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***Official*** 2012 FBG Subscriber Contest Thread (3 Viewers)
- Thread starter Ignoratio Elenchi
- Start date
Look at the standard coin flipping example.If you flip a coin each week for 16 weeks, you expect 8 heads and 8 tails. If you get heads the first two weeks, you don't expect 8 tails and only 6 heads during the remaining weeks. You still expect 7 and 7.Trying to get my brain around this...and I think I disagree with this line of thinking. I'm leaning more towards reversion to the mean.If Player X is expected to score 20 points/week for the season and comes out in week 1 over that number that would leave me to believe that future weeks should average below 20/week...unless you think that 25/week is the new normal which would change the answer.The fact that anyone thinks this boggles my mind. There is not set number of good/bad weeks or absolute end of season total for each player to hit out to. If you expected Rice to score 320 points on the season and 20 week 1. If he actually scored 25 in week one, you should now expect him to score 325 points on the season, not for him to score 295 points for the rest of the season.
No, you should just add the results of week 1 to your remaining expectations of the next 15 weeks.
CalBear
Footballguy
If a player is expected to score 20 points/week (for some very vaguely defined notion of "expected"), and he scores more than that in week 1, the only adjustment you should consider making is to adjust his per-week stats upward. Having a good week in week 1 should not do anything to make you think that your per-week projections were too high to begin with; the idea is simply nuts.
What I'm saying is say there is a 5 week seasson and you project Rice to have 10, 15, 8, 15, 22 points in each of those weeks. That's 70 points. IF Rice puts up 20 points in week 1, your projections for week 2 through 4 should stay the same because nothing about those games has changed. Thus, you can now expect him to end up with 80 points on the year. You don't downgrade the other weeks because he had a better than expected week 1. Think of it terms of flipping a coin. If you flip one 20 times, you can expect to get 10 heads and 10 tails. IF the first 10 flips are all heads, it doesn't change the fact that over the next 10 you expect to get 5 heads and 5 tails. After 10 flips you now expect to end up with 15 heads and 5 tails after 20 flips, not 10 and 10.Trying to get my brain around this...and I think I disagree with this line of thinking. I'm leaning more towards reversion to the mean.If Player X is expected to score 20 points/week for the season and comes out in week 1 over that number that would leave me to believe that future weeks should average below 20/week...unless you think that 25/week is the new normal which would change the answer.
This is not what I was insinuating. If you project Gonzo to have 8 TDs in 16 games or .5 per game. Then you should continue to expect Gonzo to score .5 TD's per game regardless of whether he scores in the first game. Beginning Projection = 8 TDsAfter week1 with TD = 1 TD in week 1 + 0.5 * 15 = 8.5 TD's for seasonAfter week1 with no TD = 0 Td's in week 1 + 0.5 * 15 = 7.5 TD's for season. You notice in either case the unknowns (the remainder of the season) remains the same, the difference comes from a single unknown becoming a known.
butcher boy
Footballguy
The coin flipping example is not a good one for this situation because NFL stats are not 50/50. If a player has a few monster weeks, defenses are going to adjust even harder to stop that player. Then maybe the offense adjusts and starts using other players more, etc etc. There's a reason all projections fall within a certain range at each position. It's because that's where players end up when its all said and done every year (with very few exceptions). Stevan Ridley is a good example of this. He had a fantastic week one, and if it continues, defenses are going to start keying in on New England's running game. What will that mean? My guess is it will mean Tom Brady takes advantage of it and goes off, potentially lowering Ridley's overall stats. That said, one week of good scores isn't enough to make me think any player is guaranteed to drop off the next week.Look at the standard coin flipping example.If you flip a coin each week for 16 weeks, you expect 8 heads and 8 tails. If you get heads the first two weeks, you don't expect 8 tails and only 6 heads during the remaining weeks. You still expect 7 and 7.Trying to get my brain around this...and I think I disagree with this line of thinking. I'm leaning more towards reversion to the mean.If Player X is expected to score 20 points/week for the season and comes out in week 1 over that number that would leave me to believe that future weeks should average below 20/week...unless you think that 25/week is the new normal which would change the answer.
Ignoratio Elenchi
Footballguy
There are more technical, statistical reasons one could use to explain why it's a fallacy to believe that it's somehow a bad thing to have "wasted" a good score in week 1, but this is a nice simple and intuitive way to see it. You thought Player X was roughly a 15 point per week player; he comes out week 1 and scores 25 points; so now you think for the rest of the season he'll be worse than you originally projected him to be? Sounds backwards, no? In your normal fantasy league, if you took a flier on a guy like Ogletree, are you now dropping him from your roster because he blew all his projected points in week 1?This is the only argument, imo, that can be made to adjust future projections based on one weeks performance. If someone performs better than expected you can adjust upward if you think you're initial assumptions were wrong. And you can adjust down if they perform worse than expected.
ratbast
Footballguy
I got ya, sorry to misrepresent. But why have you chosen to vary the 8 TD projection and not the .5 per week? That basic decision you have made is why this is all meaningless and there is no answer, it is once again how you or me want to come up with our projections, whatever we think might help us try to predict the future.
The coin flipping example is a perfect and simple illustration.The scenario you stated has nothing to do with the OPs assertion.The coin flipping example is not a good one for this situation because NFL stats are not 50/50. If a player has a few monster weeks, defenses are going to adjust even harder to stop that player. Then maybe the offense adjusts and starts using other players more, etc etc. There's a reason all projections fall within a certain range at each position. It's because that's where players end up when its all said and done every year (with very few exceptions). Stevan Ridley is a good example of this. He had a fantastic week one, and if it continues, defenses are going to start keying in on New England's running game. What will that mean? My guess is it will mean Tom Brady takes advantage of it and goes off, potentially lowering Ridley's overall stats. That said, one week of good scores isn't enough to make me think any player is guaranteed to drop off the next week.Look at the standard coin flipping example.If you flip a coin each week for 16 weeks, you expect 8 heads and 8 tails. If you get heads the first two weeks, you don't expect 8 tails and only 6 heads during the remaining weeks. You still expect 7 and 7.Trying to get my brain around this...and I think I disagree with this line of thinking. I'm leaning more towards reversion to the mean.If Player X is expected to score 20 points/week for the season and comes out in week 1 over that number that would leave me to believe that future weeks should average below 20/week...unless you think that 25/week is the new normal which would change the answer.
Coin flipping is a good example, because we're not talking about the exact probability aspect of it. We're talking about the fact that past performance doesn't change future probability. Projections fall within a certain range at each position not because of regression to the mean, but because players are limited to how many attempts and yards avg they can reasonably get. What did Ridleys performance this past week change in terms of how he'll produce this upcoming week? And as an aside, do you really believe that if Ridley keeps this up, defenses are going to start saying "Let's stop Ridley and force Tom Brady to beat us?" I don't think so.
QuizGuy66
Footballguy
-QG
butcher boy
Footballguy
Not much because one week isn't enough to change expectations. I agree with your math in how you project guys out after just one week of performance. I'm just saying that the NFL is not nearly as simple as flipping a coin and there are other factors involved that affect how guys will perform in the future.
If Ridley keeps going for over 100 yards/game then yes at some point defenses will key in on that. They wont succeed because a Tom Brady offense with a stud RB is scary as hell, but you wont see nickel/dime packages against the Patriots if Ridley turns into Arian Foster.
Instinctive
Footballguy
I don't understand how you can possibly think this. One above average week simply should not affect negatively the expected averages. He doesn't have a set amount of points. The only reasonable change in his average points that you could expect would be that he scores MORE per week, based on you underestimating his talents and being shown that in the above-expected-average week 1 performance.Also, you don't know what reversion to the mean is. Learn, then try again.Trying to get my brain around this...and I think I disagree with this line of thinking. I'm leaning more towards reversion to the mean.If Player X is expected to score 20 points/week for the season and comes out in week 1 over that number that would leave me to believe that future weeks should average below 20/week...unless you think that 25/week is the new normal which would change the answer.
northwoods
Footballguy
I love that we're arguing statistics on a one week sample, wait till we get a few more weeks into the season and watch the fireworks.Still early in the contest but the
is in mid-season form.
-QG
You choose to vary the 8 TD projection because you've projected .5 TD's every week, so you have a stream of .5 tds for 16 games. If you projected Gonzo to score a TD in the first week and only 7 in the remaining 15 games, then the 8 TD projection remains the same. And there is absolutely an answer. It's not a personal preference thing. Two examples:Gonzo TD projections by week..5, .5, .5, and so on through 16 weeks.1, 0, 1, 0, 1 and so on through 16 weeks.Regardless of which stream of projections you initially chose, you should keep the same projections for the final 15 games whether or not he scores in the first. If you projected 8 TD's for the season and he scores a TD in the first 8 games, do you think he's going to go, "Ok matt, stop throwing the ball to me in the red zone, I've reached my projection for the year". Or if he scores a TD in the first 4, is he going to say, "Matt you might want to slow down hitting me in the endzone, I've only got 4 TD's left for the year." The answer is obviously no.
ratbast
Footballguy
I think he is right, and i think you might relax a bit
Okay fine. If you roll a die 18 times, you'd expect to get each number 3 times. If the first 6 rolls come up 1, it doesn't change your expectation that over the next 12 rolls you'll get each number twice. You expect to end up with 8 1's and 2 of everything else.
Ignoratio Elenchi
Footballguy
Why wouldn't your default assumption be neither of those? You expected him to score 20 points per week. 25 isn't necessarily the "new normal," nor should you expect him to score less going forward just because he had a good week. If your projections were right, he's still a 20 point-per-week player. As others have pointed out, if you are going to make any kind of adjustment to his projections, you'd only want to adjust them upwards, because his Week 1 production may indicate that he's actually a better player than you originally projected him to be. It shouldn't lead you to believe that he's actually worse.
northwoods
Footballguy
Really? Enlighten me...I don't understand how you can possibly think this. One above average week simply should not affect negatively the expected averages. He doesn't have a set amount of points. The only reasonable change in his average points that you could expect would be that he scores MORE per week, based on you underestimating his talents and being shown that in the above-expected-average week 1 performance.Also, you don't know what reversion to the mean is. Learn, then try again.Trying to get my brain around this...and I think I disagree with this line of thinking. I'm leaning more towards reversion to the mean.If Player X is expected to score 20 points/week for the season and comes out in week 1 over that number that would leave me to believe that future weeks should average below 20/week...unless you think that 25/week is the new normal which would change the answer.
Right, but we're not discussing other factors. I totally agree that other factors can lead to altering projections. But changing future projections JUST BECAUSE someone outperformed last week and thus NEEDS to underperform another week to make up for it, is just wrong.
Ok, we can disagree here. I think defenses would rather have Patriots nickle and dime their way down the field rather than allowing Brady to pick up things in chunks. But makes no difference.
BroadwayG
Footballguy
But what if the die is playing the 49ers in week 9, maybe you don't even roll a die that week.
Tennessee_ATO
Footballguy
This is actually a huge area of discussion in fantasy baseball, and I think it's critically important in that game especially if you subscribe to the "skills" analysis as opposed to the "results" analysis. Haven't seen it discussed that much in the fantasy football context though. I don't think it has the same impact, because of the nature of volatility due to match-ups, usage, and health week-to-week. If Rice is nursing a sore ankle against the Ravens one week, you would expect less production in that week than you would 100% healthy against the Titans. Fundamentally, it goes back to the level of confidence you have in the original projections. If you felt a player would perform at a certain level before the season, does actual performance in 1/16th of the season cause you to deviate from that projection? Unless there is a clear change in roll/usage I think most would say "no". Push that to 13/16ths of the season, and I think most folks would say "yes". Where do you fall in that distribution is likely a personal decision.Using Ray Rice and the 25 actual points vs. 20 ppg projected referenced above, 5 points either way is probably not statistically significant. But assume it is. Is he "due" for a 15 point week to make-up for that 25 point week? Again, I think most would say "no". Flip it around. Is Chris Johnson "due" for a monster week because he stunk in week 1? How about Wes Welker? The analysis really isn't any different.Trying to get my brain around this...and I think I disagree with this line of thinking. I'm leaning more towards reversion to the mean.If Player X is expected to score 20 points/week for the season and comes out in week 1 over that number that would leave me to believe that future weeks should average below 20/week...unless you think that 25/week is the new normal which would change the answer.
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um ok.
ratbast
Footballguy
How did you come up with .5? By projecting 8 first. And if you saw a fluff matchup in week 1 your projections of 8 total should not change. thus there is a regression of game per game for the rest of the year to 7/15.
Ignoratio Elenchi
Footballguy
Let's say you have Gonzo projected to catch 8 TDs this season (0.5 per week). How would you adjust this projection if the NFL decided to double the length of the NFL season to 32 games? Would you:
[*]Assume he will still catch 8 TDs for the season, and therefore adjust his per game projection down to 0.25 TDs per game?
[*]Assume he will still average 0.5 TDs per game, and therefore adjust his season total projection up to 16 TDs for the year?
I'm not sure what you're talking about here... A Total Season projection becomes irrelevant after the first game. What matters is a game by game projection. So whether I came up with the .5 by first projecting 8 TD's and then assigning one to each week or projecting .5 TD's per week and coming up with 8 total is irrelevant. If I saw a fluff matchup week 1 I'd have projected more TD's in that week compared to a more difficult matchup. If I project someone for 50 yards per week, and they get 800 yards through the first 8 games, do I really change my projection to 25 per week for the next 8 games so I hit out on my initial projection?
Tennessee_ATO
Footballguy
And Wes Welker to 48/224/0.
ratbast
Footballguy
Its not irrelevant. Its the essence of this discussion. How can you project .5 tds per game?
If you look at the schedule and see that Gonzo has a cake walk in the first 4 games but then tougher the rest of the way, so you predeict he will score a TD per game in the first 4 weeks but only four the rest of the year for a total of 8. Why would you change the projection if it was correct and after 4 weeks he would have 4 tds...you would say "well he still is .05 per game for 6 more" and I would say no, i factored in the first 4 weeks of scores and he has 4 left. so he now stands at 4/12 after being 4/4 in the first 4 weeks.
If you look at the schedule and see that Gonzo has a cake walk in the first 4 games but then tougher the rest of the way, so you predeict he will score a TD per game in the first 4 weeks but only four the rest of the year for a total of 8. Why would you change the projection if it was correct and after 4 weeks he would have 4 tds...you would say "well he still is .05 per game for 6 more" and I would say no, i factored in the first 4 weeks of scores and he has 4 left. so he now stands at 4/12 after being 4/4 in the first 4 weeks.
Exactly!!!!! They should be. Let's say you have a 16 game projection for Rice:Wk 1: 20Wk 2: 20Wk 3: 20Wk 4: 20Wk 5: 20Wk 6: 20Wk 7: 20Wk 8: 20Wk 9: 20Wk 10: 20Wk 11: 20Wk 12: 20Wk 13: 20Wk 14: 20Wk 15: 20Wk 16: 20Total of 320 points. You're projection is now set and you shouldn't change it. Him scoring 25 in week 1 instead of 20, shouldn't change what you've projected for weeks 2 through 16.
BroadwayG
Footballguy
Wow, if he gets a nagging knee injury and his touches drop in half you are in trouble.
Tennessee_ATO
Footballguy
In all seriousness, there is a world of information out there on this very issue in the fantasy baseball context. The BaseballHQ forums have some extremely statistics-heavy discussions trying to identify the "right" answer to these types of questions, and anecdotal evidence really plays no roll in the analysis (the way it should be).
Football is a different animal completely, because we aren't amassing season-long stats. We are trying to maximize points every week. It doesn't matter if we have a RB who scores more than everyone else over the course of the season if he stinks in week 13 or 14. Volatility is the nature of this game when you amass points each week then wipe the slate clean for the next week. We don't project a player to score 20 points a week. We project a player to score 320 points for the season. If you think there is 0 volatility, then you really need to rethink playing this game.
Football is a different animal completely, because we aren't amassing season-long stats. We are trying to maximize points every week. It doesn't matter if we have a RB who scores more than everyone else over the course of the season if he stinks in week 13 or 14. Volatility is the nature of this game when you amass points each week then wipe the slate clean for the next week. We don't project a player to score 20 points a week. We project a player to score 320 points for the season. If you think there is 0 volatility, then you really need to rethink playing this game.
BroadwayG
Footballguy
Apparently it is as simple as a coin flips.
You're not changing it. If you thought his TD stream would be 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0 for 8 total, then after 4 games, you're still projecting 4 TD's in the last 12 games.
No, that's not what I'm saying at all. What I'm saying is if you project him for 4 TD's over the first 4 games and 4 over the next 12, and he goes and scores 5 TD's in the first 4, you should still project him for 4 over the next 12, not 3. Same if he scores 0 over the first 4, your projection over the next 12 should remain the same, with him scoring 4, not 8.
Ignoratio Elenchi
Footballguy
Whether or not a player's expected output in weeks 2-16 should be reduced because he outperformed his expected output in week 1 is really not a matter of opinion, though. It is definitely not the case.Also, bump:
Instinctive
Footballguy
I'm short on time - so why don't you say what you think it means, and I'll just correct you. That will be much quicker for me. You can do so via PM to avoid embarrassment if you wish. In a short, underexplained, super quick explanation: If his mean is 20 ppg, then reversion to it would mean (haha wordplay) you expect him to score 20 ppg the rest of the way (reverting to his mean ppg performance) rather than 25 ppg. You're not looking at reversion to the mean, what you're positing is "underperformance in order to achieve the mean I originally projected."Really? Enlighten me...I don't understand how you can possibly think this. One above average week simply should not affect negatively the expected averages. He doesn't have a set amount of points. The only reasonable change in his average points that you could expect would be that he scores MORE per week, based on you underestimating his talents and being shown that in the above-expected-average week 1 performance.Also, you don't know what reversion to the mean is. Learn, then try again.Trying to get my brain around this...and I think I disagree with this line of thinking. I'm leaning more towards reversion to the mean.If Player X is expected to score 20 points/week for the season and comes out in week 1 over that number that would leave me to believe that future weeks should average below 20/week...unless you think that 25/week is the new normal which would change the answer.
If a .300 hitter for 10 years starts his 11th season hitting .350 through 81 games, do you expect him to bat only .250 the second half, or do you expect him to bat closer to .300?
CalBear
Footballguy
No, it's not a matter of opinion. If you had specifically projected Gonzo to score a TD in game 1, you wouldn't adjust your projections for the other games downwards. Nor would you if you had projected him to score zero TDs. The projections for the other games can only rationally be adjusted in the direction of the error; it makes no sense to say "he did better than I expected, so I'm going to downgrade the rest of my projections," nor to say "man, he really sucked in game 1, I'm going to bump my projections for the rest of the year."
This is all for simplicity purposes. No one should project an exact 20 points per game. We project 10, 15, 5, 12, 14, 8, 6 and so on...Having someone beat their first week projection shouldn't downgrade their future projections JUST BECAUSE they beat their first week projection. Some situations warrent a downgrade or upgrade but it's due to situation not simply because of an artificial requirement that if you projected someone for 1000 yards, that you have to make your weekly projections fit so they hit out to that 1000 yards.
gregjcross
Footballguy
You are Right, the line of reasoning would mean that player X "MUST" score Y over Z Games.
Ignoratio Elenchi
Footballguy
I don't think anyone believes there is zero volatility. That's not Modog's point. But I'm certain you have the bolded backwards. The reason we project a player to score 320 points in a season is precisely because (a) we project them to score 20 points per game (on average, not exactly 20 points every week) and (b) we project them to play 16 games. If the season was 2 games long, or 50 games long, we wouldn't still say, "This player is projected for 320 points this season." We would adjust the season-total projection based on the number of games he's expected to play, while keeping his per-game projection about the same.
So when we say a player is projected for 320 points for the season, what we really mean is we expect him to score around 20 points a week. If he scores 30 points in week 1, we still expect him to score 20 points per week going forward (or we may adjust this upwards, but there's no valid reasaon we'd adjust it downwards). If he has a death in the family and misses week 1, we don't assume he's still going to score 320 points over the remaining 15 games.
Tennessee_ATO
Footballguy
Well, who attempts to project a player's performance in week 13 during the pre-season? I submit no one.There are 2 different (fundamentally different, IMO) discussions going on here. The first is about a player's total projected score for the season as a whole in light of his performance in week 1. The second is about a player's performance in week 1 exceeding a projection for that discrete event. They are not the same. Again, IMO they aren't even close to the same thing.Bigger picture, however, is how we view projections in the first place. Projections are, by their nature, imprecise. If we projected 20 from Ray Rice in week 1 and he scored 22, we would say that our projection was a good one. Similarly, if we projected 320 out of Rice for the season and he ended with 330, we would say that our projection was outstanding. Projections are really ranges, not a static number. They are best viewed as "X +/- Y%".
northwoods
Footballguy
Why are you bringing average into the discussion? A better example that is more analogous to fantasy football would be the number of hits or homeruns for a season. And, if I had a half season of new information I would probably be adjusting my end of year totals to reflect the season to date performance. That is not what we are talking about in the above example. We are talking about a good first week of a 16 week season...I'm short on time - so why don't you say what you think it means, and I'll just correct you. That will be much quicker for me. You can do so via PM to avoid embarrassment if you wish. In a short, underexplained, super quick explanation: If his mean is 20 ppg, then reversion to it would mean (haha wordplay) you expect him to score 20 ppg the rest of the way (reverting to his mean ppg performance) rather than 25 ppg. You're not looking at reversion to the mean, what you're positing is "underperformance in order to achieve the mean I originally projected."Really? Enlighten me...I don't understand how you can possibly think this. One above average week simply should not affect negatively the expected averages. He doesn't have a set amount of points. The only reasonable change in his average points that you could expect would be that he scores MORE per week, based on you underestimating his talents and being shown that in the above-expected-average week 1 performance.Also, you don't know what reversion to the mean is. Learn, then try again.Trying to get my brain around this...and I think I disagree with this line of thinking. I'm leaning more towards reversion to the mean.If Player X is expected to score 20 points/week for the season and comes out in week 1 over that number that would leave me to believe that future weeks should average below 20/week...unless you think that 25/week is the new normal which would change the answer.
You are wrong. If I expect Player X to average 20 points/game for the season, I expect him to score 20 x 16 or 320 points this season. If he scores 25 points in Week 1, I now expect him to score 295 points in the remaining 15 games or 19.66 points/game. That is reversion to the mean. I never suggested that his season total would be higher based off of a better Week 1. As I mentioned in my original post, if I now expect Player X to score 25 points /week then I've changed the equation and the ending season total. Also, "underperformance in order to achieve the mean I originally projected" is exactly what reversion to the mean is.
If a .300 hitter for 10 years starts his 11th season hitting .350 through 81 games, do you expect him to bat only .250 the second half, or do you expect him to bat closer to .300?
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Tennessee_ATO
Footballguy
I think we have a disagreement here. Say Rice is projected for 320 for the season. IMO, that's really a range centered on 320. Inherent in that projection is the recognition that he WON'T score 20 points every week. He might not score 20 points in a single week and still hit the projected total spot-on. If he scores 30 in week 1, do you abandon your projection immediately? Do you return to your projection if he scores 15 the next 2 weeks since he's "back on pace" or do you downgrade your projection since he's "underperformed" 2/3rds of the time?There isn't a single player on any of my rosters I think will score "around" a static number all season long. I suspect that's the same for you as well. Every week is different and somewhat unique. The player isn't unique, but his opponent and match-ups are.
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