Cracking the Code: How to Calculate Hollinger's PER Without All the Mess

John Hollinger's Player Efficiency Rating (PER) is a one-number measure of a player's per-minute productivity, and it may be one of the best basketball stats out there.

The PER is computed using a detailed, complex formula that, in essence, adds for positive stats such as rebounds, assists, and steals, and subtracts for negative stats such as shots missed or turnovers.

But the formula is too complicated. I like recreating stats by myself (as if I made it), but I could never come around to PER—who would want to go through that formula?

I decided to calculate PER—just for once—and find an easier way to compute it, using only linear weights (or multiplying a player's stats by different weights and adding them up).

Naturally, it took me three times before I finally got down the correct formula in Excel.

(My "player" was the league average player's stats prorated to 82 games, his "team's" stats were the average of all 30 teams last year, and the "league" stats were last year's league stats.)

I found the weight of a stat by adding one of that stat to the player's season totals (but not to the team or league), and finding the affect of that addition on the PER.

I was shocked to find that the PER—before adjusting it to make the league average equal 15.00—is around 0.28, so the effects looked small, although in reality they weren't.

The following table shows these effects of all stats used in the PER formula.

The column showing "Weight" is actual weight multiplied by 1,880 (explained below), and the "Approx." column shows the approximate weight if a field goal made was set to five.

So, what's up with the 1,880? That is the (approximate) adjustment used to set the weighting of the league average of above stats equal to the league average PER. In other words, using those weights to any one player will recreate his PER before you set the league average PER to 15.00.

We're almost there. The next step is the problem of making the league average PER 15.00. We can go through and actually calculate it—but that would be ironic, wouldn't it? We want to make the simplest formula to recreate PER, so we need a shortcut for this step.

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