Why Per-Game Averages Mislead

Two players both average 18 points a game over ten games.

• Player A: 17, 18, 19, 18, 17, 19, 18, 18, 17, 19
• Player B: 4, 32, 9, 28, 6, 30, 8, 27, 11, 25

Identical averages. Completely different players. A is a metronome; B is a coin flip with a good arm. If you only ever see "18.0 PPG," you cannot tell which one you are looking at.

The average is the first question, not the last. Three follow-ups recover most of what it hid:

• The spread. Standard deviation, or just the range of the middle half of games.
• The floor. What does a bad night look like? A 25th-percentile game says more about reliability than the mean.
• The shape. Is it symmetric, or does one huge game drag the average up? A single 40-point outlier moves a ten-game average by two full points.

Medians are useful precisely because outliers do not move them. If the mean is well above the median, a few big games are carrying the number.

Per-game averages also quietly mix two different things: how well a player performs, and whether he plays at all. A player who misses time, or plays limited minutes in blowouts, has games in his average that are really about availability and role, not ability.

This is why per-opportunity rates — per minute, per touch, per plate appearance — are more stable than per-game numbers. They separate the question of how good from the question of how much.