APBRmetrics

Ed Küpfer · Joined: 30 Dec 2004 Posts: 522 Location: Toronto

Some hacks I'm always flipping through my notes to look up. Figured I'd just jot them down here and bookmark the page to save me some trouble. Feel free to add your own.

Assisted % = 0.75 - AST/MIN * 1.5
This one has a standard error of about 10%.

Potential Assists = AST * (0.5 * PTS/FGM) / TS%
Thanks to Dan for this one.

In-Game Home Team Win Probability = 1 / (1 + EXP(-(0.06 + MinutesRemaining * 0.01+ HomeTeamLead * 0.34)))
This one will be the subject of a massive study this offseason. It only works on less than one quarter remaining.

For every point in team point differential, add 3 games to a team's win total over the course of 82 games. Home court advantage is worth about 3 points per game.
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ed

Ed Küpfer · Joined: 30 Dec 2004 Posts: 522 Location: Toronto

For estimating high possession players

Regress FT% and FTA/poss 20% to the mean
Regress eFG% 25% to the mean
Regress ORTG 25% to the mean
Regress DRTG 30% to the mean
Regress TO% 20% to the mean

Do not regress

DR%
OR%
AST%
BLK%
STL%

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ed

HoopStudies · Posted: Sat Apr 09, 2005 10:36 am Post subject:

Ed Küpfer · Joined: 30 Dec 2004 Posts: 522 Location: Toronto

Ed Küpfer · Joined: 30 Dec 2004 Posts: 522 Location: Toronto

Team1 Vs Team2 predictors

Ed Küpfer · Joined: 30 Dec 2004 Posts: 522 Location: Toronto

Linear Weights-style individual possession estimator:

POSS = 0.74 * FGA + 0.44 * FTA + 0.25 * OR + 0.25 * AST + TO

Points Produced estimator:

PtsProd = 1.45 * 2Made + 2.2 * 3Made + FTMade + 0.6 * OR + 0.6 * AST
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ed

mtamada · Joined: 28 Jan 2005 Posts: 127

Ed Küpfer · Joined: 30 Dec 2004 Posts: 522 Location: Toronto

{Edited by ed}

Here's a cool formula for estimating a team's final winning percentage from the within-season win%, from DennisBoz.

Ed Küpfer · Joined: 30 Dec 2004 Posts: 522 Location: Toronto

Dan Rosenbaum · Posted: Mon May 09, 2005 4:59 pm Post subject:

Hey Ed, I know things are slow around here once in awhile, but it kind of makes us all look bad if you have to argue with yourself. Very Happy

Ed Küpfer · Joined: 30 Dec 2004 Posts: 522 Location: Toronto

A linear weights-style estimator for RTG, based on the four factors. I have no idea what it's good for, but anyway:

Ed Küpfer · Joined: 30 Dec 2004 Posts: 522 Location: Toronto

After fuch mucking around, I finally came up with a logistic within-game win estimator.

mtamada · Joined: 28 Jan 2005 Posts: 127

Fascinating stuff, but is there a typo in the formula? The coefficient on MinutesRemaining is positive, so the larger the number of minutes remaining, the more negative the argument to the exponentiation function, so the smaller the denominator, and the higher the probability of a Home Team Win.

That surely can't be right; a home team with a 10 point lead with 1 minute left should have a near guarantee of victory (I get 85.4% from your formula, assuming that I typed it in correctly). As the MinutesRemaining gets larger, shouldn't we see a decrease, not an increase, in the probability of this home team winning (while still remaining substantially above 50%)? Also 85.4% seems way too low, unless the opponent has Reggie Miller or Isiah Thomas on one of their heroic playoff rampages.

My in-my-head calculations in the first paragraph, as well as the numbers in my spreadsheet (again, assuming that I haven't made any typos) both show an ever-growing probability of victory as MinutesRemaining INCREASES. That makes perfect sense for a team that is behind, but not for a team that is ahead.

Ed Küpfer · Joined: 30 Dec 2004 Posts: 522 Location: Toronto

I'm pretty sure your calculations are correct. The problem is, as you can see, that the logit fit breaks down at the extremes. It's hard for me to tell exactly what's going on here as these areas are respresent by only a few observations. In a previous effort, I also had real problems fitting a logistic curve to the extreme areas in both Points Difference and Time Remaining. All I can say for now is, hang on. I'm still accumulating data. If the fit is still poor, I may have to mix curves somehow. I'll keep everyone posted.
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ed

mtamada · Joined: 28 Jan 2005 Posts: 127

Maybe some pure curve-fitting technique, such as cubic splines is the way to go.

http://mathews.ecs.fullerton.edu/n2003/CubicSplinesMod.html
http://www.zoology.ubc.ca/~schluter/splines.html
Using your formula, I was looking for the combinations at which a team would have a 90% probability of winning. If I typed in the formula correctly, a home team with a 12 point lead always has a better than 90% chance of winning, while a team with a lead of 11 or less never has a 90% probability of winning. The first part might be plausible (but not the way the probability rises with increased MinutesRemaining), but not the second.

A friend of mine once said that he used he following as a rule of thumb: if "m" is the number of minutes remaining, then a team with a lead of 2m+7 points is practically guaranteed to win the game ("game in the refrigerator" in Chick Hearn-speak). I don't know if his rule of thumb is a good one or not, but in trying to calibrate it against your formula, I found the patterns that I've pointed out, the ones which don't seem realistic. But if you've got the data and can present, say, a table of "MinutesRemaining" and "Points Ahead" stats and the corresponding observed probabilities of winning, maybe I'll discover that the true probabilities are not what I think they should be.