "regression to the mean" was a ludicrous suggestion... all those reasons wound up being wrong.

It's very possible that 2009 was to QBs what 1995 was to WRs. It's possible that 15 years from now we'll be talking to over-optimistic fantasy owners about the time that the NFL saw 9 players pass for 4200+ yards, and even saw Eli Manning get in on the action and chip in 4k yards of his own.

At the end of the day, I'm reminded of the saying "A rising tide lifts all ships". Eli's stats last year were aberrationally high... but so where the league's as a whole. It's possible that something about 2009 just created the perfect environment for QBs to flourish, and that 2010 will return us to business as usual... but even if it doesn't, every QB in the league benefited from the environment that led to Eli Manning passing for 4,000. Regression to the mean is a perfectly valid point to bring up with respect to Eli Manning- or, really, to bring up any time a 6-year vet sees such a dramatic and unexpected jump in his production. Especially when such a jump in raw numbers results in absolutely no change whatsoever in his ranking relative to his peers.

Edit: In fact, anyone who is projecting Eli Manning's numbers to stay flat from last year, but his ranking against his peers to rise, is essentially saying that they believe in regression to the mean as it applies to every single QB in the entire NFL... except for Eli Manning.

In reading this SSOG's post I kept thinking that everything he said is entirely plausible....but it contained absolutely nothing about Eli Manning's individual circumstances......then I read the below post and it's pretty much detailed everything you need to say in response to the above.

But to the opposite end of the spectrum, Eli, I agree that you have to look at WHY his numbers took a big jump. His receiving corps is MUCH better than it had been, and Manning is still young enough that incremental improvement in his ability to execute the offense can account for a step forward. Add to that a complete degradation of the Giants defense after the early 5 game winning streak, and the commensurate erosion of the productivity of both Jacobs (all season) and Bradshaw (the final three months), and the recipe was in place for Eli to put all the pieces together. As an Eagles fan, the last thing I want to see if Eli maintain that level of PER ATTEMPT productivity and combine that with a renewed defensive vigor and a healthy tailback tandem. But that's certainly a possible, if not most likely, outcome.

 

[Warrior]

Players sometimes regress because another team now has more film on them, or are more focused on stopping them after seeing big plays over and over. In other words, when they realize that he really is an impact player, they gameplan to stop him.

This is only one reason why using regression can be very smart. Lightning rarely strikes the same place twice.

 

[SSOG]

In reading this SSOG's post I kept thinking that everything he said is entirely plausible....but it contained absolutely nothing about Eli Manning's individual circumstances......then I read the below post and it's pretty much detailed everything you need to say in response to the above.

The reason I didn't address Manning's individual circumstances is because they've already been addressed by a lot of different people. The point I was trying to make is that it's entirely possible that Eli's sudden explosion is a function of his unique circumstances last season... but it's just as possible that it was a function of the fact that apparently NFL defenses had a more difficult time stopping QBs last year than at any other point in history.There's always an argument that a player's sudden explosion was a result of his unique circumstances, so expecting regression is silly. Always. There's an argument for it with Eli Manning (the emergence of Smith/Nicks/Manningham, the demise of the defense). There was an argument for it with Isaac Bruce in 1995 (he was a 2nd year player who had plenty of room to improve). There was an argument for it with Kevan Barlow (he'd always been good, and that was the first time he'd gotten big opportunity). The point I'm getting at is that people will frequently OVER-attribute improvements to a player's individual circumstances. I have no doubt that Manning's unique factors contributed to his big year last year... but I doubt they contributed as much as the pro-Manning crowd thinks they did. After all, it's not like it was the first time Eli Manning had weapons in the passing game and a mediocre defense. In 2006, he had Burress, Toomer, Shockey, and Tiki Barber, the defensive ranks were similar to what they were in 2009... and Eli Manning passed for 3250/24/18, pretty much exactly like he did in 2007 and 2008 with worse weapons and a better defense.

 

[Creed Bratton]

In reading this SSOG's post I kept thinking that everything he said is entirely plausible....but it contained absolutely nothing about Eli Manning's individual circumstances......then I read the below post and it's pretty much detailed everything you need to say in response to the above.

The reason I didn't address Manning's individual circumstances is because they've already been addressed by a lot of different people. The point I was trying to make is that it's entirely possible that Eli's sudden explosion is a function of his unique circumstances last season... but it's just as possible that it was a function of the fact that apparently NFL defenses had a more difficult time stopping QBs last year than at any other point in history.There's always an argument that a player's sudden explosion was a result of his unique circumstances, so expecting regression is silly. Always. There's an argument for it with Eli Manning (the emergence of Smith/Nicks/Manningham, the demise of the defense). There was an argument for it with Isaac Bruce in 1995 (he was a 2nd year player who had plenty of room to improve). There was an argument for it with Kevan Barlow (he'd always been good, and that was the first time he'd gotten big opportunity). The point I'm getting at is that people will frequently OVER-attribute improvements to a player's individual circumstances. I have no doubt that Manning's unique factors contributed to his big year last year... but I doubt they contributed as much as the pro-Manning crowd thinks they did. After all, it's not like it was the first time Eli Manning had weapons in the passing game and a mediocre defense. In 2006, he had Burress, Toomer, Shockey, and Tiki Barber, the defensive ranks were similar to what they were in 2009... and Eli Manning passed for 3250/24/18, pretty much exactly like he did in 2007 and 2008 with worse weapons and a better defense.

I agree with you when people frequently over-attribute an individual's circumstances in similar situations and overlook reasons that suggest otherwise. But just because that's the case in other situations doesn't mean it applies in every situation. You're assuming that 2006 Eli Manning in the third year of his career is the same player as Eli Manning of last year. Eli's completion percentage and yards per attempt have increased gradually as his career progressed and is probably indicative of his growth as a quarterback. I believe that he has QB 5-8 upside and it has as much to do with his growth as a quarterback and his receivers as it does the other quarterbacks in the league. Roethlisberger got suspended and lost Holmes, Rivers lost his best receiver and left tackle, and it's not unreasonable to think that age catches up to Favre. You make the claim that the numbers were inflated in 2009 similar to wide receivers in 1995 and say that a "rising tide lifts all ships", but then give no reason to explain that at all. It's easy to see how that expression might explain a particular team but not the league as a whole for last season pertaining to just quarteracks. I have a much simpler explanation that isn't nearly as vague. A few quarterbacks had their situations improve or stay static and none of the major quarterbacks really missed time due to injury. Schaub, Romo, and Brady all missed significant time in 2008 and the Steelers passing attack improved while Favre played with better receivers and without a torn biceps. Those are tangible explanations for the increase in 4000 yard pasers and not some vague "rising tide"You say that Eli's improved numbers(as well as the rest of the league) were the product of NFL environment last season and then give no explanation as to what that could be. I fully expect Eli's positional ranking to increase this year and it has as much to do with Eli and his situation as well as the other quarterbacks he's competing against as well. That doesn't mean I believe in regression to the mean for every quarterback in the NFL besides Eli, it just means that I think his situation has improved while several of the other quarterbacks ahead of him last season have had their prospects worsen.

 

[griff321]

The "Brady Rule" and other player safety rules seems to be a variable in the "rising of the tide" for the position. However, how would you quantify it with such a small sample? On one hand I could see it being a wash with the removal of the push out rule but the way R. Lewis makes it sound it's like they just handcuffed the entire D from doing anything.

 

[Sigmund Bloom]

In reading this SSOG's post I kept thinking that everything he said is entirely plausible....but it contained absolutely nothing about Eli Manning's individual circumstances......then I read the below post and it's pretty much detailed everything you need to say in response to the above.

The reason I didn't address Manning's individual circumstances is because they've already been addressed by a lot of different people. The point I was trying to make is that it's entirely possible that Eli's sudden explosion is a function of his unique circumstances last season... but it's just as possible that it was a function of the fact that apparently NFL defenses had a more difficult time stopping QBs last year than at any other point in history.There's always an argument that a player's sudden explosion was a result of his unique circumstances, so expecting regression is silly. Always. There's an argument for it with Eli Manning (the emergence of Smith/Nicks/Manningham, the demise of the defense). There was an argument for it with Isaac Bruce in 1995 (he was a 2nd year player who had plenty of room to improve). There was an argument for it with Kevan Barlow (he'd always been good, and that was the first time he'd gotten big opportunity). The point I'm getting at is that people will frequently OVER-attribute improvements to a player's individual circumstances. I have no doubt that Manning's unique factors contributed to his big year last year... but I doubt they contributed as much as the pro-Manning crowd thinks they did. After all, it's not like it was the first time Eli Manning had weapons in the passing game and a mediocre defense. In 2006, he had Burress, Toomer, Shockey, and Tiki Barber, the defensive ranks were similar to what they were in 2009... and Eli Manning passed for 3250/24/18, pretty much exactly like he did in 2007 and 2008 with worse weapons and a better defense.

I agree with you when people frequently over-attribute an individual's circumstances in similar situations and overlook reasons that suggest otherwise. But just because that's the case in other situations doesn't mean it applies in every situation. You're assuming that 2006 Eli Manning in the third year of his career is the same player as Eli Manning of last year. Eli's completion percentage and yards per attempt have increased gradually as his career progressed and is probably indicative of his growth as a quarterback. I believe that he has QB 5-8 upside and it has as much to do with his growth as a quarterback and his receivers as it does the other quarterbacks in the league. Roethlisberger got suspended and lost Holmes, Rivers lost his best receiver and left tackle, and it's not unreasonable to think that age catches up to Favre. You make the claim that the numbers were inflated in 2009 similar to wide receivers in 1995 and say that a "rising tide lifts all ships", but then give no reason to explain that at all. It's easy to see how that expression might explain a particular team but not the league as a whole for last season pertaining to just quarteracks. I have a much simpler explanation that isn't nearly as vague. A few quarterbacks had their situations improve or stay static and none of the major quarterbacks really missed time due to injury. Schaub, Romo, and Brady all missed significant time in 2008 and the Steelers passing attack improved while Favre played with better receivers and without a torn biceps. Those are tangible explanations for the increase in 4000 yard pasers and not some vague "rising tide"You say that Eli's improved numbers(as well as the rest of the league) were the product of NFL environment last season and then give no explanation as to what that could be. I fully expect Eli's positional ranking to increase this year and it has as much to do with Eli and his situation as well as the other quarterbacks he's competing against as well. That doesn't mean I believe in regression to the mean for every quarterback in the NFL besides Eli, it just means that I think his situation has improved while several of the other quarterbacks ahead of him last season have had their prospects worsen.

Not to pick on SSOG, who is on the short list of the best posters on this board, but his logic here is a perfect example of the kind of use of this analysis that I disagree with. It lumps all players together and ignores differences. Why didn't the rising tide help the pass offenses of BUF, CLE, NYJ, OAK, STL, CAR, TEN, CIN, KC, TB... the NFL didn't have many problems defending the QBs of those teams. Should we just expect that players like Joe Flacco, Matt Ryan, Matthew Stafford, Carson Palmer, and Mark Sanchez have no room to improve because the NFL will have a better time defending the pass on the whole this year? Should we project an automatic regression for Drew Brees, Aaron Rodgers, Tony Romo, and Peyton Manning this year?Of course, all of those questions are easily answered... by appealing to the individual circumstances of each player. Any analysis that lumps all players together and assumes that they are affected equally by a league-wide statistical trend is just not compelling to me, and as was stated earlier in the thread, it's just a stand-in for analysis that is specific to that player. No matter how they get there, a player's results are always attributable to his individual circumstances - that includes surrounding cast, coaching philosophy, and many other things that can change without the player changing - but it is NEVER because of a league-wide trend that affects all players equally, because no such thing exists. Even if you wanted to appeal to the slippage in pass defense as the reason Eli's numbers went up, you would still have to point to his schedule facing more weak pass defenses, or plays that were made that wouldn't have been made in the past because of the decrease in the quality of pass defenses. It is just not persuasive to say, "Eli's season is unlikely to be reproduced because a lot more QBs than usual had a good season last year." We know that some of those QBs will continue to excel, some will even improve, some will drop back to the pack, and some new names will join the top players this year, and the only way to take a stab at who falls into which group is looking at a player's individual circumstances.

 

[Sigmund Bloom]

just to go one step further with this idea:

it is NEVER because of a league-wide trend that affects all players equally, because no such thing exists.

Let's say the NFL announced that defenses could no longer defend passes more than 50 yards from the line of scrimmage, and because of that, passing TDs and yardage went up 10%, then in 2011, they decided it was a bad idea and repealed the rule. Should we drop all QBs projections by 10%? Should we mistrust any QB who improved by 10% in the previous season?Of course not!Some QBs with big arms like Joe Flacco would get huge benefits from the rule. Some QBs like Matt Cassel wouldn't be helped at all, maybe even hurt because defenses could focus closer to the line of scrimmage. Some QBs would actually just improve their game and the accompanying improvement in their stats would just result from that, and yes, a few QBs would have about a 10% increase from long pass plays that would not have been there under the old rules, and it would be rational to project them with a 10% drop in the following season - but once again, the only way to get to sorting out which QBs belong in which category is by looking at individual circumstances.

 

[Portis 26]

A word or two about external influences too. I'm convinced that if the Patriots hadn't been caught out cheating the Pats wouldn't have gone 16-0 and Brady wouldn't have thrown 50 TDs that year. I think the drama of the cheating scandal created an "us against the world" mentality on that team that fuelled a desire to crush every opponent, often by running up the score. I think it's entirely likely that if the cheating scandal hadn't happened the Pats would have gone 12-4 and Brady would have thrown say 38-40 TDs rather than 50.

My point is that the cheating scandal was an external event that can't be factored into any calculations.

I'd also make a broader point which is that economics traditionally errs when it seeks to be too much of a science because it ignores the fact that it's people with irrational emotions that compose a market and they often don't behave in an orderly or predictable way. Similarly with sports and thus with fantasy - it's real people with real emotions out there and good luck trying to predict with any model how they will behave. Often the best analysts are those that are intuitive rather than calculated.

 

[ookook]

The reason the league-wide increase has a hard time accounting for Eli Manning's 2009 season is that he improved his rank relative to the other QBs who are ostensibly affected by the same factors.

The reason I project a decline is that I attribute a good part of his increase in totals to the injuries to their RBs (Jacobs and Bradshaw) and I believe they will be healthier and more productive this year. I for one do not think Jacobs is done, and if he is close to back to his prior level of play I think Manning goes down.

So to me, a salient part of the situation that led to his increase has not remained stable.

 

[ookook]

None of this should take away from what I think might be SSOG's essential points:

(a) On average, if a player has played 5 season and then puts up their best, you will tend to be wrong if you predict all such players maintain that level. You might be right about some, but don't make a habit of it.

(b) People who try to find reasons for the increase will surely find SOMETHING (much as I can starting at cumulous clouds), the question is whether they are making a "fundamental attribution error": assuming the increase was due to something about the person and not the situation. Or ignoring situational factors that affected that single season that will not be there anymore.

So even if we discount a person-based attribution for Manning (that his skill or ability has improved), could be better WRs but could be decreased rushing from RBs.

To the extent those cancel, I go with RTM.

BTW, when I do not tend to go with RTM is when a new player improves each of their first 3 seasons.

 

[BuckeyeArt]

To Bloom's broader point, I'm curious who is making a blanket "regression to the mean" argument? I'm sure they're out there, I guess I am just conditioned not to pay them any mind.

I see it applied in staff (and other) projections. I'll use your projections for Cedric Benson as an example. You have him at 16 games, 315-1250-7 for 3.97 ypc, and 20-115-0 for 5.75 ypr. You have him regressing in every category despite the perceived improvement in the passing game. Maybe you have a fundamental reason but it looks like just a blanket regression to Benson's mean.For carries, you have him dropping from 23.15 cpg (24.5 in full games) to 19.68 cpg. During Rudi's workhorse years, he got 21.65 cpg. Why would you assume a sudden shift in their rushing distribution despite the historical evidence that suggests otherwise?For ypc, you have him dropping from 4.16 to 3.97. With the addition of Bryant and the full use of Andre Smith, it should open up the running game for Benson, not close it down. The schedule isn't any harder and might be slightly easier. What would cause you to expect Benson for Benson's average to decline?For TDs, you have him essentially the same (slightly less per game). Again with the expectation of a better, more diverse offense, why wouldn't you expect an increase in his TDs per game?I don't want to turn this in to a thread about Benson but it seemed like a good example of a 'blanket application'. Yours isn't the only one either. The other 3 staff members also project a regression, although Henry's is close to projecting no change.

 

[Hoot&HoLLer]

A word or two about external influences too. I'm convinced that if the Patriots hadn't been caught out cheating the Pats wouldn't have gone 16-0 and Brady wouldn't have thrown 50 TDs that year. I think the drama of the cheating scandal created an "us against the world" mentality on that team that fuelled a desire to crush every opponent, often by running up the score. I think it's entirely likely that if the cheating scandal hadn't happened the Pats would have gone 12-4 and Brady would have thrown say 38-40 TDs rather than 50.My point is that the cheating scandal was an external event that can't be factored into any calculations.I'd also make a broader point which is that economics traditionally errs when it seeks to be too much of a science because it ignores the fact that it's people with irrational emotions that compose a market and they often don't behave in an orderly or predictable way. Similarly with sports and thus with fantasy - it's real people with real emotions out there and good luck trying to predict with any model how they will behave. Often the best analysts are those that are intuitive rather than calculated.

Good tie in to Human Action. Ludwig would be proud.

 

[Jason Wood]

To Bloom's broader point, I'm curious who is making a blanket "regression to the mean" argument? I'm sure they're out there, I guess I am just conditioned not to pay them any mind.

I see it applied in staff (and other) projections. I'll use your projections for Cedric Benson as an example. You have him at 16 games, 315-1250-7 for 3.97 ypc, and 20-115-0 for 5.75 ypr. You have him regressing in every category despite the perceived improvement in the passing game. Maybe you have a fundamental reason but it looks like just a blanket regression to Benson's mean.For carries, you have him dropping from 23.15 cpg (24.5 in full games) to 19.68 cpg. During Rudi's workhorse years, he got 21.65 cpg. Why would you assume a sudden shift in their rushing distribution despite the historical evidence that suggests otherwise?For ypc, you have him dropping from 4.16 to 3.97. With the addition of Bryant and the full use of Andre Smith, it should open up the running game for Benson, not close it down. The schedule isn't any harder and might be slightly easier. What would cause you to expect Benson for Benson's average to decline?For TDs, you have him essentially the same (slightly less per game). Again with the expectation of a better, more diverse offense, why wouldn't you expect an increase in his TDs per game?I don't want to turn this in to a thread about Benson but it seemed like a good example of a 'blanket application'. Yours isn't the only one either. The other 3 staff members also project a regression, although Henry's is close to projecting no change.

You bring up some fair points. Clayton's USOS suggests Cincy may have an easier time against the run this year versus 2009, which if true would mean I'm being overly harsh on the team's rushing situation. But truth be told the Bengals have the 4th hardest schedule in the league (overall, not speaking to vs. the fun in fantasy points), and I see a lot of ways the Bengals revert this year to a middling team versus last year's surprise run. Overall I am conservative with my projections, I've just found that's what works best over the years in terms of the site, and for providing value to people who utilize the projections (and the rankings that are born out of the projections), particularly as it relates to relative value. Before you mentioned Benson's particular projections, I wouldn't have said I'm particularly down on him. I have him at RB15, just behind Jamaal Charles and ahead of Knowshon Moreno. To me, the upside with the Bengals this year offensively comes from the passing game. If Palmer can regain his elite status (I'm not sold on that, but others are), then the additions to the receiving corps will stand to give the team more balance. I'm also not generally buying the play of the Bengals defense last year as sustainable. But your mileage may vary.

 

[Doug Drinen]

I'm going to use the term "small sample anomalous stats" (SSAS) instead of RTM here, because I think that might be a better description of what the OP was about. This post will, of course, be a massive oversimplification, but I hope it illustrates a point. Like the OP, this post isn't really about Nicks even though I'll use him as an example.

Just to pick one example of SSAS in Nicks' case last season, he had three TD catches of 50 yards or more. That's pretty rare, probably rarer than you think. Jerry Rice did it 6 times in his 18-year career. Moss has done in 5 times in 12 years.

If you look at all WRs since 1980 who had 3 or more 50-yard TDs (yes, I know some people are rolling their eyes right now, bear with me) and who played 16 games the following season (so we're factoring out injury-based regression), less than 20% of them repeated the trick the following year. And about half of those were Rice and Moss. The average was 1.3 50-yard TDs the following season. The median was one.

The above tells me that long TDs can't be counted on. They're too rare, and too dependent on many, many things that are outside the receiver's control. Three 50-yarders is a SSAS. What it tells me is that nobody has a "true mean" of three 50-yarders per year. Not Rice, not Moss, and certainly not Nicks. So his true level of play, at least in that one area, was higher last year than we can count on it being in the future.

Instead of thinking about what this means going forward, I think it's better to use it as a lens through which to view the past. Nicks had 47/790/6 last year. If you take away half the production from his three long bombs, he's at something like 45/700/4. He drops from WR28 to WR41. I think that's probably a better reflection of his true performance last season.

So, do this: write a paragraph about why you think Nicks is a breakout player for 2010. If that paragraph contains something like, "he was WR28 as a rookie, so all he needs to do is ....", replace the 28 with a 41. If it says "116 fantasy points", replace that with "95". Do you still like Nicks just as much? If so, then don't worry about the SSAS. But before you dismiss it totally, make sure to honestly ask yourself whether your opinion of Nicks has been subconsciously shaped by the fact that his stats say he was WR28 last year.

Nicks' rookie season looks an awful lot like Michael Irvin's and Tim Brown's and Torry Holt's, and it's not hard to envision a similar career path: talented young deep threat learns the position, becomes a reliable short and medium-range target, and thereby becomes a complete receiver and a stud. If that's what you see, then the piddly matter of a 20ish fantasy point difference between his "true level of play" and his rookie year stats is nothing to be worried about. If you see big improvements for Nicks, then go get him. But keep in mind that his play probably has to improve by a little bit just to stay in the same place statistically. If you see 60 points of "true level of play" improvement for Nicks, and you're right, just be aware that his stats are more likely to go up by 40 points than by 60. Again, that's no big deal. Either way, he'll still be considered a breakout and he'll help your team.

The reason this is important is because the market probably sees something like 20 points of "true level of play" improvement from Nicks. And the market will probably add that to his actual numbers from last year instead of his "moral" numbers from last year, thereby possibly making him a little overpriced.

[After re-reading this, it seems way too literal. I hope you can read through the obviously-way-too-precise example numbers to the point.]

 

[Anthony Borbely]

Interesting post Doug.

I don't have time to look, but I am curious about any change in total TDs in the year after Moss and Rice had 3 50-yard TDs. In other words, I'm wondering if their total TDs in the following year were relatively close to the total number of TDs they have in the year they had the 3 50-yarders. Maybe they had similar TD numbers, but without the longer TD receptions. Basically, my point is if the total TDs of Moss and Rice were close, then maybe it would be more fair to "shorten" Nicks' TD receptions instead of eliminating them completely. Or maybe he gets tackled at the 5 yard line instead of making it to the end zone. I know it is impossible to know exactly why Moss and Rice only had about half the 50-yard TDs the following year, but I'm wondering if it is fair to completely eliminate the entire play as you did in your post.

 

[Jason Wood]

I'm going to use the term "small sample anomalous stats" (SSAS) instead of RTM here, because I think that might be a better description of what the OP was about. This post will, of course, be a massive oversimplification, but I hope it illustrates a point. Like the OP, this post isn't really about Nicks even though I'll use him as an example.

Just to pick one example of SSAS in Nicks' case last season, he had three TD catches of 50 yards or more. That's pretty rare, probably rarer than you think. Jerry Rice did it 6 times in his 18-year career. Moss has done in 5 times in 12 years.

If you look at all WRs since 1980 who had 3 or more 50-yard TDs (yes, I know some people are rolling their eyes right now, bear with me) and who played 16 games the following season (so we're factoring out injury-based regression), less than 20% of them repeated the trick the following year. And about half of those were Rice and Moss. The average was 1.3 50-yard TDs the following season. The median was one.

The above tells me that long TDs can't be counted on. They're too rare, and too dependent on many, many things that are outside the receiver's control. Three 50-yarders is a SSAS. What it tells me is that nobody has a "true mean" of three 50-yarders per year. Not Rice, not Moss, and certainly not Nicks. So his true level of play, at least in that one area, was higher last year than we can count on it being in the future.

Instead of thinking about what this means going forward, I think it's better to use it as a lens through which to view the past. Nicks had 47/790/6 last year. If you take away half the production from his three long bombs, he's at something like 45/700/4. He drops from WR28 to WR41. I think that's probably a better reflection of his true performance last season.

So, do this: write a paragraph about why you think Nicks is a breakout player for 2010. If that paragraph contains something like, "he was WR28 as a rookie, so all he needs to do is ....", replace the 28 with a 41. If it says "116 fantasy points", replace that with "95". Do you still like Nicks just as much? If so, then don't worry about the SSAS. But before you dismiss it totally, make sure to honestly ask yourself whether your opinion of Nicks has been subconsciously shaped by the fact that his stats say he was WR28 last year.

Nicks' rookie season looks an awful lot like Michael Irvin's and Tim Brown's and Torry Holt's, and it's not hard to envision a similar career path: talented young deep threat learns the position, becomes a reliable short and medium-range target, and thereby becomes a complete receiver and a stud. If that's what you see, then the piddly matter of a 20ish fantasy point difference between his "true level of play" and his rookie year stats is nothing to be worried about. If you see big improvements for Nicks, then go get him. But keep in mind that his play probably has to improve by a little bit just to stay in the same place statistically. If you see 60 points of "true level of play" improvement for Nicks, and you're right, just be aware that his stats are more likely to go up by 40 points than by 60. Again, that's no big deal. Either way, he'll still be considered a breakout and he'll help your team.

The reason this is important is because the market probably sees something like 20 points of "true level of play" improvement from Nicks. And the market will probably add that to his actual numbers from last year instead of his "moral" numbers from last year, thereby possibly making him a little overpriced.

[After re-reading this, it seems way too literal. I hope you can read through the obviously-way-too-precise example numbers to the point.]

 

[Doug Drinen]

Interesting post Doug. I don't have time to look, but I am curious about any change in total TDs in the year after Moss and Rice had 3 50-yard TDs. In other words, I'm wondering if their total TDs in the following year were relatively close to the total number of TDs they have in the year they had the 3 50-yarders. Maybe they had similar TD numbers, but without the longer TD receptions. Basically, my point is if the total TDs of Moss and Rice were close, then maybe it would be more fair to "shorten" Nicks' TD receptions instead of eliminating them completely. Or maybe he gets tackled at the 5 yard line instead of making it to the end zone. I know it is impossible to know exactly why Moss and Rice only had about half the 50-yard TDs the following year, but I'm wondering if it is fair to completely eliminate the entire play as you did in your post.

That's an excellent point, Anthony. I was hesitant to use actual examples and actual numbers, and your post shows why. I almost certainly did overstate the importance of that one particular SSAS. Thanks for pointing it out.

 

[az_prof]

Lots of great posts in this thread; here is what I take from it all.

1) Bloom is right that some people use RTTM without thinking about whether it is appropriate or not for the SPECIFIC player.

2) Drinen is right that you need to look at specific stats since not all regress to the mean equally. He was talking about Nicks, but I would say the same thing about Chris Johnson; how many 2000 yards rushers have there been historically? How did those players do after that year? I think when you are dealing with a really unique statistic that looking at the historical record for comparable performances as a standard is a good idea. It goes back to...

3) When assessing RTTM you need to determine WHAT mean. In the case of CJ, it is the elite group of runners who have had 2000 yard seasons. It would be wrong to look at his 2008 season and assume that somehow his 2010 performance will be halfway between 2009 and 2008. That's too easy and doesn't take into account...

4) Consideration of a players prior usage and team situation. CJ couldn't have rushed for 2000 yards in 2008 because he hadn't won the starting job outright yet from Fatdale White, so his carries were lower than we can expect them to be in the future.

5) Players with a small data set are the most difficult to predict and using RTTM may cause you to miss out on some elite players while protecting you from some OneTimeOnlyStuds (OTOS). This year's big question marks are players like Jamaal Charles and Jerome Harrison--guys with only one year of meaningful work. In this case, you have to fall back on your subjective evaluation of why they excelled in that previous year: natural talent; team strategy; other players on team; schedule.

In the end, with players without a long history of production it falls back to your subjective analysis of talent and situation.

 

[SSOG]

I agree with you when people frequently over-attribute an individual's circumstances in similar situations and overlook reasons that suggest otherwise. But just because that's the case in other situations doesn't mean it applies in every situation. You're assuming that 2006 Eli Manning in the third year of his career is the same player as Eli Manning of last year. Eli's completion percentage and yards per attempt have increased gradually as his career progressed and is probably indicative of his growth as a quarterback. I believe that he has QB 5-8 upside and it has as much to do with his growth as a quarterback and his receivers as it does the other quarterbacks in the league. Roethlisberger got suspended and lost Holmes, Rivers lost his best receiver and left tackle, and it's not unreasonable to think that age catches up to Favre. You make the claim that the numbers were inflated in 2009 similar to wide receivers in 1995 and say that a "rising tide lifts all ships", but then give no reason to explain that at all. It's easy to see how that expression might explain a particular team but not the league as a whole for last season pertaining to just quarteracks. I have a much simpler explanation that isn't nearly as vague. A few quarterbacks had their situations improve or stay static and none of the major quarterbacks really missed time due to injury. Schaub, Romo, and Brady all missed significant time in 2008 and the Steelers passing attack improved while Favre played with better receivers and without a torn biceps. Those are tangible explanations for the increase in 4000 yard pasers and not some vague "rising tide"You say that Eli's improved numbers(as well as the rest of the league) were the product of NFL environment last season and then give no explanation as to what that could be. I fully expect Eli's positional ranking to increase this year and it has as much to do with Eli and his situation as well as the other quarterbacks he's competing against as well. That doesn't mean I believe in regression to the mean for every quarterback in the NFL besides Eli, it just means that I think his situation has improved while several of the other quarterbacks ahead of him last season have had their prospects worsen.

I can spell out what "a rising tide lifts all ships" means. Here is the average passing yardage per team game in each year of the past decade:2009- 218.52008- 211.32007- 214.32006- 204.82005- 203.52004- 210.5 (this was the year of the "passing explosion" as the league cracked down on PI)2003- 200.42002- 212.22001- 205.82000- 206.9The 2009 passing totals were a full 4 yards per game higher than the next highest season of the past decade, and 11 yards per game more than the average of the previous 9 seasons (207.7). The league as a whole saw a passing explosion the likes of which it hadn't ever seen before (that's the "rising tide"), and the result was 10 players reaching the 4,000 yard passing mark (those are the ships that all got lifted). I don't see any meaningful trends in that passing yardage, so it's possible that the yardage goes down hard next year and the league sees its 4,000 yard QBs reduced to the typical 3 or 4. It's also possible that it stays high and the league sees a DOZEN 4,000 yard QBs next year. Neither of which has the slightest impact on Manning's ordinal ranking vs. his peers.Now, you make a good point about some of the guys ahead of Manning and why they won't finish there again. Favre is old, Roethlisberger is suspended, Rivers is missing his weapons. At the same time, a similar case can be made for why the guys behind Eli are going to suddenly jump him. You've got Flacco, Ryan, Sanchez, Stafford, Henne, Leinart, Young, and Freeman poised to make big jumps. Jay Cutler just gained Mike Martz. Donovan McNabb has another chance to play 16 games (he scored more FP/G than Eli last season). Carson Palmer's another year removed from his injury, and he's got better weapons now.At the end of the day, Eli Manning is a guy who has finished 10th or worse for 4 straight years, even in his career year (which happened to come during the most QB-friendly season of at least the last decade). As I'm fond of saying... at this point, he is who we thought he was. Don't let him off the hook.

None of this should take away from what I think might be SSOG's essential points:(a) On average, if a player has played 5 season and then puts up their best, you will tend to be wrong if you predict all such players maintain that level. You might be right about some, but don't make a habit of it.(b) People who try to find reasons for the increase will surely find SOMETHING (much as I can starting at cumulous clouds), the question is whether they are making a "fundamental attribution error": assuming the increase was due to something about the person and not the situation. Or ignoring situational factors that affected that single season that will not be there anymore.So even if we discount a person-based attribution for Manning (that his skill or ability has improved), could be better WRs but could be decreased rushing from RBs.To the extent those cancel, I go with RTM.BTW, when I do not tend to go with RTM is when a new player improves each of their first 3 seasons.

I need to keep ookook on retainer to start following me around and clarifying what I mean better than I can explain it. That's pretty much exactly what I'm trying to say, in far fewer words than I've been using.