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Oliver-Adjusted PlusMinus

Rather than using the standard model for plus-minus, I am going to start using one of my own, which I will test on data I get on the homeschool girls team I do stats on.

Currently, the players have their own value, based on (Points Produced - Points 'Allowed') / Possessions Played In, (which I call 'net') based on their Dean Oliver ORTG and DRTG stats.

I don't strictly use the DRTG version points 'allowed,' which is =(1-stop%)*DptsPerScPoss*Dposs.
Dean Oliver admits the weaknesses of his formula, so I average this with the stats on "Defensive points allowed" that the girls' team keeps, based on how many points they were the primary reason for allowing (before converting this number to a per 100 possession number).

This "net" stat is the one I primarily use to evaluate players in practices, but in games I also use the good ol' plus-minus stat. For my purposes, I do (PlusMinus ONcourt/poss played) - (Plusminus Oncourt/poss not played) to give a sort of "teamwork" value. The plusminus stat is prone to have lots of error on its own. Especially in the case of how I measure it, it is expected that there would be a lot of error for players who play significantly low or high minutes. That is to say, those who play closer to 0% and 100% of the minutes than 50% have less samples of EITHER possessions played or possessions not played. Furthermore, plusminus does not account for improvement or decrease in team that have relatively little to do with the player in question.

Knowing the biases of both of these formulas, I thought I might use them in tandem with On-Court offensive efficiency and defensive efficiency (which I actually have for the girls team now). Furthermore, the coefficients used by people like Dan Rosenbaum in statistical plus-minus are good things to use, but using Dean Oliver's ORTG and DRTG as the modifying numbers in a formula are likely to be much more representative of a player's statistical throughput.

So, without further ado, I would like to present my method for finding the Oliver-Adjusted PlusMinus.

(Of note: I have data on players that simple box-scores absolutely do not give, and that would be relatively time-consuming to extract from play-by-play. This is: the players on the court at any given time, and the efficiency of that 5-(wo)man group has offensively and defensively)

All of this data will be extracted on a player-by-player basis from each separate substitution (i.e., each individual 5-man team. duplicates must also be taken care of).

First, we must estimate what Kevin Pelton calls the 'fudge factor' (ff) to get a predicted Offensive efficiency. We first sum all the players' on-court Usage% from the game in question; this is the 'fudge factor'. This sum is now our divisor: we now divide each player's game usage % by the fudge factor, which now gives us a sum Usg% of One. Then each player is assigned a predicted points produced, by multiplying their Usg% by their game ORTG.

For each player, we can get a predicted teammates' points produced simply by summing their teammates' (ORTG*(usg%/ff)*possessions played until next substitution. This gives us PREDICTEDteammatePProd, or, P

Then also for each individual player, we subtract their personal predicted points produced (ORTG*(usg%/ff)*possessions played until next substitution) from the actual amount of points produced in the current lineup, to give us an estimated ACTUAL number of teammates' points produced. This gives us eACTUALteammatePtsProduced or, A

By then doing P/A, we have a coefficient that estimates how a player benefits their team offensively, in effect, an adjustment factor for their teammates' ORTG, which we can call OTC. We can do the same with defensive stats (except usage is stuck at the estimated 20%), to get a coefficient for effect on teammates' DRTG, which we can call DTC.

I foresee some problems that will come about from this, and both of these will likely have to be adjusted from the obvious future stat Oc and Dc, which is how much a player's teammates affected their own ORTG and DRTG.

After bridging this unfortunately difficult gap, we can then combine a player's personal [(Points Produced / Oc) - (Points Allowed / Dc) + (Average Teammates' Points Produced * OTc) - (Average Teammates' Points Allowed * DTc) ]/(Possessions Played in*100) to get an adjusted PlusMinus.

Hopefully I can get there soon...

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