The cost of an absence
The with-and-without-you number gets quoted constantly. Here is the error bar that comes with it.
July 29, 2026 · 5 min read · 2025-26 regular season
The team is 8.4 points per game better with him on the floor. You have read that sentence, or something close to it, a hundred times. It is the standard way to put a number on what a player is worth: compare the team's scoring margin in the games he played against the games he missed.
The arithmetic is fine. The problem is that nobody ever quotes the error bar, and once you compute it the sentence mostly stops meaning anything. For all 204 qualified rotation players in 2025-26, here is what that comparison actually supports.
13.2%
Impacts distinguishable from zero
27 of 204 players
16.4
Median 95 percent interval width, points
wider than the effect being measured
14
Median games missed
about 55 would be needed
Every qualified rotation player, 2025-26
Why the intervals are so wide
Basketball scores are extremely noisy game to game. The typical team's scoring margin has a standard deviation of about 14.6 points per game — blowouts in both directions, buzzer-beaters, a bad shooting night from the opponent. Against that backdrop you are trying to detect an effect of a few points, using a sample of however many games a player happened to miss.
The median player in this set missed 14 games. Averaging 14 noisy numbers leaves a standard error of roughly four points on its own, and the difference of two averages compounds it. Work backwards from the typical effect size and a player would need to miss on the order of 55 games — three-quarters of a season — before a genuine three-to-four point impact would reliably clear statistical significance.
That is the trap. The players whose absence you most want to measure are the ones who play almost every night, and playing almost every night is precisely what makes the measurement impossible.
The estimates that do clear the bar are the wrong ones
Look at who ends up at the top of the leaderboard when you sort by raw estimate:
- Naji Marshall — +14.4 points, interval [+4.0, +24.9], from 5 games missed
- Kyle Kuzma — +14.3 points, interval [+5.2, +23.5], from 12 games missed
- Brandon Miller — +13.6 points, interval [+5.6, +21.6], from 17 games missed
- Kevin Huerter — +12.8 points, interval [+1.2, +24.4], from 5 games missed
- Ajay Mitchell — +11.4 points, interval [+4.5, +18.3], from 23 games missed
These are not the five most valuable players in the league, and the list is not even mostly stars. It is a list of players whose teams happened to play badly during a short absence. Brandon Ingram's interval spans 45 points, which is another way of saying the honest estimate is “somewhere between substantially harmful and substantially helpful.”
Sorting by a noisy estimate systematically surfaces the noisiest cases. It is the same failure as a three-point percentage leaderboard with no volume floor, which is the subject of a companion post.
What to do instead
Do not throw the metric away — report it honestly. Three things make it usable:
- Always show the interval. A point estimate with no width invites exactly the overreading this post is about.
- Gate on the absence sample, not the games played. A player who missed four games has no measurable impact no matter how many games he played.
- Prefer on-court data when it exists. Comparing possessions with a player on the floor against possessions without him uses stints rather than whole games, which buys far more sample from the same season.
Whole-game comparisons also confound aggressively. Players miss games for reasons correlated with the schedule and with their teammates: injuries cluster, rest days land on back-to-backs against good opponents, and a star's absence often coincides with other absences. None of that is adjusted for here, and it all pushes in unknown directions.
Method and limitations
2025-26 regular season · figures as of July 29, 2026
Data. 2025-26regular season only, from team game logs and per-game player box scores. Playoff games are excluded: they add higher-variance games and would count “did not play because the team was eliminated” as an absence.
Definition. Impact is the team's mean scoring margin in games where the player recorded playing time, minus its mean margin in games where he did not. Absence windows are bounded by the player's first and last appearance for that team, so a mid-season trade does not register as dozens of missed games. Intervals use the Welch standard error for a difference of independent means, at 1.96 standard errors.
Qualification. At least 20 games played, at least 20 minutes per game, and at least 5 games missed, leaving 204 players. The five-game floor is already generous; as the post argues, five games supports almost no inference.
What this does not show. This is a descriptive comparison, not a causal estimate of player value, and it is confounded by everything that travels with absence: opponent strength, rest, and simultaneous teammate injuries. The significance test treats the two sets of games as independent samples from stable distributions, which is not quite true across a season in which teams change. Margin is also not the same as wins. Nothing here is adjusted for the quality of the replacement player, so an “impact” partly measures the gap to whoever took the minutes rather than the player in isolation.