Skew Adjustment Model for Adjusted Plus Minus

[bbstats]

As I pondered the greatness that is Nick Collison yesterday, I realized that there is probably a bit of negative impact Collison has that the box score cannot measure: fouling. 'Cause homeboy fouls a LOT.

Player fouls per 48 tends to not show up on plus-minus stuff because such players SIT OUT once they get a lot of fouls.
In fact, if the following is true, then it will INFLATE a player's Net +/-:

-Player X comes into game, fouls 3 times in 5 minutes.
-Puts team into bonus earlier than expected
-Team efficiency margin decreases while player is off the court

So committing and drawing fouls cannot be accurately measured by +/-, so we should adjust it thusly with another nice all-encapsulating measure:

"As Minutes of play increases, team overall rating decreases by ___ while off-court"

So we need to find if each player has a regression equation that can well-explain and predict this (i.e. "Benched-player-minutes-played VS team efficiency margin" or something). I imagine that Collison's Net value is skewed by this slightly: it forces his off-court plus minus to be more negative.


The same can be said in reverse for players who draw a lot of fouls, of course.

[Mike G]

This issue has been brought up before, and I don't recall that it's been adequately addressed.

The same can be said in reverse for players who draw a lot of fouls, of course.

Except that the player drawing fouls is not forced to the bench.

[mystic]

As I pondered the greatness that is Nick Collison yesterday, I realized that there is probably a bit of negative impact Collison has that the box score cannot measure: fouling. 'Cause homeboy fouls a LOT.

Nice idea, but I doubt that your overall assumption is correct. He has 2.4 fouls per game so far this season. Well per 36 minutes it is 4.2, with 2.9 fouls per 36 minutes as average, Collison is fouling at an above average rate. When Collison is on the court the Thunder are committing 20.7 fouls per 48 minutes, without him 19.3. The Thunder's opponents gets in average 1.114 fta per pf, which means we can expect 23 fta per 48 min with Collison and 21.5 without. When Collison is on the court the Thunder having 23, they have 21 with him off the court, so in reality the Thunder are getting less FTA against them than expected when Collison is off the court. Thus, Collison's fouling does not effect his off-court value in a manner that Collison could be "overrated" due to that.

[bbstats]

Except that the player drawing fouls is not forced to the bench.

Ah yes, of course.

fouling at an above average rate

44% higher than average is pretty high.
At any rate, I was just using Collison as an example. Fouling (unlike usage) seems like a pretty simple adjustment to make to APM.

[mystic]

44% higher than average is pretty high.
At any rate, I was just using Collison as an example. Fouling (unlike usage) seems like a pretty simple adjustment to make to APM.

It is pretty high, but your original hypothesis was that his fouling would lead to more FTA during the time he is off the court. So, I understand your idea, but I guess Collisoon is not a good example for that.

[bbstats]

My method of measurement speaks a little differently into the situation I think, mystic.

Comparing dFTA/poss(ON) and dFTA/poss(OFF) is not adequate, because of course FTA/poss(ON) will also be high for players fouling a lot.

My suggestion was to regress:
Player's Minutes Played versus Off-court FTA/poss.

By using a player's minutes played, you are moreso asking "How does playing this player impact the bonus," rather than "What is our net dFTA per possession differential."

Hypothetically speaking, I guess my theory is this:

Team dFTA (on-court) w/ player x= a
Team dFTA (off-court)= a - b

As high Fouls per 40 players get more playing time, b diminishes.

[J.E.]

Isn't this only a problem when there's a large difference in "points per possession" when being in the bonus vs _not_ being in the bonus?
How big is this difference?

[Chicago76]

Isn't this only a problem when there's a large difference in "points per possession" when being in the bonus vs _not_ being in the bonus?

Yup. No idea of what the difference would be though. Another area this may creep in is end of game situations where teams are using a high risk strategy (3 and foul) to claw back into a game. If a disproportionately large amount of floor time for a player is as an extra shooter in mop up time, then APM offense may be artificially low. Similarly, if you're a designted fouler, then the APM defense might be artificially poor.

[bbstats]

if you're a designted fouler, then the APM defense might be artificially poor.

That's an extra-valid point, I believe.
No idea what the full impact would be, Jerry. Just postulating!


Just trying to contextualize what it means to be "off-court"

[EvanZ]

An obvious case: Tim Duncan got a technical whilst on the bench.

[Chicago76]

if you're a designted fouler, then the APM defense might be artificially poor.

That's an extra-valid point, I believe.
No idea what the full impact would be, Jerry. Just postulating!


Just trying to contextualize what it means to be "off-court"

It's easy to see situations where a team is down 6 with a minute left. Both teams get 4 poss.

Trailing team = one made three and three empty poss. 75 pts per 100 poss.
Leading team = 7 of 8 from the line. 175 pts per 100 poss.

Net trailing team +/- = -100 pts/100 poss.

You're a shooting specialist that only gets 30 poss/game and your team was even for the first 26 of those poss. The team is net zero when you are on the court for normal poss. But they're -33.3 pts/100 when you're on the court for all 30 poss. Maybe this balances out if they put you on the court when the team is leading as an extra foul shooter. Maybe this is rare enough that it doesn't have a huge impact. I don't know.

But I could definitely see how it would impact a specialist getting 1200 minutes a year (what this guy would likely get playing a full season at 30 poss/game).

[Crow]

It would be interesting to hear if there's a large difference in "points per possession" when being in the bonus vs not-being in the bonus and how the difference arises / shows up at the 4 Factor level. I would hope somebody with the play by play database and the coding skills will tackle this.

If you had that data, I would think it would be possible, with effort, to go back and assess some level of penalty to players who fouled and helped create a bonus situation (shared with the players who kept fouling) and opponent FT scoring beyond expected normal offensive efficiency.

[bbstats]

Just a quick update here.

I used BBR's Play Index+ and found the following for OKC's lineups (90 poss or more) for the past 3 years.

FTA per 100 (w/ Collison): 27.4
FTA per 100 (w/o Collison): 23.4


So this myth is *busted*, at least for Collison.