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This is a good point. After all, Brees regressed in 2012 and still led the league in passing yards and passing touchdowns.
You never known the mean for a player, because a player's mean is constantly changing based on situation (i.e., supporting cast, age, coaching philosophy, etc.). But that doesn't mean you can't get a good idea of a range of means, and more importantly, know when something is far outside the range of what the player's true mean is.
Agreed.
I love when people use all kinds of statistical analysis when trying to offer me trades. I guess the main reason would be, WHY are you offering me the deal if you think your side is better??
You will never know a player's individual mean, but that's not really what regression to the mean is about. (If you knew a player's individual mean, you wouldn't have to do any regression: you'd just project him to achieve his individual mean.) The mean we're talking about is really the mean of all the players who, all things considered, seem most similar to the player in question in terms of physical talent, team situation, etc. (And since our initial expectations about a player will be determined by how players similar to him have performed, you can think of "regression to the mean" as "regression to our initial expectations.") To keep things somewhat simple so that we can use an example straight from Chase's article, let's say we're doing Year N projections for a quarterback that we really don't know anything about. All we know about him is that he's an NFL quarterback, so our initial expectation is that he'll be an average NFL quarterback. (This is a reasonable expectation because most NFL quarterbacks are somewhere around average, and anyway there are about as many significantly above average QBs as significantly below average QBs, so the two latter groups generally cancel each other out.) In Chase's article, go down to the table where he lists 12 NFL QBs (Brew Drees through QB12). If the universe of NFL quarterbacks consist only of those 12 QBs, our projection for any randomly selected QB that we know nothing about (and is therefore equally likely to be any of the listed QBs) would be 3,920 yards. That's the (equally) weighted average of all 12 QBs' expected performances, and so that's our Year N projection. Now suppose that in Year N, our mystery QB actually ends up in the 4,800-4,959 yard range. As Chase states in the article,
That depends on how big the sample size is, and how far away from the mean it is. It's a sliding scale. For any given sample size, the further away it is from the mean, the more likely it is to be anomalous. And for any given result, the smaller the sample is, the more likely it is to be anomalous.To take an extreme example, suppose we expect Giovani Bernard to average 4.2 yards per carry. On his first carry, he rushes for 50 yards. That is very likely quite anomalous: we should update our expectation from 4.200000000 only to 4.20000001 or so. In other words, a sample size that small and that far away from our previous expectation is not very likely at all to be close to right rather than completely wrong.
It's worth pointing out something here which many people miss. The ypc expectation for future carries is only marginally adjusted upwards. The ypc expectation for all his carries, including the 50-yarder he just ripped off, goes up by 50 yards. So if you project him for 250 carries and 4.2 ypc (1050 yards), after the 50-yarder you should probably project him to get another 249 carries at 4.2 ypc, for 1096 yards and a season total of 4.38 ypc.
Yes, you've got the basic concepts right, though I can add a few details tomorrow when I'm back on my desktop.
Note post #14 by Maurile where he says things like:
The mean of an average RB in the league is not what you would be using dealing with Adrian Peterson. Unless of course you believe the total of Peterson and his situation is that of an average RB in the league.The easiest example with Peterson (also mentioned in MT's post) is Peterson's 2012 6.0 ypc. Do you think that's average production for someone like Peterson who was in Peterson's situation? Or do you think it was more of an outlier, even for an Adrian Peterson?If you think the latter, then even if you think Peterson's 2013 situation is exactly the same, you should probably project a lower ypc for him this year.
I do not think or believe any of those things you suggest.
I think staff members' projections are generally lower because they don't remove injuries. Projections should be made on a per game basis, since we choose starters that way. When people use injuries as a reason for regression to the mean, I don't think they are looking at things the right way, at least for the purpose of FF.
I respect MT's work. Have for a long time now. That is why I like to check my numbers against his once I finish mine, as I usually have to come back to earth quite a bit. On the flip side of that my projections tend to be higher across the board than most. I think that is ok since that is happening with all of my player projections. Part of that is I have been bumping passing yardage because of the league trending upwards in passing yardage for quite some time now. I am wondering if this won't be reaching it's peak soon however and we may have a year where numbers fall back again before stabilizing. I do not think the plays and passing yardage can continue going up indefinitely. How many more plays will coaches like Chip Kelly add to that over next few seasons? At some point soon I think this will plateau but I do not think we are quite to that point yet.
I agree here. I was just saying I think most of their projections look at end of year stats rather than per game stats.
This raises an important point that often goes unstated.Regression analysis is a mathematical tool. We feed a bunch of data into a computer, we make it buzz and whir for the better part of a few milliseconds, and it returns to us some statistical projections based on a bunch of fancy math formulas.Whenever we're using any mathematical tool, we have to be cognizant of what data we're feeding into it and what we're leaving out. The more useful data that we feed into it, assuming we're doing things correctly, the better the output will be. But real life is extremely complicated in all kinds of ways, so our mathematical models will necessarily be gross simplifications. We simplify in part by leaving out a lot of data that it's not practical to include. A simplified model will never be perfect, but general insights can be gained from such models that are likely to apply to more complicated scenarios as well; so they can be quite useful as tools.Certain principles are much easier to understand in the context of simplified situations. They are certainly much easier to explain in the context of simplified situations. So when trying to explain a certain concept, we might often say something like: "Pretend that all you know about a player is that he caught 55 passes for 979 yards last season." The statement means that that's all we're feeding into our mathematical tool, which will therefore remain ignorant of the player's height, his speed, his route-running skills, his quarterback's accuracy, and what he had for breakfast this morning. There's a lot we're not telling our computer about him, but nonetheless "55 catches for 979 yards" is at least something to go on, and it's definitely enough to demonstrate the essence of a concept like regression to the mean.Regression analysis can have lots of parameters or just a few. It's much easier to perform when it has just a few, so that's how it's often done, especially when it's done for expositional purposes.A very simplistic version of regression to the mean might go like this: for any WR who caught at least 35 passes in any season during the past decade, we feed into our computer a list of his receptions and receiving yards that season, and his receptions the following season. Then we ask our computer, "Computer, what formula that predicts receptions in Year N+1 based on his receptions and receiving yards in Near N will give us the smallest total error?" It will tell us something like "15 + 0.7 * (receptions in Year N) + 0.02 * (receiving yards in Year N)". [i'm just making that answer up; I'm not sure whether it's close to the real answer.]A more complicated, and probably more accurate, version would feed into the computer not just last year's catches and yards, but also other data from last season (yards after the catch, drop rate, etc.) as well as data from previous seasons, maybe data from college production (especially for younger players), maybe data about the player's speed or hands or jumping ability and so on.So if your point about Cecil Shorts is that you don't want to do projections for him by telling a computer "pretend all you know about him is that he caught 55 passes for 979 yards last season," I don't think anyone would disagree with you. That doesn't mean that the concept of regression to the mean is useless. It just means that it's not a substitute, especially in its crudest form, for a fuller, more nuanced analysis.The concept from regression to the mean that will always be relevant and useful, however, is this: when a player outperforms your previous expectations, it might be because your expectations were right on the mark and his outlying performance was strictly a consequence of a small sample size; or it might be because you had previously underrated him, and his performance was not an outlier at all, but accurately reflects his true ability. Most likely, though, the truth is somewhere in the middle of those two possibilities. Therefore, your future expectations should be higher than your previous expectations were, but lower than a continuation of the player's actual recent performance.
Since the truth is probably somewhere in between, your revised expectations for his future YPC should probably be higher than 4.7 but lower than 6.0. Where in between those numbers should it be? There's a sliding scale. The more confident you were previously in your estimate of 4.7 YPC, the closer to 4.7 it should be. The greater the sample size that the 6.0 YPC was generated from, the closer to 6.0 it should be. In fact, if you can specify those criteria precisely, there are mathy ways to estimate exactly where in between 4.7 and 6.0 your new projection should be. (As always, the math would be based only on statistical information; extraneous factors, like injury news or a new offensive system or whatever, would have to be accounted for separately.)
Right. Part of the challenge is figuring out whether a player is truly elite, or whether his elite-looking performance was merely a sham. But if you know that he's truly elite, you wouldn't be regressing him toward the overall NFL mean; you'd be regressing him toward the mean of the true elites.
I actually don't use similarity scores at all. I think that using similarity scores would probably be the best way to do projections for rookies. I don't do it simply because I haven't spent the time yet to build that model. So for rookies, I just kind of wing it. But in the future I do plan to use something like similarity scores for them.For veterans, I do not use similarity scores because once a player has at least 30 or so runs or receptions, I think using information from his own individual past performance is more useful than using information from the performances of other players who were kind of like him in some ways, and this becomes more and more true with each additional run or reception he notches on his belt.Another note here. A player's rushing yards will be his rushes times his yards per carry. His receiving yards will be his targets times his catch rate times his yards per reception.In my opinion, regression analysis or something similar (I prefer Bayesian inference analysis to more traditional least-squares regression) can be very useful for projecting yards per carry, receptions per target, and yards per reception, but is nearly useless for projecting the number of carries or targets. (I project carries and targets by considering what type of offense the player is in and what role I think he'll have in it — stuff that I don't think regression analysis can very usefully help with.) Moreover, when we're projecting rushing yards for a player, getting his yards per rush right is generally far less important than getting his number of carries right. A running back whose long-term YPC is in the 75th percentile (about 4.35) will average only about 10% more yards per carry than one whose is in the 25th percentile (about 3.9). But RBs typically vary in their number of carries by far, far more than 10%.So in projecting an RB's expected yards this season, I think something like regression to the mean can be pretty helpful for the relatively minor component of the projection, but nearly useless for the more important component.Like I said in a previous post, I don't think anyone will tell you that regression to the mean is the be-all and end-all in doing player projections. Similarly, I don't think a player's speed is the be-all and end-all, or that his draft position is, or that his wonderlic score is. I don't think any one piece of data or any one type of analysis is the holy grail. All of these factors, and many more, are tiny pieces of a large puzzle. All deserve consideration. I think Chase's article did a good job of explaining the concept of regression to the mean. Maybe somebody else can write an article on the importance of a player's speed. Our job as fantasy owners is to make whatever use we can out of all the various concepts and information available. Understanding regression to the mean can be only a small part of that, but every little bit helps.
It means it's more likely to be heads again.Before the coin was flipped, we were expecting 0.5 heads per flip. On the first flip, however, we actually got 1.0 heads. So our revised projection going forward should be somewhere between our previous projection and the obtained result: somewhere between 0.5 and 1.0 heads per flip.It should probably be around 0.5000001 heads per flip, give or take.The reason for the increase is that the result of the first flip must cause us to increase our estimate of the probability that it's actually a two-headed coin, or is otherwise somehow biased in favor of heads (while decreasing our estimate of the probability that it's biased in favor of tails). Suppose that one out of every million coins is double-headed while another one out of every million coins is double-tailed, and the remaining 999,998 out of every million coins are perfectly fair. Before the first flip, the double-headed and double-tailed coins were equally probable, and therefore canceled each other out, so our projection would be exactly 0.5 heads per flip. After the first flip, we've completely ruled out that the coin is double-tailed, so the double-headed and double-tailed possibilities no longer cancel each other out, and we should project more than 0.5 heads per flip. (If we are 100% certain that the coin is fair, then this doesn't apply, and we would still project 0.5 heads per flip.) The "regression to the mean" way of thinking about this is to say that we've observed a rate of 1.0 heads per flip over a small sample size, and our projection going forward should be revised downward from that to something less than 1.0 heads per flip, toward the mean (i.e., our previous expectation) of 0.5 heads per flip. In this case, way, way down, nearly all the way back to the mean.
I think if we get to 14000 rush attempts, the total number of plays will decrease. The number of plays run per team game has been pretty steady throughout NFL history, and I wouldn't assume it's just going to increase in 2013.
That's one of the things I'm changing in my projections method this season.
That is sort of what I was thinking is that if the rushing attempts rose to 14000 again that perhaps that would grind enough clock that the passing attempts might decrease somewhat. One team that I think will increase its rushing attempts in 2013 are the Titans. There may be some other teams that do as well.
I agree somewhat. I think people put too much emphasis on using past stats to predict a specific player's future performance.However, I think the area where a solid understanding of math and running a few numbers can be a real advantage for a fantasy owner is in devising a strategy regarding how to approach each position. There are so many different scoring setups and so many different alignments in terms of lineup requirements. Basically, I think the math is huge in determining stuff like "do I need to make sure I get a top TE?" "Should I draft a QB early?" Stuff like that...The cross position comparisons (WR A vs. RB X) really do require some math in my opinion. The WR A vs. WR B type stuff doesn't take too much math and should be based more on talent, situation, etc.
my brain went
I can only shake my head at Tanner9919's post here.Tanner9919 said:my brain went
good stuff though,thanks!
if you're saying that A. Peterson will undoubtedly go back to being a 1400 yard RB this season, I agree. history tells us he won't come close to repeating the numbers this season..( regression the year after 2k season)..
to those who think Peterson is still the #1 RB at 1.01, I'll offer D. Martin as an alternative..he gets back two pro bowl linemen,and
his role will be expanded even further in year 2..so while ADP will regress, D. Martin should progress
The issue is how many samples do we need before we stop saying it's "luck" and start saying it's just the way it is.Maurile Tremblay said:Tom: It's finally here! Week one of the NFL season!
Jerry: I know, I'm really excited. I have Montee Ball on my fantasy team and he's starting tonight against the Ravens.
Tom: Yeah. Oh, look, the game is starting.
Jerry: Broncos ball. Kickoff is a touchback. Here's the first offensive play.
Tom: Ooh, a handoff to Ball and . . . LOOK AT HIM GO!
Jerry: Wow, a 40-yard run on his first play. That's a great sign! Nothing much has changed between the last play and this one coming up. It's the same offensive line, same system, same coaching, and so on, so I don't see why he won't break off another 40-yard run.
Tom: LOL.
Jerry: I'm serious.
Tom: He's not going to break off another 40-yard run. Trust me.
Jerry: Why not? What's changed since the last run?
Tom: Nothing has to have changed. It's just that 40-yard runs are pretty rare. They don't happen very often. He got lucky that his first carry was a 40-yarder, but he's very unlikely to repeat it on his second carry.
Jerry: Lucky? Are you watching the same game I am? That wasn't luck. He made a great cut at the line then accelerated through the hole, broke a tackle, and outran the linebacker until the safety got the angle on him.
Tom: Well, yeah, it was a very nice run, but --
Jerry: But nothing. It was not luck. That was all skill. The line blocked skillfully and Montee Ball ran skilfully. It's not like his skill is going to deteriorate all of a sudden after one play. So name one reason why he's unlikely to run for 40 yards again on the next play.
Tom: Regression to the mean.
Jerry: That's a cop-out. It's not a real reason. I mean, give me a reason that makes sense. Did he injure himself on the first play? Did his offensive line get tired running down the field? Did the defense pick up a tell on him that will help them diagnose the play better? Give me a real reason!
Tom: There are a great many reasons that he might not rush for 40 yards on the next play. Maybe his blocker will slip. Maybe Ball will fumble. Maybe he won't be able to bounce it outside this time because the defensive end will have better contain. Maybe the middle linebacker won't hesitate on his first step this time. I could go on forever. There are about a million reasons why somebody -- even Montee Ball -- might not rush for 40 yards on any given carry. The reasons why he might not do it are far more numerous than the reasons why he might do it. That's why 40-yard rushes are so rare, and that's all I mean by "regression to the mean."
Jerry: But you don't know that 40-yard rushes are rare for Montee Ball. Sure, they're rare for dopes like Adrian Peterson, but they might be common occurrences for Ball.
Tom: Here's why that's unlikely. For Ball to commonly run for 40 yards like it's nothing out of the ordinary -- for that to be anywhere near his average run -- he'd have to be the most awesome running back in the history of awesomeness. That's possible, but it's a needlessly extraordinary way to explain his 40-yard run on his first carry. I mean, either he's the best running back ever and that was an ordinary carry for him, or he's a fairly ordinary running back and that was an exceptional carry. Which is more likely? Well, the best running back ever occurs about once per universe, while 40-yard carries by ordinary running backs happen several times a week during the NFL season. Since "once per universe" is a lot less common than "several times a week," I'm going to bet on the second possibility.
Jerry: I guess that makes sense.
Tom: It's the same with Drew Brees throwing for over 5400 yards in 2011. Either he's the best quarterback in the history of ever and that was an ordinary season for him, or he's merely a future Hall of Fame quarterback (but lacking super powers) and he got a bit lucky in 2011.
Jerry: But that's what I take issue with. It's not luck. He's tremendously skilled.
Tom: Semantics. I'm using "luck" as a synonym for "positive variance." Brees doesn't get the exact same result on every play or in every season. Some seasons end up being statistically better than others. There's variance. The ones that are particularly good constitute positive variance, and the ones that are particularly bad constitute negative variance. Moreover, an awful lot of his variance has nothing to do with his own skill. It has to do injuries, weather, strength of schedule, playcalling, and about a zillion other things. I like to call all the stuff that's out of his control "luck," but you can call it something else if you want to. Either way, it's variance. The point is that throwing for 5,400 yards is probably on the positive side of Brees' variance; and if so, he's likely to regress to the mean rather than repeating the feat.
Jerry: Maybe he will, but that's another thing I take issue with. It seems like a cop-out to just say "regression to the mean" without giving a more concrete reason why.
Tom: You can think of it as a burden-of-proof issue. Since 5,400-yard seasons are so exceedingly rare, I don't think a person has to explain why Brees won't throw for 5,400+ yards. Rather, a person has to explain why Brees will throw for 5,400+ yards. The default position is that he won't. The reason that's the default position is because, as with Montee Ball's 40-yard run, there are many, many more reasons why a person (even Drew Brees) might not throw for 5,400+ yards than there are reasons why he might. The reasons are too numerous to list, which is why we say "regression to the mean" as shorthand.
Jerry: Whatever. You may not have noticed with all your blabbing, but it's almost halftime and Montee Ball has rushed for 480 yards on 12 carries.
Tom:
It's not hindsight. The only people who didn't project Brees for over 5000 yards again in 2012 were those who were so hung up on Regression to the Mean and calling his 2011 season "luck," that they over-discounted his 2011 performance.
If things go well for Brees, then yeah, he can throw for 5,000 yards in 2013, too. But regression to the mean understand that things don't always go well all the time. Brees could get hurt, in which case he would way undershoot his projections. The Saints could pass way less, in which case he's not going to hit 5000 yards again.
But they are not the same thing. I agree with you that they are the same thing in principle, but not in practice.
But this is a thread about the concept. I agree you should question "regression to the mean" as the only argument in a player spotlight thread. It would be great if someone could clearly state all the luck factors they saw the in year N.
This is the Internet age. There is no reason why you would ever just have "N stats." This is a FF community. There is no reason why we shouldn't be delving into reasons for stat variations instead of just saying that stats will vary.
Twenty-six.
Really good stuff MT, and I'm on board with pretty much everything you said. I think we probably draw the "luck" line differently, and maybe that's where the big difference is.
