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APBRmetrics The statistical revolution will not be televised.
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gabefarkas
Joined: 31 Dec 2004 Posts: 1313 Location: Durham, NC
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Posted: Tue Oct 12, 2010 8:06 pm Post subject: |
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mtamada wrote: | Sorry, late reply here. My expansion starts with an example: one of the major ways of utilizing regression to the mean is with Stein estimators. The classic example is if it's two weeks into the baseball season and you see a player who's currently batting .412, and you want to predict what his batting average for the rest of the season will be, you do not (if you're smart) use the unbiased estimate of .412. You want to purposely use a biased estimate, and regress to the mean, because extreme performances are unlikely to be sustained.
The key word is extreme. Stein estimators are remarkable because "extreme" and "mean" can be used in a variety of situations; the baseball example is intuitively obvious, not so obvious is that the mean that you regress to doesn't even have to be the mean of baseball players' batting averages (although obviously, the more similar the variables are to each other, the better the Stein estimator will perform, e.g. if you have data on that same player from other seasons, that can be better than using the mean of all other baseball players). | Are you referring to the James-Stein estimator, or Stein's unbiased risk estimate? |
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mtamada
Joined: 28 Jan 2005 Posts: 377
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Posted: Thu Oct 14, 2010 3:24 am Post subject: |
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schtevie wrote: | [...]
But invoking "regression to the mean" arguments won't help much in justifying low-ball estimates for the Heat |
The lowest of the lowball, yeah sure there are always people who make goofy forecasts, they have their own obscure reasons. Regression to the mean is a moderate correction to apply, it doesn't create weird forecasts -- but it applies to everybody (everybody who's extreme that is; people near the mean can be expected to have minimal regression).
schtevie wrote: | primarily because what appears to be an extreme estimate, isn't really.
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Well that is indeed part of the art of forecasting: recognizing what is extreme and what is not. .412 is extremely high for a batter but quite low for an NBA field goal shooter. LBJ is if not the top player in the league, one of the top players. Therefore his forecasts ought to be extreme, yes?
Yes. But they still should be regressed. Every extreme forecast should be. (Though I'd guess that it's easier to wait until the very end and regress Miami's forecasts overall, rather than for each individual player.)
schtevie wrote: |
If one is looking for such a reason, it can be found by invoking the assumed concavity of the basketball production function. |
In other words, diminishing marginal returns, or in basketball terms, "there's only one ball on the court", i.e. too many superstars start reducing each other's production. The harder question is do they reduce each other's efficiency. I do not know what the models or evidence show. But your original point about the unrelatedness of regression to the mean still applies here: regardless of whether we assume concavity or linearity, the bottom line still holds: if your forecast is an extreme one, and you haven't applied any regression to the mean yet, do so now. The fact that they Heat are loaded with superstars means that they should be forecast for a lot of wins. But beware of a doctrine of exceptionalism, which claims that they are immune from the laws of statistics.
The 2008 Celtics rolled to 66 wins and a championship. But what happened in 2009 and 2010? The 1969 Lakes had a Big 3 that makes the Heat's look puny -- and won 55 games. The 1977 Sixers had perhaps the two best forwards in the league plus 4 former or future All-Stars, and won 50 games. The 1977 Knicks had 4 All-Pros, and won 42 games. The 2004 Lakers had 4 future Hall of Famers, and won 56.
Last edited by mtamada on Thu Oct 14, 2010 3:30 am; edited 1 time in total |
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mtamada
Joined: 28 Jan 2005 Posts: 377
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Posted: Thu Oct 14, 2010 3:26 am Post subject: |
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The former, I was not familiar with the latter, although apparently it can be used to derive the former. |
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back2newbelf
Joined: 21 Jun 2005 Posts: 279
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schtevie
Joined: 18 Apr 2005 Posts: 414
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Posted: Thu Oct 14, 2010 11:59 am Post subject: |
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Dang. I should have gotten in on the action at 63.5...
Mike, I think that there is value in being more precise when employing the term "regression to the mean" (RTTM). There are two distinct types of phenomena generating the results we see with NBA, league-wide win estimates across seasons, but it is only the first phenomenon that should be meaningfully associated with the term.
The first is statistical, the second for the lack of a better term, is fundamental or model-based (and with this, the zero-sum constraint on the estimation exercise is an important factor).
What I am referring to as "statistical" is the RTTM you observe when, on average, the kids of tall parents don't grow up to be quite as tall. The counterpart in the NBA is when a team because of truly transient good fortune generates wins in excess of what its "genes" would predict, and the following year (all else equal, which it never is) tends to regress to its expected ability.
What I am calling fundamental or model-based phenomena are the effects of all factors that would fit in the "true" NBA production function (that what G*d would reveal, were she so inclined).
One thorny unknown of particular importance in this regard is the precise effect of aging and injuries. But the general story is known and agreed upon. Younger players improve as their skills and knowledge of the game improve. Past their peak, athleticism deteriorates and the propensity for injury increases.
And how does this class of variables (and their variability) influence apparent RTTM? Well, in the ways we are used to expecting, but this result has nothing to do with the "laws of statistics". Apparent RTTM obtains because of the additional fact that better teams tend to have more minutes played by players at their peak, hence more prone to aging and injury effects, and also because the NBA is a zero-sum league (i.e. the games "unexpectedly" lost due to injury and aging, disproportionately suffered by the better teams, pad the win totals of the below-average younger, healthier teams)
As a thought experiment, imagine we lived in an alternate universe where human physiology was different, such that the young rather than the old tended to be injury-prone, and the league had a really hard salary cap instead of a soft one. Much of the apparent RTTM would vanish.
In light of these arguments, we can (kind of) interpret the recent Celtics' history that was mentioned. The last three years saw win totals of 66, 62, and 50 games.
The first issue is: to what win total should the Celtics have rolled in the first year of the Big 3? (The same question as for the Heat this year.) And the answer is, of course, that I don't really know the precise answer. Nobody does, but 66 is probably pretty close to what the "one true model" (approximated best by APM) would have predicted. KG was out for a stretch and played relatively poorly, just prior and after, but, then again, maybe Paul Pierce was playing "above his age" during the season. Etc.
But that emphasizes the main point: the expected value of this production function for the year in question is what matters for a prediction, and no adjustment for RTTM should be made ex post. (If one ends up requiring ad hoc adjustments, it necessarily implies that the model being used to generate predictions is incomplete and giving systematically biased results.)
What then of the following two years? All that can be said is that the trajectory is entirely consistent with fundamentals, but beyond that I have no firm idea as to how they should have been expected to perform. The 62 games seems about right, and last year, my sense is that they endured quite a few "excess" injuries. But I don't have any great confidence about that statement. And what to expect this year? I wish I had a clue. My guess is that they will "regress" to something above 50 wins. And that is the point. |
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Crow
Joined: 20 Jan 2009 Posts: 829
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Posted: Thu Oct 14, 2010 6:37 pm Post subject: |
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The Heat line might move again depending on whether Wade & James are considered ready & 100% closer to or on opening day or are still that way 2-4-8 weeks in, if they adjust the line and still take bets. At least in the abstract it should. |
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Rhuidean
Joined: 11 Mar 2010 Posts: 40 Location: East Bay, CA
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Posted: Thu Oct 14, 2010 7:17 pm Post subject: . |
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Schtevie: You've build a model that tells you X. You also have prior knowledge Y about the situation. Unless you have the utmost confidence in your model X and its results, then it makes sense to consider Y also.
From what I've seen (certain ad-hoc down-weightings of APM/SPM values that people used for LBJ, Wade, and Bosh, weighted APM/SPM values that lead to something close to 100% wins), it doesn't seem as if we should have utmost confidence in most of the models just yet. So incorporating prior knowledge makes some sense. |
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back2newbelf
Joined: 21 Jun 2005 Posts: 279
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Posted: Sat Oct 23, 2010 8:22 am Post subject: |
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Can anyone explain me what this vegas line means?
Atlanta Hawks Over 46.5 (-115) Under 46.5 (-105)
specifically the "-115" and "-105".
Obviously they didn't like their initial projection anymore and changed it a bit, but in what direction?
Also, I want to take back my earlier comments about the Knicks. They added more players than I remembered and Stoudemire looks good (at least in pre season) |
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haralabob
Joined: 11 Apr 2007 Posts: 27
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Posted: Sat Oct 23, 2010 12:35 pm Post subject: |
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back2newbelf wrote: | Can anyone explain me what this vegas line means?
Atlanta Hawks Over 46.5 (-115) Under 46.5 (-105)
specifically the "-115" and "-105".
Obviously they didn't like their initial projection anymore and changed it a bit, but in what direction?
Also, I want to take back my earlier comments about the Knicks. They added more players than I remembered and Stoudemire looks good (at least in pre season) |
Assume these lines started out as;
Over 46.5 -110
Under 46.5 -110
You'd have to bet $110 to win 100 in profit on either the over or the under.
You know have to bet $115 to win 100 on the over and only $105 to win $100 on the under.
Rather than change their forecast to 47 wins, they move the "juice" to discourage over bettors and encourage people to bet the under. |
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HoopStudies
Joined: 30 Dec 2004 Posts: 706 Location: Near Philadelphia, PA
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Posted: Sun Oct 24, 2010 3:40 pm Post subject: |
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Am I mistaken or did this thread not actually have anyone's actual predictions in it? _________________ Dean Oliver
Author, Basketball on Paper
The postings are my own & don't necess represent positions, strategies or opinions of employers. |
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back2newbelf
Joined: 21 Jun 2005 Posts: 279
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Posted: Mon Oct 25, 2010 10:55 am Post subject: |
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Code: |
Boston 53
NewJersey 28
Toronto 25
NewYork 37
Philly 27
Cleveland 35
Milwaukee 42
Chicago 45
Detroit 26
Indiana 31
Orlando 59
Miami 63
Washington 28
Atlanta 48
Charlotte 41
Utah 49
Minnesota 27
Denver 46
Oklahoma 51
Portland 52
GoldenState 36
Sacramento 36
Lakers 54
Phoenix 48
Clippers 27
Memphis 39
Houston 40
SA 49
Dallas 52
NO 36
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I'll add more comments later today
If I write "player X is good", it means my rating said he was good. Obviously the rating system could have been wrong. I'm just too lazy to write "my rating system blabla" everytime.
"+" means I think it's good for the team (even if they lost a player)
Boston: Lost Rasheed (+)
Cleveland: Vegas has them at 29.5. Absolutely do not agree. Better Coach(+), still a solid starting 5.
Dallas: More Haywood, Chandler (+)
Denver: Vegas has them at 43.5. No idea why
Detroit: Lost their second best player from last year (Jerebko) (-)
Indiana: Watson was strong for them last year (-)
Clippers: Lost Camby (-). I think they would win <20 without Griffin
Lakers: Barnes is good (+). Kobe doesn't look very healthy and Bynum doesn't start the season (-)
Bucks: Lost Ridnour (-). Do not like Chris Douglas Roberts (-)
Wolves: Replaced players in their (by far) two worst positions, PG and SG (Ridnour for Flynn, Johnson for Brewer) (+)
Philly: Lost their best player in Dalembert and brought in a bad players in Hawes and Nocioni(!) (-)
Phoenix: Vegas has them at 41.5. I don't know. Last time everybody thought the Suns would take a huge hit in the standings, they were just fine (back when Stoudemire missed an entire season)
Portland: (Maybe?) More minutes for Batum/Przybilla/Oden/Camby (+)
Sacramento: No Nocioni, more Dalembert, Cousins, Landry (+)
Washington: No Brandan Haywood (-)
The overall method looked like this:
1. Compare last season depth chart with projected depth chart. Look for significant changes in projected production using https://docs.google.com/leaf?id=0An1RF2rWzwSwdC1MU0d6cVNwaWs2Tk83WEctUmhqRGc&sort=name&layout=list&pid=0B31RF2rWzwSwNmNjOGM5YjYtMjc5Ni00MzViLWFkYTEtYWZmODQyNmI2MmE1&cindex=8
2. Drift everybody a bit to the middle
3. I had the west winning way more than last year. Adjust for that
4. Adjust for significant changes in division strength
Last edited by back2newbelf on Tue Oct 26, 2010 9:48 am; edited 3 times in total |
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Ed Küpfer
Joined: 30 Dec 2004 Posts: 787 Location: Toronto
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Posted: Mon Oct 25, 2010 11:14 am Post subject: |
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The Painted Area compiled forecasts from Vegas, John Hollinger, Kevin Pelton, and Kelly Dwyer.
Code: | EAST Vegas JH KP KD
MIA 64 66 60 70
ORL 55 55 52 60
BOS 53 51 42 50
CHI 46 48 51 49
ATL 46 46 35 48
MIL 45 49 42 48
CHA 38 30 32 38
NYK 35 37 44 41
PHI 35 43 33 35
IND 34 31 34 28
WAS 33 30 22 31
DET 31 32 27 19
CLE 29 29 39 12
TOR 26 22 35 31
NJN 25 26 40 27
WEST Vegas JH KP KD
LAL 56 56 46 57
OKC 51 49 48 47
POR 51 55 55 50
SAS 50 54 49 55
DAL 50 48 48 52
UTH 48 47 41 52
HOU 47 46 36 46
DEN 43 46 49 50
PHX 41 38 37 52
NOH 40 45 49 44
MEM 38 36 39 40
LAC 36 27 27 38
GSW 32 32 49 21
SAC 28 28 43 26
MIN 23 26 30 13
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KevinP hates me and loves David Lewin. That's what I'm getting from this. _________________ ed |
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Kevin Pelton Site Admin
Joined: 30 Dec 2004 Posts: 979 Location: Seattle
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Posted: Mon Oct 25, 2010 11:53 am Post subject: |
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Ed Küpfer wrote: | KevinP hates me and loves David Lewin. That's what I'm getting from this. |
Yes, the "do I like their analyst?" factor is heavy in my projections. There are few differences, but if we track this again, my final offering is here:
http://www.basketballprospectus.com/article.php?articleid=1219 |
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back2newbelf
Joined: 21 Jun 2005 Posts: 279
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Posted: Mon Oct 25, 2010 3:43 pm Post subject: |
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haralabob wrote: | Assume these lines started out as;
Over 46.5 -110
Under 46.5 -110
You'd have to bet $110 to win 100 in profit on either the over or the under.
You know have to bet $115 to win 100 on the over and only $105 to win $100 on the under.
Rather than change their forecast to 47 wins, they move the "juice" to discourage over bettors and encourage people to bet the under.
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Thank you.
Does anyone have a "chance that they'll blow their team up/have a firesale to tank for the lottery"-factor in their predictions?
Cleveland and New Orleans (if Paul doesn't return to form) seem like likely candidates |
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BobboFitos
Joined: 21 Feb 2009 Posts: 201 Location: Cambridge, MA
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Posted: Tue Oct 26, 2010 2:37 am Post subject: |
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back2newbelf wrote: | haralabob wrote: | Assume these lines started out as;
Over 46.5 -110
Under 46.5 -110
You'd have to bet $110 to win 100 in profit on either the over or the under.
You know have to bet $115 to win 100 on the over and only $105 to win $100 on the under.
Rather than change their forecast to 47 wins, they move the "juice" to discourage over bettors and encourage people to bet the under.
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Thank you.
Does anyone have a "chance that they'll blow their team up/have a firesale to tank for the lottery"-factor in their predictions?
Cleveland and New Orleans (if Paul doesn't return to form) seem like likely candidates |
I'm assuming this is what caused the Denver free-fall (they opened at 49.5 I believe and now stand at 43.5) _________________ http://pointsperpossession.com/
@PPPBasketball |
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