Taking averages of basketball stats?

[GHack101]

What is the best way to take an average of a basketball stat? Do different teams have different half-lifes? Different half-life per stat? Is there any work done on what is a more consistent metric then taking an average across all games?

[Nate]

What is the best way to take an average of a basketball stat? Do different teams have different half-lifes? Different half-life per stat? Is there any work done on what is a more consistent metric then taking an average across all games?

It depends on the question you want to answer with the stat and what data you have available: People certainly like to do stats per minute played or possession instead of games when they want to measure player quality. Sometimes people do 'per leverage' stats when they talk about 'clutch factor.' Similarly, there are other kinds of averaging that come up when people start talking 'hot hand.' People definitely talk about performance per salary cap hit.

[GHack101]

What is the best way to take an average of a basketball stat? Do different teams have different half-lifes? Different half-life per stat? Is there any work done on what is a more consistent metric then taking an average across all games?

It depends on the question you want to answer with the stat and what data you have available: People certainly like to do stats per minute played or possession instead of games when they want to measure player quality. Sometimes people do 'per leverage' stats when they talk about 'clutch factor.' Similarly, there are other kinds of averaging that come up when people start talking 'hot hand.' People definitely talk about performance per salary cap hit.

That makes sense. I think what I'm trying to figure out here, is if say I want to measure steals from recent performance over the last 10 games. [g1, g2, g3...g10]. Why is an average of steals over those 10 games, better then say an averaged weighting more recent games more or vice-versa? What if recent steals don't reflect projected performance? Do the answers to these questions change on a per stat basis?

[Nate]

...
That makes sense. I think what I'm trying to figure out here, is if say I want to measure steals from recent performance over the last 10 games. [g1, g2, g3...g10]. Why is an average of steals over those 10 games, better then say an averaged weighting more recent games more or vice-versa? What if recent steals don't reflect projected performance? Do the answers to these questions change on a per stat basis?

Your best bet (though it will probably be a pretty weak prediction) is probably to just average the 10 games.

Supposing you want to optimize the weighting of the prior games, you can collect a bunch of historical data, and do a linear regression to see which of the previous 10 games was the best predictor for the upcoming performance in the past. (I haven't tested, but I expect you'll find that they're all about the same.)

The number of steals per game is pretty small, so there's going to be a relatively large amount of noise identifying single anomalous games with any reasonable confidence is going to be nearly impossible. Things that happen more frequently - like rebounds - are going to give better predictions. Even so the prediction could be awful because it's not controlling for something important. For example the player isn't on the court by himself, and the opposition changes every game. The other team's philosophy regarding pace or 3 pointers could affect a stat like rebounds a lot more than the player's intrinsic skill.

[Statman]

What is the best way to take an average of a basketball stat? Do different teams have different half-lifes? Different half-life per stat? Is there any work done on what is a more consistent metric then taking an average across all games?

It depends on the question you want to answer with the stat and what data you have available: People certainly like to do stats per minute played or possession instead of games when they want to measure player quality. Sometimes people do 'per leverage' stats when they talk about 'clutch factor.' Similarly, there are other kinds of averaging that come up when people start talking 'hot hand.' People definitely talk about performance per salary cap hit.

That makes sense. I think what I'm trying to figure out here, is if say I want to measure steals from recent performance over the last 10 games. [g1, g2, g3...g10]. Why is an average of steals over those 10 games, better then say an averaged weighting more recent games more or vice-versa? What if recent steals don't reflect projected performance? Do the answers to these questions change on a per stat basis?

I would say, if you were trying to do something a little more "predictive" for fantasy bball, weighted per game stat totals is a decent general way to go. you could weight by game # (game 1 is 1, game 62 is 62 - then divide compiled stat totals by compiles weight total). Weight per game minutes as well, so you can calculate weighted per minute stats in case you know for sure a guy will be getting a big minutes uptick beyond the weighted results.

But, in terms of general player ratings, since every game counts the same - per possession is probably the best bet (adjusts for pace).