APBRmetrics

I've been working on some talent distribution things, and had a question:

In theory, what is the worst a player could be, as denominated by a plus/minus stat?

In theory, once a player is bad enough, he will effectively be useless on both ends of the court. At that point, no matter how much worse the player gets, he will not have an effect on the game--the game will be 4-on-5 at both ends of the court.

This indicates to me that the talent distribution for plus/minus stats will look like a power law distribution or a low-K Gamma distribution.

But my question would be--what is that lower limit? Any guesses? -20? A player could in theory be worse if he wasn't playing optimally, like shooting a bunch of times and never making it. But what should the theoretical lower limit be?

Would that player be purposely trying to ruin the teams chances of winning, or would he just be extremely terrible at basketball? The latter would include shooting alot even though he's got no chance of making the shot. The former would include running into teammates, throwing the ball in your own hoop etc

By what plus/minus metric ? Just straight up "hockey +/-" or vanilla RAPM, SPM, or BPM ?

Are we assuming hypothetically, or 'in real life'? In real life, if I got on the court in an NBA game, I could only muck up the offense so much because my teammates would never pass me the ball. Hypothetically, if they treated me like I could actually play, I imagine I could actually perform worse.

I'm assuming that all players are trying to win, and are acting approximately optimally. So if you're bad enough, you'll get frozen out and basically the rest, assumed to be average NBA players, would play 4 on 5.

That would effectively mean that, say, 99.5% of the population will have the same effectiveness in an NBA game. I'm trying to get an idea of what that effectiveness level is, in actual points per 100 possessions. The talent pool distribution curve will have an asymptote at that location.

I'm interested in what that actually is, which should be independent of metric.

Some players have approached -10 on offense in moderate samples, though they perhaps shouldn't have shot the ball at all if that were their true talent level. Perhaps about -10 would be a lower bound on offense? Not sure about defense, seems like it could be worse on defense.

Wouldn't a team of such non-players lose by more than 50 pts/game?
It might be 100, if opponents weren't inclined to empty the bench early on. In that case, -20 is conceivable, for a 'project' type player who also lacks confidence when he gets to play.

Mike G wrote:Wouldn't a team of such non-players lose by more than 50 pts/game?
It might be 100, of opponents weren't inclined to empty the bench early on. In that case, -20 is conceivable, for a 'project' type player who also lacks confidence when he gets to play.

No, this is a case of 1 bad player playing with 4 league-average players. How much would such a team lose by to a team with 5 league-average players?

DSMok1 wrote:I've been working on some talent distribution things, and had a question:

In theory, what is the worst a player could be, as denominated by a plus/minus stat?

Mathematically speaking, it's arbitrarily negative. Beyond that you have to pick your constraints and assumptions.

Realistically, it's not going to be worse than making an otherwise average team lose 200 to 0, so -2 points per minute, or -1 point per possession pair.

Nate wrote:

DSMok1 wrote:I've been working on some talent distribution things, and had a question:

In theory, what is the worst a player could be, as denominated by a plus/minus stat?

Mathematically speaking, it's arbitrarily negative. Beyond that you have to pick your constraints and assumptions.

Realistically, it's not going to be worse than making an otherwise average team lose 200 to 0, so -2 points per minute, or -1 point per possession pair.

That seems excessive. I'm tying to identify a realistic number for what a team would do if the fifth player has no NBA skills, but the other four are average NBA players.

Well, 4 on 5 can't happen in the NBA without some pretty heavy stuff, but it has happened in the NCAA. There was a Clemson UNC game in 1998 where that happened in garbage time, and I think it happened this year, but I can't remember the teams.

If you think it's a gamma, can't you pull some random samples and compare them to actual NBA ratings to see what looks close? Then you'll have the distribution and will know the asymptote.

xkonk wrote:If you think it's a gamma, can't you pull some random samples and compare them to actual NBA ratings to see what looks close? Then you'll have the distribution and will know the asymptote.

Trying to figure out how to do this. Right now I'm investigating what kind of curves fit well the right tail of the actual NBA talent pool, with the assumption that this right tail is also that of the general populace.

If you want to model it as 4 on 5, finding a 100 plays on video that were 4 on 5 based on a guy on the ground or not past half court would give you a starting point.

Crow wrote:If you want to model it as 4 on 5, finding a 100 plays on video that were 4 on 5 based on a guy on the ground or not past half court would give you a starting point.

Yeah, but that sounds like a lot of work. I was hoping to just get several good opinions and then sort of take the average!

Worst guy on BPM playing 10-100 minutes was -10. No effort at all is probably 2-3 times worse than worst pro, so I'd guess -20 to -30. A zone should keep opposing offense to 120-130 offensive efficiency. Guys chucking up 3s should be able to put up close to 100 offensive efficiency.