Player Efficiency Rating (PER) Explained: Formula and Limits

Player Efficiency Rating (PER) is John Hollinger's attempt to sum up a player's box-score production in one number. It adds up the good things a player does, subtracts the bad, puts the result on a per-minute basis, adjusts for team pace and then rescales it so the league average is exactly 15.00 every season. It is still one of the most widely quoted all-in-one stats, which makes it worth understanding, including where it misleads.

What goes into PER

Basketball-Reference publishes the full formula. In plain terms it credits a player for:

• made field goals and made threes;
• made free throws;
• assists, with made field goals discounted by how often the team's baskets are assisted, so a basket is not counted twice;
• offensive and defensive rebounds (offensive boards are worth more, since they are scarcer);
• steals and blocks.

It charges him for missed field goals, missed free throws, turnovers and personal fouls. Most of the weights are expressed in terms of the league's value of a possession (league points divided by league possessions) and the league's defensive-rebound rate, so they update every season instead of being fixed constants.

The three steps

1. Unadjusted PER (uPER). The weighted credits minus the debits, divided by minutes played. This makes PER a rate stat: a bench player and a starter are compared per minute, not by totals.

2. Pace adjustment. Players on fast teams get more chances to rack up box-score stats, so uPER is multiplied by league pace divided by team pace: aPER = uPER × (lgPace / teamPace).

3. Normalise to 15. PER = aPER × (15 / lg_aPER), where lg_aPER is the league-average aPER that season. By construction the league-average player is 15.00, which makes PER comparable across seasons in relative terms.

Worked example of steps 2 and 3

The inputs here are illustrative, chosen to show the arithmetic. Suppose a player's unadjusted PER is 0.536, his team plays at 102 possessions per 48 minutes, the league at 99, and the league-average aPER that season is 0.400.

aPER = 0.536 × 99 / 102 = 0.520. His raw production is scaled down about 3% because his fast team gave him extra possessions.

PER = 0.520 × 15 / 0.400 = 19.5. That is about 30% more production per minute than the league average of 15. Without the pace adjustment he would have been credited with 0.536 × 37.5 = 20.1, so pace alone moved him by 0.6 points of PER.

How to read the scale

Because the average is fixed at 15, PER is easiest to read relative to that line. Hollinger's own rough guide, reproduced on Basketball-Reference's PER page, puts about 20 at borderline All-Star level and around 30 at an MVP-calibre season; a rotation player typically sits in the low-to-mid teens. Basketball-Reference only ranks PER leaders who meet a minutes threshold, because a per-minute stat on a few dozen minutes is mostly noise.

Where PER misleads

• Defense is barely there. Only steals, blocks, defensive rebounds and fouls enter the formula. A player who contests every shot and never gets beaten off the dribble but rarely steals or blocks the ball looks average.
• Volume is rewarded. A made shot earns more than a missed shot costs, so shooting more at below-average efficiency can still raise PER. Read it alongside true shooting percentage and usage rate.
• Role is ignored. Spacing, screening and off-ball movement do not show up in a box score at all.
• Minutes are only the denominator. PER says how productive a player is per minute, not how much total value he added; a 25 PER in 12 minutes a night is not a 25 PER in 36.

How HoopVantage rates players instead

We do not publish PER. The HoopVantage model builds each player's impact rating from box production per 100 possessions together with his team's scoring margin with him on and off the floor (explained in player impact and on/off), then checks the result the only way that matters: whether projected game margins beat simpler baselines in a walk-forward backtest. PER remains a useful quick summary of box-score production; just do not mistake it for a complete measure of value.