The "Law of Averages" (1 Viewer)

[mlwinokur]

This is how this discussion began in another thread.

QUOTE (jurb26 @ Sep 13 2004, 12:32 AM)

I need nothing as I have sured up a week 1 win (58.8 - 49).  I do however have S.Smith playing in the game.  Would like to see him get limited action as I like the law of averages for the rest of the season if he does little.  

QUOTE (mlwinokur @ Sep 13 2004, 12:37 AM)

I take it that the wink means you're kidding...I hope you're kidding because otherwise you're just nuts!!! 

QUOTE (jurb26 @ Sep 13 2004, 12:43 AM)

Nope, very serious. The man will put up numbers this year, that much I know. I would just rather they come in a week when I "need" them more. 

QUOTE (mlwinokur @ Sep 13 2004, 1:02 AM)

Does anyone else agree with jurb26's logic?  

QUOTE (jurb26 @ Sep 13 2004, 01:18 AM)

The same logic that tells me that CMart will not finish the season with 3136 yds rushing this season. Or do you think that after his week one performance this is now a realistic goal?

My answer to this is simple: No, I don't beleive that CMart will finish the season with 3136 yards, but I also don't think he's gonna finish with exactly 1215 yards (Draft Dominator projection). That from now on he will average fewer yards per game to reach the 1215 yard total is nonsense.See, I'm having trouble understanding how a great performance one week can possibly hurt a player in a future week. Can someone please explain this to me?

Edited for style and grammar

 

[Maurile Tremblay]

See I'm having trouble understanding how a great performance one week can possibly hurt a player in a future week.

It could possibly hurt him in a future week if defenses game plan against him more strongly than they otherwise would have . . . but the "law of averages" reasoning here is fallacious.

 

[bueno]

One data point does not a trend make. Just because he may have had his best game of the year on opening day doesn't mean he won't come close to making projections. He will have a bad week here and there, possibly an injury that will compensate (in whole or in part) for this week.If I had CMart and thought someone was dumb enough to think he could repeat this week every week, I'd be trading him to that person for the best stud or two on his team.

 

[StuntMonkee]

I fully understand the reasoning here. Its pretty simple. Each player will only have so many big games. Especialy players at the C. Martin level. It does no good if all of your players have monster weeks the same week, you would rather spread it out, thus increasing your odds of winning future games. For example, the Steve Smith poster could care less if he plays tonight, where as on the other hand I need him to come out and throw 150 yards and a couple TD's. I need this week to be his monster week, and my other players that feel flat (lewis, barlow, duece, mason, plax, coles. . .ect) to have big weeks the week that Smith has a down week.A team that wins by 1000 points 1 week becuase they all performed the #1 game the same week wont help you the rest of the season. . .unless you play in points only league.

 

[ookook]

Yeah, is a weird twist on the old Gambler's Fallacy. Does not work because they are independent events. Only if the average were fixed ahead of time would this logic work...and it is most certainly not. Smith doing poorly tonight will in no way increase the odds fo him doing well later. And perhaps the opposite.

 

[bueno]

One data point does not a trend make. Just because he may have had his best game of the year on opening day doesn't mean he won't come close to making projections. He will have a bad week here and there, possibly an injury that will compensate (in whole or in part) for this week.If I had CMart and thought someone was dumb enough to think he could repeat this week every week, I'd be trading him to that person for the best stud or two on his team.

 

[Dave Dodson]

See I'm having trouble understanding how a great performance one week can possibly hurt a player in a future week.

It could possibly hurt him in a future week if defenses game plan against him more strongly than they otherwise would have . . . but the "law of averages" reasoning here is fallacious.

We have a winner.

 

[Jungle1]

Look at it this way.Let's say we are going to flip a coin 16 times. The CoinFlipDominator predicts that 8 of those will be heads and 8 will be tails.So on Week 1, I flip a head. By the logic in this thread, my chances of flipping a tail on Week 2 would be greater than 50%. Doesn't make sense.

 

[smcindoe]

Yeah, is a weird twist on the old Gambler's Fallacy. Does not work because they are independent events.

Bingo.I wrote an article about this sort of nonsense last year.

 

[Maurile Tremblay]

Each player will only have so many big games.

But we don't know how many. Our estimate for Curtis Martin should have just gone up, and our estimate for Jamal Lewis should have just gone down.Jungle1's coin-flipping analogy is correct. (Even though, strictly speaking, NFL games are not completely independent trials. But they're independent enough for purposes of this thread.)Suppose I predict that, over the course of 16 coin flips, there will be eight heads. The first flip lands heads. My updated projection: there will be 8.5 heads. If the second flip also lands heads, I'm moving my projection up to 9. If the first 15 flips are all heads (and I'm sure it's an honest coin), I'm moving my projection up to 15.5.

 

[jazz12pg]

Keep in mind, a projection of 1215 yards on the year isn't based on him getting exactly 76 yards rushing in every game this year, either. It's based on a good games versus bad teams and bad games versus good teams, etc.Martin has had EIGHT <50 yard games the last two years. And he had 174 yards in a game last year and only finished with 1300 yards. So 196 yards in the first game doesn't mean 1215, or close to it, is now unlikely. And who's to say the projections didn't have him at 196 for this week anyway

 

[jurb26]

I fully understand the reasoning here. Its pretty simple. Each player will only have so many big games. Especialy players at the C. Martin level. It does no good if all of your players have monster weeks the same week, you would rather spread it out, thus increasing your odds of winning future games. For example, the Steve Smith poster could care less if he plays tonight, where as on the other hand I need him to come out and throw 150 yards and a couple TD's. I need this week to be his monster week, and my other players that feel flat (lewis, barlow, duece, mason, plax, coles. . .ect) to have big weeks the week that Smith has a down week.A team that wins by 1000 points 1 week becuase they all performed the #1 game the same week wont help you the rest of the season. . .unless you play in points only league.

This is exactly what I mean right here. This was not intended to be some sort of rule (I admit I missused the word) and this entire thing is blown way out of proportion. I was really just being selfish is all. I would much rather Smith had a BIG day when I needed it. If he has a big one tonight it almost feels wasted on my end as I have already won anyway. Basically I have a set of projections for Smith that he I feel he should eventually, one way or the other, come very close to by the end of the season. Therefor, I would not want him to skew those numbers very early on seeng that I don't "need" them right now. Now I fully understand that all are independent events, and am not trying to state otherwise. I was mearly looking at this as the most benificial way to my team as possible. For example: I'm sure every martin owner would be VERY HAPPY to see him continue to put up nearly 200 yds a week. This however is proven to be VERY unlikely. It really just falls in line with the buy low, sell high trade philosophy. Guys who had huge weeks (by huge I mean far greater than what can/should be normally expected) are likely to see reduced prouctivity over the course of the year. The same would be opp for guys like McAllister and Lewis. These are guys who are bound to put up very good season ending numbers, so better days are to be expected. This is no "rule" by any stretch, basically just playing the percentages.

 

[Maurile Tremblay]

Guys who had huge weeks (by huge I mean far greater than what can/should be normally expected) are likely to see reduced prouctivity over the course of the year.

Reduced compared to the huge week they just had, but so what?Their expected future productivity should not be reduced, however, compared to what their expected future productivity would have been anyway.

 

[The Amalgamated]

Each player will only have so many big games.

But we don't know how many. Our estimate for Curtis Martin should have just gone up, and our estimate for Jamal Lewis should have just gone down.Jungle1's coin-flipping analogy is correct. (Even though, strictly speaking, NFL games are not completely independent trials. But they're independent enough for purposes of this thread.)

Suppose I predict that, over the course of 16 coin flips, there will be eight heads. The first flip lands heads. My updated projection: there will be 8.5 heads. If the second flip also lands heads, I'm moving my projection up to 9. If the first 15 flips are all heads (and I'm sure it's an honest coin), I'm moving my projection up to 15.5.

I'm having a hard time sorting out my thoughts on this:1. The coin flipping analogy does not apply as your own first comment suggests. These are not independent,random, events. They are independant tests of skill and strategy. And, in fact, it is the poster who suggests that the law of averages will help him that is actually asserting that these games are random. He's saying "it should be tails so it can be heads next time."

2. I'm not suggesting that the original advocate of this notion of the "law of averages" is correct but he does have a point about expected outcomes. He has an expectation (a projection if you will) of what Steve Smith will do over the course of the season. Therefore, one game is not terribly important except that he recieves points in this "random" way and history tells him that a reciever of Steve Smith's skill and team and other unquanifable qualities will score x points. After week 1 he will score x minus week 1. In his mind, the less week one is, the better. You can argue that's not true but not based on mathmatical probability

3. Your original post that a high or low first week might impact how we view the rest of the season reveals the fact that these events are not random and only nominally independent. And therefore, the law of averages doesn't apply but neither is his logic necessarily flawed. Back to the expectations for Steve Smith -Using a number as an example Smith will score appromimately 10 tds this season. If he doesn't score 1 week one, one can still expect 10 tds but over the next 15 weeks. Now, this doesn't mean one shouldn't adjust projections as you suggest but, I would argue, that adjustment is just judgement and not compensation for a random occurrance (as in your coin flip example).

I don't know if any of that is clear but I'm procastinating here.

 

[Maurile Tremblay]

Back to the expectations for Steve Smith -Using a number as an example Smith will score appromimately 10 tds this season.  If he doesn't score 1 week one, one can still expect 10 tds but over the next 15 weeks.

This is the part that's wrong.The original 10-TD projection included a possibility that he'd score a TD (or several) in week 1.That didn't happen, so the original projection should be reduced.Let's say the original 10-TD projection included 0.6 TDs for week 1. Since the actual number was zero, the end-of-year projection should generally be reduced by about 0.6 TDs (more or less, depending on how he and the Panthers looked).Carry it further to make it more obvious. Let's say Smith scores two TDs through his first 15 games. Are you going to project an 8-TD game to finish the season?

 

[jurb26]

I'm having a hard time sorting out my thoughts on this:

1. The coin flipping analogy does not apply as your own first comment suggests. These are not independent,random, events. They are independant tests of skill and strategy. And, in fact, it is the poster who suggests that the law of averages will help him that is actually asserting that these games are random. He's saying "it should be tails so it can be heads next time."

2. I'm not suggesting that the original advocate of this notion of the "law of averages" is correct but he does have a point about expected outcomes. He has an expectation (a projection if you will) of what Steve Smith will do over the course of the season. Therefore, one game is not terribly important except that he recieves points in this "random" way and history tells him that a reciever of Steve Smith's skill and team and other unquanifable qualities will score x points. After week 1 he will score x minus week 1. In his mind, the less week one is, the better. You can argue that's not true but not based on mathmatical probability

3. Your original post that a high or low first week might impact how we view the rest of the season reveals the fact that these events are not random and only nominally independent. And therefore, the law of averages doesn't apply but neither is his logic necessarily flawed. Back to the expectations for Steve Smith -Using a number as an example Smith will score appromimately 10 tds this season. If he doesn't score 1 week one, one can still expect 10 tds but over the next 15 weeks. Now, this doesn't mean one shouldn't adjust projections as you suggest but, I would argue, that adjustment is just judgement and not compensation for a random occurrance (as in your coin flip example).

I don't know if any of that is clear but I'm procastinating here.

Thank you. This is about as good as you can put it IMO. #2 is right on.

 

[cstu]

Due to the fact that a 200 yards, 2 TD game wasn't expected for Martin, his projections should go up. While he was expected to have good games, I think this one was outside the expected range. I think a 50-100 yard increase in his total and one more TD would be appropriate. However, I always thought his projections were too low for a guy that plays well every year. The lack of TD's scares people, but if you agree with the "law of averages" you would have thought 2 TD's was too low and that he would go back closer to his average yearly TD total.

 

[jurb26]

Back to the expectations for Steve Smith -Using a number as an example Smith will score appromimately 10 tds this season.  If he doesn't score 1 week one, one can still expect 10 tds but over the next 15 weeks.

This is the part that's wrong.The original 10-TD projection included a possibility that he'd score a TD (or several) in week 1.That didn't happen, so the original projection must be reduced.Let's say the original 10-TD projection included 0.6 TDs for week 1. Since the actual number was zero, the end-of-year projection should generally be reduced by about 0.6 TDs (more or less, depending on how he and the Panthers looked).Carry it further to make it more obvious. Let's say Smith scores two TDs through his first 15 games. Are you going to project an 8-TD game to finish the season?

Using this logic here. One would believe that Martin is almost likely to finish with 3,000 yds. Do you actually think that as well? Projections are not based on strict per game averages. Players will have high points and low points. The logic you are using here completly ignores that fact. You are sighting games as independent events in no way linked together (which I would disagree with to a point). Yet at the same time are revamping projections basied on 1 independent event (game 1). Which one is it? Your arguement is contradicting. If you see the games as independent, then even though Martin had nearlly 200/2 in game one, your projections for the rest on the season and thus week 2 would be back to the original per game basis you sight. Not upgraded or down graded from the preseaon rank. If you use the % as I do, then you will expect that this huge game will result in reduced productivity in relation to week 1 and thus less probability to have further big games.

 

[The Amalgamated]

Back to the expectations for Steve Smith -Using a number as an example Smith will score appromimately 10 tds this season. If he doesn't score 1 week one, one can still expect 10 tds but over the next 15 weeks.

This is the part that's wrong.The original 10-TD projection included a possibility that he'd score a TD (or several) in week 1.That didn't happen, so the original projection should be reduced.Let's say the original 10-TD projection included 0.6 TDs for week 1. Since the actual number was zero, the end-of-year projection should generally be reduced by about 0.6 TDs (more or less, depending on how he and the Panthers looked).Carry it further to make it more obvious. Let's say Smith scores two TDs through his first 15 games. Are you going to project an 8-TD game to finish the season?

I think the only reasonable aswer to the question do you change Smith's projection after week one is maybe (and again reveals why this isn't probability). I would have to assume that if since no player can score .6 tds a game, anyone projecting that he would score ten would have to understand that those tds are going to come in some apparently random fashion (and now I use random again in a non mathmatical way to simply indicate that they won't come .6, .6, .6 etc.).The 10 td projection must have taken into account the possibilty that he would not score a td week 1.So if he scores 0 it must be expected that in the 10 td projection he will have no tds at least 6 times a year. And therefore one might reasonablly keep the projection at ten. If he scores 2 perhaps one might want to go higher but, I would argue, especially after just one week, that changing the projections might be an overreaction. With all this stuff, its possible that changing projections might be a better judgement than others, but that not because Smith's tds are random but because your judgement of his totals have changed (ie Smith has a really good game, Delhomme looks better than expected, etc.).

 

[mlwinokur]

Each player will only have so many big games.

But we don't know how many. Our estimate for Curtis Martin should have just gone up, and our estimate for Jamal Lewis should have just gone down.Jungle1's coin-flipping analogy is correct. (Even though, strictly speaking, NFL games are not completely independent trials. But they're independent enough for purposes of this thread.)

Suppose I predict that, over the course of 16 coin flips, there will be eight heads. The first flip lands heads. My updated projection: there will be 8.5 heads. If the second flip also lands heads, I'm moving my projection up to 9. If the first 15 flips are all heads (and I'm sure it's an honest coin), I'm moving my projection up to 15.5.

I'm having a hard time sorting out my thoughts on this:1. The coin flipping analogy does not apply as your own first comment suggests. These are not independent,random, events. They are independant tests of skill and strategy. And, in fact, it is the poster who suggests that the law of averages will help him that is actually asserting that these games are random. He's saying "it should be tails so it can be heads next time."

2. I'm not suggesting that the original advocate of this notion of the "law of averages" is correct but he does have a point about expected outcomes. He has an expectation (a projection if you will) of what Steve Smith will do over the course of the season. Therefore, one game is not terribly important except that he recieves points in this "random" way and history tells him that a reciever of Steve Smith's skill and team and other unquanifable qualities will score x points. After week 1 he will score x minus week 1. In his mind, the less week one is, the better. You can argue that's not true but not based on mathmatical probability

3. Your original post that a high or low first week might impact how we view the rest of the season reveals the fact that these events are not random and only nominally independent. And therefore, the law of averages doesn't apply but neither is his logic necessarily flawed. Back to the expectations for Steve Smith -Using a number as an example Smith will score appromimately 10 tds this season. If he doesn't score 1 week one, one can still expect 10 tds but over the next 15 weeks. Now, this doesn't mean one shouldn't adjust projections as you suggest but, I would argue, that adjustment is just judgement and not compensation for a random occurrance (as in your coin flip example).

I don't know if any of that is clear but I'm procastinating here.

There is an old say in sports: "That's why they play the game"The fact of the matter is that our projections aren't always right. After game one Curtis Martin may be on pace for something like 1350 yards instead of the 1215. We call this "over-achieving". There is, of course, the opposite "under-achieving". In order to win at fantasy football, i think you need to be flexible enough to adjust your initial projection. Otherwise, you might trade away all your overachievers for a bunch of underacheivers.

 

[ds857]

yes, each game is close to being independent of each other, but the key word being close. because some teams could be playing for the run and reduce martin's yardage and/or TDsThe coin flip example is a good one, but the flaw is:If you flip a coin 100 times, you expect the number of heads and the number of tails to come out almost to be 50/50. Thus, even if your first 10 flips of the coin turn up heads, AND your chance of the next coin flip being a head is 50/50, there will be enough coin flips in the next 89 flips where the result is tails to get the total of heads vs tails back to around 50/50So, if you expect curtis martin to put up 1300 yards, then in the next 15 games, martin will only have about 1100 yards or so. You can not predict that martin will have a bad game the next game based on the law of averages, but you can predict that over the next 15 games, if your predictions are right, then martin will have a few games where he has a poor gameso if you change your projections based on the first game, then of course the law of averages will not work because the end result is not the same. but if you dont change what your expectations are, then the law of averages is a very valid point if you dont want to "waste" a big week if you dont need it. it only depends on whether you are willing to change your projections or not. just because someone scores 3 TDs, doesnt necessarily mean your projections will go up to the point where he'll score 48 TDs for the season, but if someone scores 3TDs in game one, and you projected him to score 10, then maybe you will bump his projection up to about 11 or 12 TDs for the season, but that doesnt mean the law of averages doesnt apply, its only because you changed the end result that the law of averages does not apply

 

[jurb26]

yes, each game is close to being independent of each other, but the key word being close. because some teams could be playing for the run and reduce martin's yardage and/or TDsThe coin flip example is a good one, but the flaw is:If you flip a coin 100 times, you expect the number of heads and the number of tails to come out almost to be 50/50. Thus, even if your first 10 flips of the coin turn up heads, AND your chance of the next coin flip being a head is 50/50, there will be enough coin flips in the next 89 flips where the result is tails to get the total of heads vs tails back to around 50/50So, if you expect curtis martin to put up 1300 yards, then in the next 15 games, martin will only have about 1100 yards or so. You can not predict that martin will have a bad game the next game based on the law of averages, but you can predict that over the next 15 games, if your predictions are right, then martin will have a few games where he has a poor gameso if you change your projections based on the first game, then of course the law of averages will not work because the end result is not the same. but if you dont change what your expectations are, then the law of averages is a very valid point if you dont want to "waste" a big week if you dont need it. it only depends on whether you are willing to change your projections or not. just because someone scores 3 TDs, doesnt necessarily mean your projections will go up to the point where he'll score 48 TDs for the season, but if someone scores 3TDs in game one, and you projected him to score 10, then maybe you will bump his projection up to about 11 or 12 TDs for the season, but that doesnt mean the law of averages doesnt apply, its only because you changed the end result that the law of averages does not apply

All goods points.Basically iI think this comes down to weather or not you change porjections DRASTICALLY due to 1 week of performance. To that I say NO. I have S.Smith for about 1300/10. If he goes for 160/2 in week one, I will adjust them a bit to show the extra production. Maybe bump him up to 1350/11 for the season. however I will still expect numbers very close to the original projection. I make the projection (and would assume most due) factoring in the fact that some games will be big and some bad. I do know that every week will not be big for any player though. It is just not realistic. So I would rather the big weeks come when I need them more. In short, it takes more than just one week for me to DRASTICALLY change my original projections. If come week 4 or 5 CMart is still close to that 200 yds per game. I will then assume I have missed the boat on the value of CMart this year. one week however is not enough data to make that call on just yet IMO.

 

[Maurile Tremblay]

Back to the expectations for Steve Smith -Using a number as an example Smith will score appromimately 10 tds this season.  If he doesn't score 1 week one, one can still expect 10 tds but over the next 15 weeks.

This is the part that's wrong.The original 10-TD projection included a possibility that he'd score a TD (or several) in week 1.That didn't happen, so the original projection must be reduced.Let's say the original 10-TD projection included 0.6 TDs for week 1. Since the actual number was zero, the end-of-year projection should generally be reduced by about 0.6 TDs (more or less, depending on how he and the Panthers looked).Carry it further to make it more obvious. Let's say Smith scores two TDs through his first 15 games. Are you going to project an 8-TD game to finish the season?

Using this logic here. One would believe that Martin is almost likely to finish with 3,000 yds.

I have no idea how you're figuring that, but you're evidently misunderstanding something I wrote.

 

[jurb26]

Carry it further to make it more obvious. Let's say Smith scores two TDs through his first 15 games. Are you going to project an 8-TD game to finish the season?

No, of course not. But you are dealing with 2 VERY DIFFERENT events here. There is a HUGE difference between adjusting projectons after a data group of 15 weeks and a data group of 1 week.

 

[smcindoe]

If you flip a coin 100 times, you expect the number of heads and the number of tails to come out almost to be 50/50. Thus, even if your first 10 flips of the coin turn up heads, AND your chance of the next coin flip being a head is 50/50, there will be enough coin flips in the next 89 flips where the result is tails to get the total of heads vs tails back to around 50/50

If I read you right, you're arguing that if you set out to flip a coin 100 times and the first ten all come up heads, you should expect that 50 of the 90 remaining flips will be tails. If so, this is a near-perfect example of the gambler's fallacy in action.

 

[ookook]

I am pretty certain that based on logic if Steve Smith has a bad game 1 his expected per week projection for remainder of the season HAVE TO GO DOWN NOT UP. Really, really. To suggest otherwise is succumbing to some fallacy or another. I am not a logician, but I think I am very solid ground as a statistician that the slope between performance in week 1 and performance of the mean of weeks 2 thru 16 is POSITIVE not NEGATIVE. This is so easily proven it would be silly to go to the effort.

 

[ookook]

BTW, the above post only pre-supposes that on average there is a small postive correlaiton between performance across the weeks of a season. In fact, it is non-small and positive.

 

[Maurile Tremblay]

but if you dont change what your expectations are, then the law of averages is a very valid point . . .

It's really just the gambler's fallacy. It's logically invalid, not valid. I am sure of this. (It's not that difficult.)But I won't try to change your mind. Read smcindoe's article, or just think about these concepts more on your own . . . if you feel like it. If you don't feel like it, no biggie. The type of error you're making probably won't cost you any championships in fantasy football -- it doesn't come up often enough to be all that important.

 

[The Amalgamated]

Carry it further to make it more obvious. Let's say Smith scores two TDs through his first 15 games. Are you going to project an 8-TD game to finish the season?

Obviously not, but the data set is vastly different from 1 game and 15. If he has 2 TDs after one game will I necessarily adjust...again, I can only say the answer is maybe.If he has 2 after 15, yes. But, I'll likely have stopped playing Smith around week 7 (earlier I hope) and abandoned my projections for him altogether. That being the case, we once again come back to the question of is FF performance akin to flipping a coin. The answer when looking at your obvious example is no. In fact, it is more like if he has 5 points every week for the last 15 weeks we (hopefully) can predict with greater accuracy his next performance -- something we would both agree we could not do with a coin (if we flipped it 15 times and it came up heads 15 times it wouldn't help us to predict what the 16th flip would be).

 

[Maurile Tremblay]

BTW, the above post only pre-supposes that on average there is a small postive correlaiton between performance across the weeks of a season. In fact, it is non-small and positive.

Yes.

 

[Dave Dodson]

I think there is a bit of a fundamental issue here that is being overlooked. The issue I have with it is the 1,215 yard projection and its validity. A simple calculation tells us that Martin’s mean yards per season is 1,296. More importantly however, the standard deviation of yards per season is 158 yards (granted quite low for an NFL back over 9 seasons; by comparison, Emmitt Smith’s Std Dev = 277, Corey Dillon’s = 291).This tells me that I can be 68% confident in my estimation that for 2004, Martin will rush somewhere within +/- 1 Standard Deviation of his average seasonal rushing yardage. Not rocket science I know, but that gets me to a range of 1,454 on the high end to 1,137 on the low end.I didn’t look, but if FBG’s preseason estimate was for 1,215 yards, our range would be 1,373 to 1,056. What does this mean? His first game is essentially meaningless. If we went purely off statistical averages we’d project Martin for 1,296 this year, his career average. This is good for 81 yards a game. This means week 1 was 116 over what we would have expected, but well within our predicted range of 1,454 to 1,137, since if he averaged 81 yards a game from here on out he’d come in with 1,412 on the season. If we predicted him to rush for 75 yards per game and instead he rushed for 197 week one, that only puts him at 122 over our estimations, again well within our predicted range of 1,373 to 1,056 since if he averaged 75 yards a game from here on out he’d come in with 1,322 on the season.I think we, fantasy football players as a whole, tend to try and oversimplify statistics and probability to make it fit our needs. Flipping a coin and an NFL running back’s performance are not even in the same stratosphere of predictability.In college statistics class, I can recall collectively flipping a coin 10,000 times in class for 10 trials. The max standard deviation was less than 1%, or 50 out of 10,000 flips. Compare this to Martin’s annual rushing yardage standard deviation of 158 yards, which equates to over 12%.Bottom line, if Martin rushes for 1,137 or 1,454 yards this year, we should be no more or less surprised than we would be if we flipped a coin 10,000 times and came up with 4,950 heads or 5,050 heads…statistically speaking, the likelihood is about the same.

 

[Maurile Tremblay]

Carry it further to make it more obvious. Let's say Smith scores two TDs through his first 15 games. Are you going to project an 8-TD game to finish the season?

No, of course not. But you are dealing with 2 VERY DIFFERENT events here. There is a HUGE difference between adjusting projectons after a data group of 15 weeks and a data group of 1 week.

Projections are about the future.If you reduce your end-of-year projections from 10 to 9.4 based on a zero-TD first game, you are not changing your projections. You're just acknowledging what already happened in the past.

If you keep your end-of-year projections at 10, you are chaning your projections. You're not only changing them based on a sample of a single week, but you're changing them upward based on a poor performance. Since weekly production has a positive correlation (as ookook notes), this is nonsensical.

 

[The Amalgamated]

I am pretty certain that based on logic if Steve Smith has a bad game 1 his expected per week projection for remainder of the season HAVE TO GO DOWN NOT UP.

I have no problem with this conclusion. It however, again, demonstrates why predicting the results of FF and predicting random events (coin flips, lottery numbers, roulette numbers and the like) are not the same.

 

[smcindoe]

Someone in this thread mentioned "buy low, sell high". While that's an excellent strategy, it doesn't really apply here.

If you have a guy projected for 800 totalyards and in week one he goes off for 150 total yards, you do not "sell high" because you now believe he only has 650 yards left. You actually raise your expectations for that player, but you sell high because you hope to find someone who will unreasonably inflate their own projections based on the small one-game sample size and therefore overpay.

 

[Maurile Tremblay]

I am pretty certain that based on logic if Steve Smith has a bad game 1 his expected per week projection for remainder of the season HAVE TO GO DOWN NOT UP.

I have no problem with this conclusion. It however, again, demonstrates why predicting the results of FF and predicting random events (coin flips, lottery numbers, roulette numbers and the like) are not the same.

If football performances were completely independent events like roulette, this "law of averages" thinking would be wrong.Since they're not independent events, but are actually positively correlated, this "law of averages" thinking is even more wrong.

 

[mlwinokur]

If you flip a coin 100 times, you expect the number of heads and the number of tails to come out almost to be 50/50.  Thus, even if your first 10 flips of the coin turn up heads, AND your chance of the next coin flip being a head is 50/50, there will be enough coin flips in the next 89 flips where the result is tails to get the total of heads vs tails back to around 50/50

If I read you right, you're arguing that if you set out to flip a coin 100 times and the first ten all come up heads, you should expect that 50 of the 90 remaining flips will be tails. If so, this is a near-perfect example of the gambler's fallacy in action.

the only time an expectation of 50/50 can be made reguarding a coin flip is when the sample size of coin flips approaches infinity. Proir to that variations from 50/50 are only localised statistical variations from the expected outcome.Ok, suppose you flipped a coin 100 times, and it come up heads every time. You should expect tails to come up more often from now on as you approach an infinite number of coin flips. The question is: how many flips will it take for tails to catch up? The answer is that there is no way to know. It may take a 100 trillion coin flips before tails catches up.If you follow that, here's the part that may blow your mind. There is an existencial question. When does the sample size begin and to whose coin flipping it limited. That is, if you flipped heads 100 times in a row does that mean that the total is (heads:100 tails:0) or should you count all the previous coin flipps you have made? Is heads really ahead by 100 flips? What about the guy in china flipping a coin? If he flips tails does that count in your total?let me know if your head exploads.

 

[-OZ-]

Let me see if I understand this right.Based on "logic" we should all try to trade players who did well in week 1 for players that played horribly? (given they are within the same tier)people should be chomping at the bit to trade Dunn for Duckettor Q Griffin for Charlie Garnerjust to name two examples.At the same time, I'm not going to be trading for Cedrick Wilson.My projections now are based on the next 16 weeks, with some adjustments as I see how players are used.

 

[ookook]

His first game is essentially meaningless.

This also would assume a non-positive relationship between week 1 performance and subsequent weeks' performances. But is positive, so after week 1 it is statistically sound to increase C-Mart's predicted performance for the next week. Of course, one could very sensibly take into accoutn past years' performance...which is what I assume the original projection was based on.

 

[Maurile Tremblay]

Ok, suppose you flipped a coin 100 times, and it come up heads every time. You should expect tails to come up more often from now on as you approach an infinite number of coin flips.

Each flip has an expectation of 0.5 heads and 0.5 tails, regardless of previous results. (Assuming a fair coin.)

 

[Dave Dodson]

I am pretty certain that based on logic if Steve Smith has a bad game 1 his expected per week projection for remainder of the season HAVE TO GO DOWN NOT UP. Really, really. To suggest otherwise is succumbing to some fallacy or another. I am not a logician, but I think I am very solid ground as a statistician that the slope between performance in week 1 and performance of the mean of weeks 2 thru 16 is POSITIVE not NEGATIVE. This is so easily proven it would be silly to go to the effort.

Take Jamal Lewis for last year and get back to me.This is just a gross oversimplification on your part.

 

[The Amalgamated]

BTW, the above post only pre-supposes that on average there is a small postive correlaiton between performance across the weeks of a season. In fact, it is non-small and positive.

Yes.

Hold on. If there is a strong, positive coorelation between ff performance across weeks of the season (again, something I would agree with) then you are not describing random, independent events -- which is what 10, or 16 or 100 coin flips are.I thought that the jurb was being accused of buying into the fallacy that these events were related. That he could predict likely future outcomes based on past outcomes. Now I'm hearing don't hope for a bad game because it likely indicates more bad games down the road. I'm not foolish enough to say that this is some sort of logical fallacy but it seems to me that believing Steve Smith's first game performance won't be a predictor for his entire season is just as reasonable as saying it will be.

 

[Dave Dodson]

His first game is essentially meaningless.

This also would assume a non-positive relationship between week 1 performance and subsequent weeks' performances. But is positive, so after week 1 it is statistically sound to increase C-Mart's predicted performance for the next week. Of course, one could very sensibly take into accoutn past years' performance...which is what I assume the original projection was based on.

Week one carries no more weight than any other week in your analysis but you don’t seem to be acknowledging that.

 

[ScoobyDoo]

All I want to know is if this means that Barlow and C. Brown will score more touchdowns the next 15 weeks, or less.Sounds like less.

 

[jurb26]

Carry it further to make it more obvious. Let's say Smith scores two TDs through his first 15 games. Are you going to project an 8-TD game to finish the season?

No, of course not. But you are dealing with 2 VERY DIFFERENT events here. There is a HUGE difference between adjusting projectons after a data group of 15 weeks and a data group of 1 week.

Projections are about the future.If you reduce your end-of-year projections from 10 to 9.4 based on a zero-TD first game, you are not changing your projections. You're just acknowledging what already happened in the past.

If you keep your end-of-year projections at 10, you are chaning your projections. You're not only changing them based on a sample of a single week, but you're changing them upward based on a poor performance. Since weekly production has a positive correlation (as ookook notes), this is nonsensical.

Huh? I make a projection of 10 tds in a season KNOWING full well that a 10 td season can in now way, shap, or form = a td per week. Therefor, why after 1 week with 0 tds (a given fact seeing a projection of 10 in 16 weeks) would I view this as bad? There is no way at this point he can really underperform from the td standpoint. Only outperform it, which I contend may or may not be good for me seeing the projections I have made. To make this simply. I have already in a 10 td projection accounted for at LEAST 6 weeks for which I think Smith will not scorea td. So him scoring 0 on a night when I don't need them any way is rather meaningless and good for me. If he does howeer out produce my expectations then its really just gravy. If he scores 2 or 3 tds, I can easily assume I had misjudged his overall performance. If he scores 0, I was expecting at least 6 weeks of 0 anyways. At this point it doesn't seem as though I can loose. Hope this makes some sort of sense.

 

[smcindoe]

If you follow that, here's the part that may blow your mind. There is an existencial question. When does the sample size begin and to whose coin flipping it limited. That is, if you flipped heads 100 times in a row does that mean that the total is (heads:100 tails:0) or should you count all the previous coin flipps you have made? Is heads really ahead by 100 flips? What about the guy in china flipping a coin? If he flips tails does that count in your total?

OK, sure, but what about the unobservable cat under a box flipping a coin? Does he count too?

 

[ookook]

I thought that the jurb was being accused of buying into the fallacy that these events were related.

I think the coin flip thing is a red herring.What I "accused" was presuming the relationship was negative not positive. That is why it is a "weird" permuation of gambler's fallacy. The events are dependent and positively correlated. To believe they are unrelated or lower scores make higher scores more likely in subsequent games is not supprted by the data.

 

[The Amalgamated]

If football performances were completely independent events like roulette, this "law of averages" thinking would be wrong.

Since they're not independent events, but are actually positively correlated, this "law of averages" thinking is even more wrong.

This is where we differ. Especially given that jurb is talking about one game. Jamal Lewis has already been mentioned and, I doubt that you are actually making the arguement that a one week sample should dramatically change our expectations for most players. And that brings me back to Smith. If Smith doesn't have a big game this week, I wouldn't be too worried. I'd still expect his performance to match my expectations. and therefore, just as I had concieved before the season began, I'd expect some big games from Smith.At some point in the season, you are correct. But, again, I doubt that you'll actually argue that that point is after week 1.

 

[ookook]

Week one carries no more weight than any other week in your analysis but you don’t seem to be acknowledging that.

I think we are in agreement here. I would definately weight week 1 performance LESS than last year's (which is a composite of 16 or so).I tried to study this once and gave up. My heuristic was to give last year about a weight of .8 and week 1 .2 weight.Then week 2 last year .7 and this years current average .3, etc.Surely, one could start to include other predictors like SOS fo this years' moving average.What I think is flat out wrong statistically is (a) not to adjust next week's projection at all, or (b) adjust it upward in the presence of poor performance.

 

[jurb26]

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.

 

[ds857]

QUOTE (ds857 @ Sep 13 2004, 04:26 PM) If you flip a coin 100 times, you expect the number of heads and the number of tails to come out almost to be 50/50. Thus, even if your first 10 flips of the coin turn up heads, AND your chance of the next coin flip being a head is 50/50, there will be enough coin flips in the next 89 flips where the result is tails to get the total of heads vs tails back to around 50/50 If I read you right, you're arguing that if you set out to flip a coin 100 times and the first ten all come up heads, you should expect that 50 of the 90 remaining flips will be tails. If so, this is a near-perfect example of the gambler's fallacy in action.

yes... probability says that in the long run, the probability of having heads vs tails is 50/50... thus given the number of tosses, whether it was 100 or 1000 or 10,000, around half will come up as heads and half tails. i think the gamblers fallacy is that if 10 heads comes up, the next one has to be tails, but that is not the case. i'm not saying the next game martin will have a crappy game in his next game, and i'm not saying he will have a great game, but that in the long run, he will come back to where the projections are (if correct). you may adjust the projections, but if you do, then all i'm saying is that of course the law of averages doesnt work, because then you're adding in a second variable. but if you keep your projections the same then there will be a time where martin will have a bad game.casinos always win because the odds are on their side. if you're up 1000 bucks, do you expect that if you keep gambling that you will continue winning money? no because the odds of the casino coming out ahead are greater than the player coming out ahead IN THE LONG RUN. It might take 10 years for you to lose your money, but you will lose it if you keep playing

QUOTE (jurb26 @ Sep 13 2004, 01:39 PM) QUOTE (Maurile Tremblay @ Sep 13 2004, 03:08 PM) Carry it further to make it more obvious. Let's say Smith scores two TDs through his first 15 games. Are you going to project an 8-TD game to finish the season? No, of course not. But you are dealing with 2 VERY DIFFERENT events here. There is a HUGE difference between adjusting projectons after a data group of 15 weeks and a data group of 1 week. Projections are about the future.If you reduce your end-of-year projections from 10 to 9.4 based on a zero-TD first game, you are not changing your projections. You're just acknowledging what already happened in the past.If you keep your end-of-year projections at 10, you are chaning your projections. You're not only changing them based on a sample of a single week, but you're changing them upward based on a poor performance. Since weekly production has a positive correlation (as ookook notes), this is nonsensical.

your yearly projections are based on what happens throughout the course of a year. one game should not change those projections. if you're projecting steve smith to have 0.6 TDs/game, then there will be some games where he has 1TD and some where he has none because we all know its impossible to have 0.6 TDs every game.thus if steve smith doesnt gets zero TDs in the first game and you change your yearly projection from 10 TDs to 9 TDs, then you are changing your projections as there is no way you could have projected Smith to have exactly 0.6 TDs in his first gameif you keep your year end projections the same, you are changing your projections, but only on a PER GAME basis, not on the final value. just like in the coin toss example, if 10 heads comes up, the next one can still be a head, but in the LONG RUN, there will be more tails than heads, with of course a standard deviation as DD stated. As DD also stated, the first game is meaningless because there is the fact that there is a standard deviation