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Introducing The Holy Grail II: Offense & Defense (featuring UNC v. UNLV)

Accurate +/- data thanks to Adrian Atkinson (@freeportkid on twitter), editor of the Tar Heel Tip-off.

In this year's College Basketball Prospectus, I introduced "The Holy Grail" - a very simple formula for estimating true player offensive impact per possession based on Offensive Rating and Possessions Used. Not only does this describe player production (R^2 value of .65 against "true" player production), but it only requires a couple of inputs.

Unfortunately, this does not give us the whole picture: no defense, and no admission that "intangibles" could be in effect that are described by traditional plus-minus. This is especially useful when trying to analyze one game: the more causal/correlative statistics we have to offset any issues of sample size, the better**. Enter my new NCAA stat, which we will simply call "Efficiency Impact."

By using statistics to predict "true" player production, we can estimate a player's overall impact (offense + defense) rather than just offense. For an idea of the depth of this formula, these are the main parts of its tabulation:

  • Offensive Rating & Possessions Used
  • Defensive Rebound Percentage
  • Steal Percentage (Steals/Opponent Poss)
  • Block Percentage (Blocks / Opponent 2FGA)
  • Assist Rate (Assists / Team FGM)
  • Offensive & Defensive Efficiencies, both On & Off-Court
    and more...

READER'S NOTE: I have adjusted the +/- to be taken into account based on the number of possessions played; for NBA players, I estimated the amount of "noise" (inaccuracy) introduced based on low sample size, and adjusted accordingly. The same methodology is used here.

Here are the main inputs from the UNC in the UNLV game:
(In the "adjusted" categories, positive is always good, negative is always bad).

MIN%AST%STL%BLK%DR%POS%ORTGadj offense (on)adj defense(on)adj offense(off)adj defense(off)
Hairston. P.J.
McAdoo, James M.
Bullock, Reggie47.510.
Hubert, Desmond2.
Watts, Justin5.
Strickland, Dexter72.513.
Marshall, Kendall77.542.
Henson, John*
Zeller, Tyler*
Barnes, Harrison*

And here are the results:

Statistical +/- per 100Adj. +/- per 100Efficiency Impact (per 100)Efficiency Impact (Game)
Hairston. P.J.18.812.265.132.09
McAdoo, James M.12.402.233.912.05
Bullock, Reggie-0.581.450.920.51
Hubert, Desmond31.050.185.670.17
Watts, Justin3.98-0.200.510.03
Strickland, Dexter2.00-1.73-1.45-1.23
Marshall, Kendall0.33-1.84-1.87-1.69
Henson, John*-7.06-0.89-2.38-2.22
Zeller, Tyler*-8.64-2.24-3.73-2.61
Barnes, Harrison*-3.84-3.36-3.90-3.41

Hairston's insanely high offensive rating (204.9) on nearly 20% of UNC's possessions during his minutes, in addition to UNC's overall improvement in efficiency leads to Hairston leading the Heels for the game. The big 3 boys*, on the other hand, didn't even break 90 in terms of ORTG, and played for much of the game.

Desmond Hubert only really played in one possession, but grabbed an offensive board and made a free throw, thus the high usage/high ORTG and impact per 100.

I will continue posting these, especially for Carolina games as Adrian's +/- data is more reliable than StatSheet's, but I am willing to analyze more games.

* - I don't think anyone calls them that, but I just did.
** - In this prediction formula, I have largely canceled out statistics that covariate heavily, leading to coefficients that have very low p-values. Each of these in tandem lead to a rating that is well-adjusted (for example, I have found time and time again that Offensive Rating overrates players' shooting efficiency, so this formula inserts a negative term against True Shooting Percentage). Using plus-minus data is similar: why should we trust a player's box-score rating if their team did considerably worse while they were on the floor?

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