Taking a single anecdotal example does not change the pattern or direction of the reliationship. Off quadrant cases are guaranteed as long as correlation is less than 1.0.Not only is picking a single example like that pretty bad form, but is exactly the sort "gross oversimplification" you just accused. Note the irony.
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The "Law of Averages" (1 Viewer)
- Thread starter mlwinokur
- Start date
The Amalgamated
Footballguy
Well, it seems you did both but as I said in my first thread, I was trying to work this out as I wrote about it but, at least for me, the question of gambler's fallacy was critical. And everyone was jumping on him saying that these events were unrelated. I've been equivicol this entire thread. Suggesting that there is a right answer to the question, If Steve Smith does mediocre this week will he do well in the following weeks has no right answer --certainly not one from probability. Each FF player would have to make informed decisions on what a week 1 performance means.
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mlwinokur
Footballguy
Right, which why it is only after an infinite number of flips that the even split will occur.(note also that depending on the width of the coin there is also the varying but minute possibility that it will land on edge. Only a two-dimensional coin could produce a true 0.5 heads/0.5 tails expectation.)Each flip has an expectation of 0.5 heads and 0.5 tails, regardless of previous results. (Assuming a fair coin.)
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Here is the fundamental source of disagreement. I think that statistically you have to or else you are putting on blinders. But the adjustment need not be all that very much. But having one fewer games to get the 8 (or whatever) projected TDs would be hard to ignore. Even on a weeklly average if I had projected .6 TDs per week and someone goes 0 week one, I would have to move this to .5 TDs for week 2.
jurb26
Footballguy
You seem to be missing the point that when you make a projection of 10 tds in 16 games. You accept the fact that AT THE VERY LEAST 6 of those 16 weeks will not result in a TD. So why throw on the panic button after 1 week of 0 tds? Sorry, but I have more confidence in my projections then that. If after 5 weeks, hehas only 1. Well then I have to start asking myself what I missd and what is a more realistic projection. Not after 1 week though.
Dave Dodson
Footballguy
That comment by me was in response to this statement:This is so easily proven it would be silly to go to the effort. made by you.I am at work and don't always have time to fully develop what I'd like to say.I actually think on the surface you are correct, but as far as application goes, I'd tend not to be interested in using the output you are striving for.I bet I can find 100 players from last year whose week 1 performance was well under or over their season ending totals oppositely correlated from your predictions. Jamal Lewis was one that I knew off hand, I’d have to assume given a few hours I could find tens if not hundreds more.
The Amalgamated
Footballguy
And I should have noted that you were consistent in your conclusion throughout that the actual possible coorelation here was positive and dependent and that jurb was ignoring the possibility that a bad week one might not be the best thing to hope for.That is actually something that might be interesting here -- week one performance coorelated to year long performance.
Correct.
He was being accused of the fallacy that they are negatively correlated because if he uses up too many of his total yards in week one, he won't have as many left over for weeks 2-15.That is the gambler's fallacy.
It applies where events are not correlated, and it applies even more strongly where the events are in fact positively correlated.
Predicting Steve Smith's future performance depends on lots of things.The only one being discussed here as a fallacy (and it really is a fallacy) is that if he does poorly in week 1, he'll do better than he otherwise would have in weeks 2-15 because he won't have "used up" as large a portion of his EOY numbers reserve.
jurb26
Footballguy
Yes, it may in fact be likely that I have udervalued them. However, lets not forget that this is still only 1 week of play. To drastically change your stance on a player due to such a small sample of data does not seem logical IMO. I don't make projections thinking the will be "right on." I make them with a window or margin of error. Just like CMart and Griffin out produced any projections they had this week, next week or 2 weeks from now they could very well drastically underperform them. Every player will have good days and bad ones. Heck, this could be the olny good day for either RB all year long, we don't know this yet.
Not as "bad" -- as below what was expected. You were expecting him to maybe have 0 TDs, maybe 1, maybe 2, or maybe 3. The overall expectation for TDs was therefore positive, even if it was only fractional.If he actually gets zero TDs, therefore, he came in below expectations (but within the expected range of expectations).
"At least" six weeks is different from an expectation of six weeks. For example, when you project 10 TDs, you are saying that he will have more than zero TDs in "at least" one week. But you are expecting him to score in more weeks than that.When Smith gets zero TDs in week one, you're still expecting him to get zero TDs in "at least" six weeks -- but your expectation for his scoreless weeks should have just gone up.
It was, at best, neutral for you. The "at best" scenario would apply if games are independent events like roulette spins. It was, more probably, bad for you, since weekly performances seem to be positively correlated.
jurb26
Footballguy
You keep sighting this as a "fallacy" when there is in fact no way to possible know right now if it is or is not. This is my major problem with its application in FF. We do know in coin flipping or other COMPLETE EVENTS OF CHANCE that it would be. However, this is a football player and thus human being. Not an object of CHANCE. He palys in a scheme dictated week to week by coaches, Ds, and the tempo of the game. These are what we call VARIABLES. Something missing from the "gamblers fallacy." I fully believe that S.Smith is capable of around 1300/10 this season. I make this projection EXPECTING full well that he will have a bad game here or there and a very good game here or there. Regardless though I expect him to finish with close to those numbers. Even if he does very bad week 1 I still view his talent and abilty as enough to put him close to that projection. 1 week, good or bad, does not and will not drastically change that IMO.
It will not dramatically affect my future expectations for most players. That is, if before the season started, I had expected Jamal to rush for 1500 yards in weeks 2-15, then I may still have that same expectation notwithstanding week 1. But my expectation of his week 1 stats are of course changed. They went from 100 yards to 54 yards (or whatever he actually had).
My reasoning applies for week 1, or even for the first half of week 1, or even just for the first play of the first game.If I originally expected J.Lew to get 1600 yards rushing on the season, and if I expected him to get 5 yards on his first carry . . . then if he only gets 4 yards on his first carry I'd reduce my EOY projections down to 1599.
The first carry already happened. On his remaining carries I may not change my expectations. But his first carry at -1 from expectations is in the books.
It is applicable to Jamal Lewis hasn't "used up" very many of 1600 yards yet, so he'll get the rest of them in future weeks.That's exactly as fallacious whether we're talking about coin flips or fantasy football . . . unless you can show that week 2-15 performance is negatively correlated with week 1 performance, which it's not.Let me just state that I hate the "gamblers fallacy in application to Fantasy Football. The gamblers fallacy deals with completly independent events OUTSIDE OF THE CONTROL OF HUMANS. Fantasy sports and football do not. Players will have good weeks and bad weeks. This can not in any way be realated to that of flipping a coin though. A coin flip is total chanced to which side it lands on and independent and unpredictable or projectable every time. Football players however have different skill sets and game planes to factor into the mix. The realation is not even close IMO. A team can scheme to take away a guy 1 week and the next a team forgets about him. There are actual VARIABLES to concider when projecting fantasy performacne and the gamblers fallacy ignores this resounding fact.
Maybe some of you guys can convince me that it is applicable though.
This is a classic statement of the gambler's fallacy.
M
mojorizin
Guest
I'd simply say that as Cleveland has figured out how to play some semblance of defense, his projection drops automatically to 1100 - where it belongs.
Voice Of Reason
Footballguy
#1 Projections mean nothing. Because you, Joey B, or any other outside obserber says that a players will score a certain amount of TDs, gain a certain amount of yards, etc have no bearing on how that player performs.
#2 There is no "law of averages." Averages are a tool to measure things that once happened and try to predict the future. A law of averages would mean that the measurement of past things changes the events of the future, that would be the same flaw as thinking that the reason a hurricane smashed into Florida was because the projected path on the wather channel said it would.
#3 Some of you have a incorrect understanding of probablitiy and statisics. If you flipped a coin 10 time and it came up heads, then you flipped it 990 more times, the odds that there would be more heads than tails outcomes would be more than 50-50.
#2 There is no "law of averages." Averages are a tool to measure things that once happened and try to predict the future. A law of averages would mean that the measurement of past things changes the events of the future, that would be the same flaw as thinking that the reason a hurricane smashed into Florida was because the projected path on the wather channel said it would.
#3 Some of you have a incorrect understanding of probablitiy and statisics. If you flipped a coin 10 time and it came up heads, then you flipped it 990 more times, the odds that there would be more heads than tails outcomes would be more than 50-50.
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jurb:
What are your current week 2-15 projections for Steve Smith?
Are you seriously going to increase those projections if he does poorly this week, and decrease those projections if he does really well this week?
There's an argument to be made for not changing your week 2-15 projections based on week 1. Week 1, after all, is just one week. Small sample size and all.
But there's no reasonable argument for revising your projections upward when a guy does worse than expected, or for revising your projections downward when he does better than expected.
What are your current week 2-15 projections for Steve Smith?
Are you seriously going to increase those projections if he does poorly this week, and decrease those projections if he does really well this week?
There's an argument to be made for not changing your week 2-15 projections based on week 1. Week 1, after all, is just one week. Small sample size and all.
But there's no reasonable argument for revising your projections upward when a guy does worse than expected, or for revising your projections downward when he does better than expected.
CalBear
Footballguy
This is part of the same fallacy. As the number of coin flips goes to infinity, the margin of error goes to zero on a percentage basis. However, the expected absolute error increases the more you flip the coin--all the way out to infinity. In fact, the probability of the expected number of heads (m) equalling exactly half the total number of flips (n/2) approaches zero as n approaches infinity.
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The Amalgamated
Footballguy
You've speculated that week 1 performance is positively (and significantly) coorelated to overall performance but you haven't provided any evidence. Intuitively, I'm willing to buy that, but statisicians usually don't like to rely on intuition. And, of course, as was mentioned earlier, if the coorelation of last years performance is stronger than week 1's then you have other data that might make more sense to pay attention to.
Code:
If I originally expected J.Lew to get 1600 yards rushing on the season, and if I expected him to get 5 yards on his first carry . . . then if he only gets 4 yards on his first carry I'd reduce my EOY projections down to 1599.The first carry already happened. On his remaining carries I may not change my expectations. But his first carry at -1 from expectations is in the books.Excellent point.
The Amalgamated
Footballguy
I've been resisting saying this but it is my understanding that there have been recent speculations in theoretical mathmatics that this actually is not the case. I can't provide a link or anything but I know I heard a report discussing the notion that, in practice, this may not be true. Now maybe I'll waste some time on google.
cstu
Footballguy
People, people, people, don't you realize that these "projections" are basically "guesses" based on information we had before the season even started?You can change your projections based on the performance during the season (and would be stupid not to).
One game isn't a good predictor of an entire season, especially for a WR, so I think it's too early to tell who's going to outperform their projections and who's not. However, the preseason projections factored in questions about every player, whether it's over-coming injuries, too old, too young, etc. By seeing how the players are answering the questions you can redo your projections for the rest of the season.
If I am wrong, why did people pick up Boldin after week 1 and not just stick with his preseason projections?
It's obvious that weekly performances are positively correlated. I'm not going to spend time gathering evidence for that point.
Of course. But to the extent week 1 is worth paying attention to at all, a poor performance is not a plus, and a good performance is not a minus.
LOL. I think Boldin outperformed his EOY projections in week 1 alone. So maybe some "law of averages" people expected him to get negative yards in weeks 2-15.
The Amalgamated
Footballguy
Hmm. I guess it is easier to make arguements when you feel free to say whatever you feel like and to make assertions without evidence. And really its the paranthetic note that's important there. Is week 1 performance significantly correlated? I don't expect you to gather any evidence for this but feel free to assert you're wrong and I'm right in the next post.
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Dave Dodson
Footballguy
I just looked at 250 players from last season. The entire analysis would be much more fun if I had projected points vs. actual, but this took me about 4 minutes to do and that would take a lot longer 
94 players had higher opening weeks than their average points for the season.156 players had lower opening weeks than their average points for the season.Jake PlummerL TomlinsonManningLewisT Gonzalez all stand out as major underperformers in week 1.BoldinChambersGallowayWardall stand out as major overperformers in week 1.14 players under performed their season averages by more than 10 points in week 1. 28 players over performed their season averages by more than 10 points in week 1.Using week 1 to predict the average points per week over the next 15 weeks yields an R Square of .26, with an F Stat of 89 and P Values of less than 5% FWIW (not much but what the hell 
) All of this and I still come back to my earlier post and what Maurile is saying as well, a poor performance in week 1 is not really a plus, and a good performance in week 1 is not really a minus.You can gains some generalizations from what I have posted but not anything worth betting on IMO.
94 players had higher opening weeks than their average points for the season.156 players had lower opening weeks than their average points for the season.Jake PlummerL TomlinsonManningLewisT Gonzalez all stand out as major underperformers in week 1.BoldinChambersGallowayWardall stand out as major overperformers in week 1.14 players under performed their season averages by more than 10 points in week 1. 28 players over performed their season averages by more than 10 points in week 1.Using week 1 to predict the average points per week over the next 15 weeks yields an R Square of .26, with an F Stat of 89 and P Values of less than 5% FWIW (not much but what the hell ) All of this and I still come back to my earlier post and what Maurile is saying as well, a poor performance in week 1 is not really a plus, and a good performance in week 1 is not really a minus.You can gains some generalizations from what I have posted but not anything worth betting on IMO.
The Amalgamated
Footballguy
Thanks Dave. That's interesting and some actual info! 
1. I said "It could possibly hurt him in a future week if defenses game plan against him more strongly than they otherwise would have." That is correct. It could possibly hurt him if that happens. 2. I said "It's obvious that weekly performances are positively correlated." This is also correct. They are positively correlated, and this is obvious.
There's no contradiction between those two statements, any more than there's a contradiction between saying that a coin could possibly land on heads six times in a row, but that the first and sixth flips are not correlated.
As for your paranthetic note, you're misattributing it to me because I never said that week 1 and weeks 2-15 are "significantly" correlated. I'll stand by it anyway, though. They are significantly correlated.
Use week 1 as a predictor for weeks 2-15 for any previous year, and you'll find it does significantly better than random -- and the correlation is positive, not negative.
The Amalgamated
Footballguy
Now I'm really beating a dead horse here but I guess you gotta do what you're good at.
I don't think that's a fair characterization of what jurb said. He wasn't asserting that a poor week was a plus or even a good week a minus just that he hoped Smith would do well in the future (and that that was somehow related to week 1 -- d'oh)Dave Dodson
Footballguy
Thanks!Thanks Dave. That's interesting and some actual info!
Dave Dodson
Footballguy
To be honest, I was kind of late to the fun so I was just kind of tossing that out. I didn't read what jurb even saidNow I'm really beating a dead horse here but I guess you gotta do what you're good at.
lol - sorry bout that
From the first post in this thread:
He's saying that a bad week 1 would be a plus for weeks 2-15.
smcindoe
Footballguy
There are about three or four different discussions going on here, some of which are useful (correlation of week-to-week performance), and some of which are not (jurb desperately trying to change the subject from his original argument to something more sensical).
The bottom line is that Maurice and others are right about the Gambler's Fallacy. How much it really applies to fantasy football is up for debate, of course. I could even see the argument that a Smith owner who had his week one matchup in the bag would want him to do poorly -- fewer touches means less chance of injury, and if Smith plays badly he's less likely to be the focus for defensive co-ordinators the rest of the month.
But to argue that you should root against him so he doesn't "use up" his projections is just wrong. That's where the fallacy comes in, which is all people were trying to point out.
The bottom line is that Maurice and others are right about the Gambler's Fallacy. How much it really applies to fantasy football is up for debate, of course. I could even see the argument that a Smith owner who had his week one matchup in the bag would want him to do poorly -- fewer touches means less chance of injury, and if Smith plays badly he's less likely to be the focus for defensive co-ordinators the rest of the month.
But to argue that you should root against him so he doesn't "use up" his projections is just wrong. That's where the fallacy comes in, which is all people were trying to point out.
Correct.
The Amalgamated
Footballguy
Actually, I don't think the discussion has ever been "should" he root against him. Such an argument would really take us into a kind of post modernist world that I don't think would be very useful. I'm willing to concede that jurb's rooting will have no affect whatsoever on Smith's performance this week or the season!
Dave Dodson
Footballguy
This is true, but isn't it so partially due to the fact that nearly all if not all of the data points are positive? If you started with a benchmark other than 0, say 10 points as the floor for RB scoring or something, we could see some negative correlations don't you think?
The Amalgamated
Footballguy
Yes, he said that, he also said this:
Exactly. In other words, a poor week 1 would be a plus for weeks 2-15.
The Amalgamated
Footballguy
No problem. I'd be better off today if I hadn't read what jurb said -- at least I'd be prepared to teach tomorrow. I doubt my students are going to want to hear about this discussion or the Packer game which will prevent me from preparing later. I'd better get some work done.To be honest, I was kind of late to the fun so I was just kind of tossing that out. I didn't read what jurb even saidNow I'm really beating a dead horse here but I guess you gotta do what you're good at.
I don't know what benchmark you used, but it shouldn't be zero points.The predicting formula will bey = mx + bwhere y = "weeks 2-15 PPG", x = "week 1 points", and m and b are whatever optimize the accuracy of that equation. (Non-linear equations might produce better results, but lets keep it simple.)When I claim that week 1 and weeks 2-15 are positively correlated, I'm just saying that m will be positive for the best values of m and b. I would certainly not expect the best value of b to be zero. (b will almost certainly also be positive, and m will be between 0 and 1.)(Excel uses regression analysis to find the best-fitting line; I assumed that's how you did it, but maybe not.)
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What kind of students do you have that they wouldn't want to hear about the Packer game?
The Amalgamated
Footballguy
Minnesotans!
jurb26
Footballguy
OK, all those jumping aboard here. Answer me thiso players have good weeks and bad weeks threw the course of a 16 game season? Yes or No?Does a good week 1 ensure a great season to come? Yes or NO?Does a bad week 1 ensure a bad season to come? Yes or No?Does it make sense to DRASTICALLY change and adjust projections after a sample size of 1 game? Yes or No?Finally, could someone please illoistrate to me exactly what kind of credibility the "gambler fallacy" hold in the world of FF? Cuase I have still heard no good arguements.
o players have good weeks and bad weeks threw the course of a 16 game season? Yes or No?Does a good week 1 ensure a great season to come? Yes or NO?Does a bad week 1 ensure a bad season to come? Yes or No?Does it make sense to DRASTICALLY change and adjust projections after a sample size of 1 game? Yes or No?Finally, could someone please illoistrate to me exactly what kind of credibility the "gambler fallacy" hold in the world of FF? Cuase I have still heard no good arguements.
Yes.OK, all those jumping aboard here. Answer me this
No.
No.
Sometimes. See Anquan Boldin 2003 or Charles Rogers 2004.
I don't understand the question. Fallacies properly have zero credibility.
CalBear
Footballguy
"Please don't dominate the rap, jack,if you've got nothing new to say."OK, all those jumping aboard here. Answer me this
