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I think that Brady's week 1 performance has virtually no bearing on his week 2 performance, other than that he is the player he is and he's on the team he's on. It's not like defensive coordinators haven't seen film of Brady before.
It's better to have a dud week when it's a non-elimination week, but having a dud week in week 1 doesn't make it any more or less likely that you'll have a dud week in week 11.
I think we agree on the end result, if your cheap guys didn't go off week 1 then you shouldn't be worried. I completely agree with this, most of the cheap guys don't have the opportunity week 1 because of their spot on the depth chart. They need to outperform those ahead of them or need an injury to happen. For example, I have Redman on my roster on the chance Mendy goes down with an injury. I would make this selection again, even knowing his week 1 results.The rhetorical distinction here is between not being worried and others (not trying to ascribe this to you) thinking that poor week 1 performances are predictive of better future performances. I can agree with the former because future performance is variable and week 1 results play a small role on future performance. I do take issue with the latter. Let's take the example of Peyton Hillis, by most measures he had a poor week 1. I think he will get better because his talent and opportunity indicate he is better than his week 1 stats, but his lack of stats week 1 is not causing better performance in the future. It is more like regression to the mean.
I understand. I'm not implying that Fitz is just as hungry now as he was pre-contract. But by all accounts, Fitz is a true pro that cares about the game and cares about his performance. Anyway, the original post said that Fitz was no bargain at that price. That's simply false.I made a similar statement in another thread I started about money and effort. I think it happens. Your work your ### off to achieve and then you finally arrive. I think it is only human there is a bit of a letdown, a sense of relief. It is like training for an ironman, you train to peak at a certain time. You cannot maintain the peak, thats why it is called a peak. Once you peak there is a letdown. The doers, the professionals, strive to peak again, to acheive greater status, but initially I think there is a letdown. Doesnt mean they are forever lazy, just I think likely to underachieve short term. If you won the lottery, you may continue to work, but I would bet, your quality of production would drop, initially.This. If Fitz isn't the most talented WR in the league, he's in the top three. That makes his price a bargain. What, you think he's going to get lazy because he's getting paid? These guys are professionals with pride in their work ethic. There's more at stake here than just money.
Fitz was the 5th most expensive WR at $28. I'm having difficulty understanding how that's a "bargain." If you mean he'll put up the same or better stats than Andre Johnson for $5 less, then I guess I see what you mean. But I wouldn't call any of the priciest players at each position a bargain. You're paying a steep price for his projected stud production.May be just a coincidence, and I'll admit I didn't look very much into it, but the rosters of the top performing teams this week, seemed to be more more of the lower quantity/higher quality variety.Also I'll take your stats one step further and post (assuming normal distribution) the probability of scoring over 200 in a week (which I figure is what you need the last 3 weeks to have a shot at winning)
Size Rosters AvScore StDev 18 3568 165.77 21.72 5.75%19 1393 166.54 20.99 5.55%20 1059 167.74 20.95 6.18%21 836 168.41 20.28 5.97%22 766 168.26 19.37 5.06%23 641 168.27 19.68 5.34%24 547 169.84 20.15 6.72%25 396 169.99 19.17 5.87%26 415 170.43 17.76 4.80%27 296 169.97 19.01 5.71%28 269 169.93 17.56 4.34%29 214 171.67 17.51 5.28%30 376 171.56 17.58 5.29%
Yes it does, unless you think its equally likely that he will pass for 8,000 yards as he will 4,000 yards on the season. It doesn't make it any more or less likely on any specific week like you keep saying, but at some point his numbers will have to trend towards his realistic projections even if they're on the high end of them. 4,000 yards divided by 16 games is 250/game. Assuming he has a few huge games like last night, then that means that some of his games will have to be below 250 to get to these realistic projections unless you think he ends the year with some unrealistic, record smashing yard total, which is a different argument.
This is what I meant in my original post. He's not a bargain at that price if you follow FBG projections. Guys like VJ and Wallace were much better values.
Roosters is spelled wrong.-QG
You absolutely are invoking the gambler's fallacy. You're basically saying, "Since player X already had their good / bad performance, they'll likely not have another similar performance in the future."edited to expand on this:Brady has thrown for 517 yards once in 146 regular season games. His likelihood of throwing 517 again in any given future week is also about 1 in 146 games. The odds will not be higher or lower because he already did it in week 1. That's an over simplification, but I think it makes my point.But yes, I agree with you that if you're going to have a dud week, it's better in a non-elimination week. That statement is true and has no bearing to the argument above
(edited again because I had brady's # of regular season games incorrect. 
)
That's not what I'm saying at all. Read the rest of the conversation.
I think it kind of is the point you are getting at.
I don't think anyone believes that Brady will average 500 yds a game. But the question is what is his new projected season total based on his week 1 performance. If we go with your ~250 a game prior to week 1, I think a reasonable estimate for his season totals would be 4,267 which is 517 + 15*250. I think this is a better estimate than maintaining a projection of 4,000 and saying he is going to perform under expectations at some undetermined point in the future. I can also buy Ignoratio's argument that there is some positive correlation between weeks, in this case that Brady's performance means maybe our initial projections were wrong and need to be revised upwards. I just don't understand how week 1 is negatively correlated with rest-of-season results (other than reversion to the mean).
I think those are reasonable year end projections too. But I dont believe for a second he will actually have exactly 250 yards each game here on out. He will have a few more monster games and a few less than stellar games yardage wise that even everything out. It happens every year to each player at each position. Go look at the stats. All I've been saying from the beginning is that it's best to have one of these inevitable "down" weeks on a non-elimination week and vice-versa because if you believe in the realistic consensus year end projection, the numbers have to meet there at the end of it all.
Right on, I don't mean to suggest that there is no variation in week-to-week performance but only that taking a per-game average gives a starting point for projecting season total stats conditional on stats already accumulated.As to the second part about the inevitability of down weeks, I think we just view this differently. Not trying to convince you over to the other side, but want to quote CalBear here as I think he puts it quite nicely:
You just keep repeating the same fallacy. Look at it this way: In weeks 2-17 last year, Tom Brady threw for 3642 yards and 33 TDs. If you knew only that information and not his season totals, what would you project as his week 1 totals? Don't you see that it's completely irrelevant whether he threw for 200/1 or 500/3 in game 1?
OK, here's another way to look at the fallacy; if Brady was projected last year to throw for 3700 yards and 34 TDs, and after week 16 was sitting at 3699 yards and 34 TDs, does that mean that in week 17 you would expect him to throw for 1 yard and zero TDs?
No, it doesn't. The fact that he had 500+ yards in one game does not make it more or less likely that he will have a dud game in the future. He will most likely have dud games in the future, but it has nothing to do with his week 1 performance.
You mean other than the two guys who were injured prior to week 1 and were inactive in week 1 as a result of said injuries?Haven't posted my squad yet...put up 186 with Moore out...no injuries in week one.
Matthew Stafford $18 32.25
Colt McCoy $10 22.25
-------------------------------------
Darren McFadden $28 16.10
Felix Jones $23 14.10
Chris Wells $16 18.20
Tim Hightower $14 17.20
Deji Karim $3 8.70
Ben Tate $3 17.60
Marion Barber $3 0.00
-------------------------------------
Larry Fitzgerald $28 9.20
Kenny Britt $21 30.60
Dez Bryant $21 16.10
Lance Moore $10 0.00
Nate Burleson $8 13.00
Bernard Berrian $5 0.00
Antonio Brown $3 3.40
---------------------------------------
Jimmy Graham $15 17.60
Lance Kendricks $6 3.30
Evan Moore $2 14.00
--------------------------------------
Olindo Mare $2 3.00
Mike Nugent $2 11.00
Jay Feely $2 4.00
---------------------------------------
Houston Texans $3 13.00
Denver Broncos $2 9.00
Jacksonville Jaguars $2 4.00
Even if your projections are rough (which mine are as I mentioned), my point still applies. Here's another way to look at it.. looking at Brady's actual stats from 2010. He had 6 games where he threw under 200 yards. In 2009 he had 3 (5 games under 250 yards). Hell, in his record breaking year, 2007, he had 3 games under 250 yards. The fact is, he and every other good player are going to have numbers that fluctuate from week to week, and some of those are going to be down weeks and some are going to be amazing weeks. This is fact. So knowing this, wouldn't you rather have one of these down weeks on a non-elimination week? I sure would.
I would rather him have a bad week on a non-elimination week, of course. But the fact that he had a good week in no way suggests that he's more likely to have a bad week in the future. Week 1 is in the past; his chance of having a bad game in week 2 is exactly the same as it was before week 1.
I think we are really close on this, completely agree that there will be week-to-week variation for all players. Just wanted to focus on the bold for a second. Lets use a roulette wheel as an analogy. Observing results of Roulette shows that the ball will land in red sometimes, black on others and green on occasion. If the roulette wheel has come up red 9 straight times, does this make black more likely on the next spin?
Jumping in late here, and I know you guys are beating this horse more than expected, but I think both sides are right to a certain extent.First of all, the roulette wheel example does not really apply. Brady's stats are not perfectly random. Defenses adjust, game plans change, and coaches get smarter. I think what is being argued on the other side is that this is NOT a coin flip or a spin of the wheel. NE's game plan was perfect against the perfect D. Now other coaches will adjust to what NE did making it harder to repeat that performance. NE may switch it up and run the ball next game to compensate. The point being made is that IF NE was going to break out this game plan against this D, it would have been nice to do it later in the year because the perfect storm probably will not happen again.
At Iggy's house
Player Year Proj Yd Wk1 Yd Act Yd GmsPeyton Manning 2010 4242 433 4700 16Tom Brady 2009 4191 378 4398 16Donovan McNabb 2008 3234 361 3916 16Tony Romo 2009 3672 353 4483 16Tony Romo 2007 3555 345 4211 16Drew Brees 2008 4052 343 5069 16Eli Manning 2007 3304 312 3336 16Tom Brady 2005 3845 306 4110 16Jay Cutler 2007 3349 304 3497 16Peyton Manning 2009 3859 301 4500 16Jay Cutler 2008 3349 299 4526 16Philip Rivers 2010 4368 298 4710 16Tom Brady 2007 3817 297 4806 16Jon Kitna 2007 3684 289 4068 16Peyton Manning 2007 4281 288 4040 16Carson Palmer 2005 3475 280 3836 16Jay Cutler 2009 3535 277 3666 16Peyton Manning 2006 4015 276 4397 16Eli Manning 2010 3671 263 4002 16Tom Brady 2010 4280 258 3900 16Peyton Manning 2008 3825 257 4002 16Eli Manning 2009 3257 256 4021 16Peyton Manning 2005 4552 254 3747 16Sam Bradford 2010 3673 253 3512 16Philip Rivers 2009 3683 252 4254 16Matt Ryan 2010 3659 252 3705 16Jake Plummer 2005 3664 251 3366 16Joe Flacco 2010 3575 248 3622 16Jake Delhomme 2008 3356 247 3288 16Eli Manning 2006 3528 247 3244 16Carson Palmer 2009 3500 247 3094 16Matt Hasselbeck 2005 3654 246 3455 16Kyle Orton 2009 3265 243 3802 16Drew Brees 2010 4235 237 4620 16Jon Kitna 2006 3163 229 4208 16Matt Hasselbeck 2007 3278 222 3966 16Marc Bulger 2006 3685 217 4301 16Philip Rivers 2008 3222 217 4009 16Eli Manning 2008 3281 216 3238 16Jake Delhomme 2005 3456 212 3421 16Jason Campbell 2009 3154 211 3618 16Drew Brees 2005 3464 209 3576 16Brett Favre 2007 3573 206 4157 16Brett Favre 2005 3766 201 3881 16Trent Green 2005 4000 200 4014 16Kurt Warner 2008 3103 197 4582 16Carson Palmer 2007 3931 194 4131 16Brett Favre 2008 3190 194 3472 16Drew Brees 2007 3896 192 4428 16Philip Rivers 2007 3450 190 3152 16Aaron Rodgers 2009 3791 184 4434 16Josh Freeman 2010 3376 182 3451 16Steve McNair 2006 3232 181 3050 16Aaron Rodgers 2008 3420 178 4038 16Drew Brees 2006 3197 170 4418 16Brett Favre 2006 3620 170 3885 16Matt Schaub 2009 3652 166 4770 16Tom Brady 2006 3798 163 3529 16Jake Plummer 2006 3240 138 1994 16Ben Roethlisberger 2008 3326 137 3308 16Jason Campbell 2008 3220 133 3245 16Carson Palmer 2006 3636 127 4035 16David Garrard 2009 3385 122 3597 16Brett Favre 2009 3151 110 4202 16Philip Rivers 2006 3312 108 3388 16Matt Schaub 2010 4093 107 4369 16Mark Sanchez 2010 3386 74 3291 16David Carr 2005 3274 70 2488 16Jay Cutler 2010 3435 372 3274 15Ben Roethlisberger 2009 3376 363 4328 15Drew Brees 2009 4300 358 4388 15Kurt Warner 2009 3661 288 3758 15Kerry Collins 2005 3987 265 3759 15Aaron Rodgers 2010 4264 188 3922 15Ben Roethlisberger 2007 3547 161 3154 15Marc Bulger 2008 3427 158 2720 15Matt Cassel 2010 3246 68 3116 15Matt Hasselbeck 2009 3156 279 3029 14Matt Ryan 2009 3517 229 2916 14Steve McNair 2005 3455 219 3161 14Donovan McNabb 2007 3530 184 3324 14Donovan McNabb 2009 3510 79 3553 14Tony Romo 2008 3915 320 3448 13Aaron Brooks 2005 3360 192 2882 13Jake Delhomme 2006 3492 186 2805 13Jason Campbell 2010 3273 180 2387 13Joey Harrington 2005 3450 167 2021 13Matt Hasselbeck 2006 3504 210 2442 12Michael Vick 2010 3353 175 3018 12Marc Bulger 2007 4048 167 2392 12Ben Roethlisberger 2010 3915 0 3200 12Byron Leftwich 2005 3536 252 2123 11Matt Schaub 2007 3092 225 2241 11Matt Schaub 2008 3285 202 3043 11Donovan McNabb 2006 3640 314 2647 10Derek Anderson 2008 3306 114 1615 10Donovan McNabb 2005 3688 257 2507 9J.P. Losman 2007 3179 97 1204 9Marc Bulger 2005 4354 362 2297 8Trent Edwards 2009 3220 212 1169 8Rex Grossman 2007 3182 145 1411 8Trent Green 2006 3548 90 1342 8Aaron Brooks 2006 3365 68 1105 8Kurt Warner 2006 3586 301 1377 7Daunte Culpepper 2005 3999 233 1564 7Matt Hasselbeck 2008 3464 190 1216 7Alex Smith 2007 3169 126 914 7Kevin Kolb 2010 3478 24 1197 7Tony Romo 2010 4221 282 1605 6Drew Bledsoe 2006 3432 246 1164 6Brian Griese 2005 3351 213 1136 6Matt Leinart 2007 3638 102 647 5Carson Palmer 2008 3841 99 731 5Daunte Culpepper 2006 3566 262 929 4Jon Kitna 2008 3294 262 758 4Chad Pennington 2005 3180 264 530 3Jake Delhomme 2007 3119 201 626 3Chris Simms 2006 3312 133 585 3Matthew Stafford 2010 3623 83 535 3Tom Brady 2008 4197 76 76 1
This is a good point. The idea is that small rosters have higher variance, so while the average scores favor large rosters, the small rosters have a greater chance of putting up the highest total for any given week. This week, small rosters were proportionately more likely to score 200+ points than larger rosters (which might have a lot to do with the fact that they're proportionately more likely to have Tom Brady as their QB1). The problem I have with this is that the playoffs are a cumulative three-week total, not a single week. The top of the leaderboard this week was littered with 18-20 man rosters. That will often be the case. But I suspect once we start tracking the rolling three-week totals, like we did last year, you'll see this advantage disappear. The variance that presumably makes a small roster more likely to score 230 points on any given week also means it's not likely to do so three weeks in a row. My reasons for believing large rosters >>>>>>>> small rosters has little to do with how they'll perform in the final 250, but even there I think I'd still rather have a higher-average, lower-variance large roster than a lower-average, higher-variance small roster.'Modog814 said:
Yup, but 2 of those 4 are definite junk entries, 2 having 5+ high cost QB's and a 3rd may be a junk entry with Peyton Manning as Highest $ QB.
For one thing, the overwhelming majority of entries are 18-20 man rosters. They are going to dominate every area of the standings at this point. (ETA: "overwhelming majority" and "dominate" are a bit hyperbolic but you understand the point. Small rosters are going to be well represented everywhere you look, just because there are so many of them right now.)For another thing, there will probably be tons of "junk" entries at the bottom of the standings for at least the first couple of weeks until they're all weeded out.
I'm going to respectfully disagree with you. If a single small roster has a greater chance of breaking 200 in any given week compared to a large roster, then (assuming there is independence between weeks) it has a greater chance of breaking 600 over 3 weeks.
Size Rosters AvScore StDev Exp 3 week 3 wk StDev 18 3568 165.77 21.72 497.31 37.62014354 0.317%19 1393 166.54 20.99 499.62 36.35574645 0.288%20 1059 167.74 20.95 503.22 36.28646442 0.383%21 836 168.41 20.28 505.23 35.12599038 0.349%22 766 168.26 19.37 504.78 33.54982414 0.227%23 641 168.27 19.68 504.81 34.08675989 0.261%24 547 169.84 20.15 509.52 34.90082377 0.476%25 396 169.99 19.17 509.97 33.20341398 0.335%26 415 170.43 17.76 511.29 30.76122234 0.196%27 296 169.97 19.01 509.91 32.92628585 0.311%28 269 169.93 17.56 509.79 30.41481218 0.151%29 214 171.67 17.51 515.01 30.32820964 0.254%30 376 171.56 17.58 514.68 30.4494532 0.254%Absolutely. For me the small vs Large roster debate comes down to 2 ideas:1) For those in support of large rosters, the final 250 is basically a lottery. And that the best strategy is to get the highest chance of getting a ticket to that lottery 2) For those in support of small rosters, the whole thing is basically a lottery, and your chances of getting to the top 250 are slim anyway. You need things to go right to get there, but their thought is if things do go right, I want the highest chance of winning that lottery as possible. Most of the people in group 1, believe that group 2 is wrong in the assumption that having a smaller roster increases their chances in the round of 250. I think it's been pretty well proven (from last couple years) that a larger roster is way more likely to get you to the top 250. Anyone arguing otherwise, i don't think is paying attention.Personally I think I'm one of the few in group 1 that actually think that group 2's thesis isn't necessarily incorrect. I'm just not sure if the advantage is large enough to warrant going with a smaller roster.
This is awesome, thanks for this. I took a quick look at some relationships and found some interesting though not entirely surprising results.Data prep:The Turk was kind enough to share some stats with me, related to the earlier discussion about week 1 stats. I haven't really looked at them yet
and probably won't until later today, but figured I'd share them so everyone can manipulate them to make whatever point they want.
For each of the last six years, this is the preseason top 20 QBs (according to Dodds), the year, their projected passing yards for the season, their actual week 1 paassing yards, their actual passing yards for the season, and their number of games played. Some of these, like 2008 Brady or 2010 Roethlisberger, should maybe be excluded (or not) depending on what you're trying to show. Just quickly eyeballing the stats, it looks like players who outperformed their projections in week 1 tended to outperform their projections for the year, i.e. a big week 1 performance isn't "offset" by lower stats later in the year, but rather their season total is adjusted upward. But that's just an impression from glancing at the list (and maybe my preconceived notions of what I expect the data to show), so I don't know if that's really the case. Anyway:
Good work, i was going to do something similar, but this saves me the effort.
Another thing I'll add, looking at only the players playing 14 games or more, it seems that in general pre-season projections are too conservative on a per game basis (I think I saw something like 16 yards per game too conservative. Although this broke down to about 23 yards underestimated for players who performed above average in week 1, and 9 yards underestimated for players who performed below average in week 1.)This is awesome, thanks for this. I took a quick look at some relationships and found some interesting though not entirely surprising results.Data prep:The Turk was kind enough to share some stats with me, related to the earlier discussion about week 1 stats. I haven't really looked at them yet
and probably won't until later today, but figured I'd share them so everyone can manipulate them to make whatever point they want.
For each of the last six years, this is the preseason top 20 QBs (according to Dodds), the year, their projected passing yards for the season, their actual week 1 paassing yards, their actual passing yards for the season, and their number of games played. Some of these, like 2008 Brady or 2010 Roethlisberger, should maybe be excluded (or not) depending on what you're trying to show. Just quickly eyeballing the stats, it looks like players who outperformed their projections in week 1 tended to outperform their projections for the year, i.e. a big week 1 performance isn't "offset" by lower stats later in the year, but rather their season total is adjusted upward. But that's just an impression from glancing at the list (and maybe my preconceived notions of what I expect the data to show), so I don't know if that's really the case. Anyway:
Excluded QBs with less than 8 games (8 games is admittedly arbitrary) played and Roethlisberger from last year (Suspended)
Converted season data into per game averages so we have an apples-to-apples comparison for QBs with less than 16 games played
Testing whether we should keep pre-season projections or update for week 1 stats:
Tried to predict actual per game averages based on two approaches: 1)pure pre-season projections and 2) Week 1 stats + pre-season average projection for the remainder of the games.
The regressions had an r-squared (amount of variation explained) of 25.13% for the first approach and 33.77% for the second approach. This indicates that we should be updating pre-season projections for week 1 stats and not stay true to the pre-season projection.
Testing Iggy's hypothesis that there is positive correlation between week 1 out performance and rest of season out-performance:
This is effectively going a step beyond part 2 above and saying that in addition to counting week 1 stats, we should also update our pre-season per game projections. Here I did a regression on week 1 out-performance predicting average out-performance in other weeks. The r-squared was weak at 7.12%, but there is a positive relationship and the coefficient estimate indicated that for each 100 yards you threw above your per-game average based on pre-season projections, you were on average going to throw for an additional 12 in other games above your pre-season per game average.
Using this to update our projections from part 2 above, we come up with an r-squared of 38.49%. Higher than the other two approaches.
Bottom line
Based on this data, not only is a good week 1 performance not predictive of future poor performance, it is slightly predictive of even more good performances (relative to pre-season projections). And Iggy was right.
Thanks, OC. This is much appreciated.
I will only speak for myself, but this isn't what I took issue with.I think most were arguing against this point, which I maintain is 100% false:
You specifically state above that having a dud in week 1 makes it more or less likely that you'll have a dud at some point, but not necessarily in a single week. I maintain whether you have a dud in one week or do great in one week doesn't make it more or less likely that you will have a dud in the future other than possibly telling us something about that player's talent level (which is indicative of duds or good games moving forward).
Thanks OC! This is awesome and really appreciated.
Can't wait to use it this weekend.I think the problem is that you make it sound like each player has a pre-determined amount of "dud" games. And by them having one in the week 1, you've essentially avoided it and have one less to deal with over the course of the season.
That's not quite what I said but I can see how that can be inferred. There are no pre-determined amount of duds, but if you assume that a) any given stud will have the occasional dud week, and b) these studs will still put up stud-like numbers on the season, then there can only be a handful of these dud games for both conditions to be true. Obviously, if this holds true, it's best to have these duds early on. To use the Brady example, a lot of people thought I meant that since Brady had a good week 1 then that means he has to have a dud week to compensate. That's not really it. I think Brady will have one or more dud weeks in the future, not because of his week 1 performance, but because he (and every other stud) does every season and if he doesn't then he'll end up with a season that smashes every record in the book which I don't think anyone agrees will happen.
I think I understand the confusion here.
I think everyone can agree that if you're going to have a dud week (and statistically, you will) it's better to have it on a week that doesn't matter.The bolded part is the fallacious argument that you're getting pushback about. Yes, we're being pedants.
I'm in this group too. It's a fascinating statistical question, one that someone (smarter than me) could explain.
