EDIT/UPDATE: This formula, like Dean Oliver's is based on some good theory, but as I have examined it more, it is a very poor measure of defensive success. If you need a quick fix, the following explains player defense better than the formula described:

~~Woo! This one took a lot of work, but I think I have all of the theoretical errors taken care of. It's very similar to Dean Oliver's box-scoreformula, but with a few important adjustments:~~

*(Points Allowed On Court / Possessions Played) - (Points Allowed Off Court / Possession Off-Court)***'Points allowed'**are assigned individually based on estimated output per possession in units of 0, 1, 2, and 3, based on Ryan Parker's bachelor essay (Rather than only assigning players Stop values that add a marginal 'DefensivePointsPerScoringPossession' per stop)

**Defensive possessions**used are calculated by the

**marginal**-used-possessions from our estimates; The base rating still lies close to 20%, but is modified only in part by blocks/stls/pf/dr.

**quick definitions for the uninformed:**

**DFG%**= opponent's Field Goals Made / opponent's Field Goal Attempts

**DOR%**= opponents Offensive Rebounds / (opp. off. reb + team def. reb)

**PF**=player personal fouls

**dFTA**= Free Throw Attempts by opponents

**tmBlk**= (team)blocks

**DR**= player defensive rebounds

**dFT%**=opponent's Free Throws Made / opponent's Free Throw Attempts

**dFGA**=opp's field goal attempts

**dFGM**=opp's field goals made

**d3PM**=opp's made three pointers

**Stl**= player steals

**Poss**= team possessions, as estimated here

**Let the math begin!**

**tMin%**(team minute %)= .2 * minutes / game minutes = minutes / team minutes

**PossPI**(possessions played in)= Team Possessions * tMin% * 5

**FMW**(forced-miss-weight) = (dfg%*(1-dor%)) / (dfg%*(1-dor%)+(1-dfg%)*dor%)

**eFFTA**(estimated forced free-throw-attempts) = (.6033*PF^1.2132)

**FFTA**(forced free-throw-attempts) = uafFTA * (dFTA/team's Sum of(uafFTA))

**FMstops**(stops from forced misses)=(Blk + .tMin%*(dFGA-dFGM-tmBLK))*FMW*(1-dOR%) + DR*(1-FMW)

**0pdp**(zero-points-defensive possession)

**1pdp**

**2pdp**

**3pdp**

**dPA**=1pdp + 2*2pdp + 3*3pdp

**dPOSS**=0pdp + 1pdp + 2pdp + 3pdp

**DRTG**=100*(dPA/dPOSS)

**dUSG%**=dPOSS/dPossPI

**Edit:**If you're wondering how effective this really is, check out the ratings applied to NBA players with median minutes or more, and converted the ratings to defensive win shares. Compare this with basketball-reference's 2010-2011 season by Defensive Win Shares.

To be clear, is your FMW (forced-miss-weight) going to the offensive player's counterpart defender; and if and presumably so given your text, what basis did you use for the play by play defensive position assignments with the NBA data?

ReplyDeleteFMW (forced-miss-weight) going to the offensive player's counterpart would be a big change from Oliver's Defensive Rating as is varying the % of defensive possessions faced from an assumed flat 20%.

Have you compared the values in your formula to Evan Zamir's EZPM?

Would you be willing to lead in running correlations for your defensive measure, Defensive Win Shares, EZPM and defensive Adjusted +/-?

Given that your data is in .pdf here I don't immediately know how to get it in Excel without re-doing the data-entry. Is there a way to do that or to get your data in a Excel file?

Crow

Hey Crow.

ReplyDeleteI don't have the excel file handy, but I can later today. FMw is spread throughout the entire team (not counterparts). I've toyed with the idea of counterparts, but have been slowed down by the difficulties in acquiring such data. I would like to, however, find a way to make this data more specific.

My current favorite methodology of regression is to find the least squares of some statistical estimate (like WS/48 or Offensive and Defensive Ratings) in tandem with Net +/-, and regress against Adjusted +/-. This is what I plan to do next.

I've had a hard time keeping up with Zamir's numbers (he posts too many links for my small mind!), although his metrics seem pretty theoretically sound. I was planning on running against unadjusted defensive plus-minus yesterday; however, I don't think Barzilai's APM adjusts for defense? On his site he lists Unadjusted Defensive On/Off/Net...

I'd like to think that a non-linear metric like this tells us some things that statistical +/- metrics can't, but I'm having a hard time believing that.

*by statistical +/- I meant all +/- (On-Court, Net, APM, SPM)

ReplyDeleteThanks for the clarification that your metric is not based on counterpart shot defense at this time.

ReplyDeleteBacn2newbelf's site

http://stats-for-the-nba.appspot.com/

has the only public and current offensive and defensive splits for Adjusted +/-.

An Excel file of your data or your data side by side with defensive Adjusted +/- would be appreciated but when you get to it, no rush.

I now understand what defensive possessions and dUSG% are based on here; and since counterpart shot defense is not currently used, these estimated values are rough guidelines and not as precise as they appear.

ReplyDeleteI'm starting to compare my data to b2b's RAPM for total, offense, and defense, using the 3yr estimates for him and 3-yr averages for ezPM. Hopefully, something interesting comes out of it.

ReplyDelete