Standard deviation in sports

Two golfers, one average

Suppose two golfers each play ten rounds on the same course and both average exactly 72. Here are their scores:

Both lists sum to 720. Golfer A's sample standard deviation is 1.41 strokes, golfer B's is 3.94, nearly three times as large. A almost always shoots within a couple of strokes of 72. B posts the best round of either player, 66, and also the worst, 78. The mean alone would call them equal. If you want to check the arithmetic, paste either row into the standard deviation calculator.

Try it: standard deviation calculator

Golfer B's ten rounds are already filled in; replace them with golfer A's, or with your own scores, points or lap times.

Open the full standard deviation calculator for more examples and the sample vs population choice explained.

Which player do you want?

It depends on the score you need. Treat each golfer's rounds as roughly normal with the mean and SD above (a simplification, but a useful one) and ask how often each shoots 68 or better, or 76 or worse. Using a continuity cut-off of 68.5 and 75.5, the normal distribution calculator gives:

If a 72 will comfortably make the cut, A is the safer pick: B blows up to 76 or worse almost one round in five. If the leader is at 68 and your player has to go low on the final day, A will get there less than once in a hundred rounds, while B does it nearly one time in five. Coaches and fantasy players make exactly this trade: the steady option when protecting a position, the high-variance option when chasing.

The symmetry in the table comes from the normal model, which is symmetric by construction. Real golf scores tend to have a longer tail on the bad side, since a disaster hole adds several strokes while a great hole saves one or two, so treat these as illustrations of the idea rather than predictions.

Two basketball scorers

The same pattern in another sport. Two hypothetical guards each average 20 points over eight games:

The SD also changes how you read a single game. Q scoring 31 is (31 − 20) ÷ 8.62 = 1.28 standard deviations above his average. P scoring 23 is (23 − 20) ÷ 2.00 = 1.50 above his. The smaller number of points is the more unusual night, because P so rarely strays from 20. That is a z-score, and it is the fair way to decide whether a player is genuinely hot or just having one of his normal good games.

Comparing consistency across sports with the CV

A standard deviation carries the units of the data: strokes, points, seconds. That makes it useless for comparing a golfer with a sprinter. The coefficient of variation fixes this by dividing the SD by the mean:

CV = s / x̄ × 100%

Here are four hypothetical athletes, each measured over a series of events:

The sprinter's times, 10.05 to 10.21 seconds, have a CV of about half a percent, while even the steadier basketball player varies by 10%. That does not make the sprinter a more disciplined athlete. Scoring in basketball depends on teammates, opponents, minutes played and a count of discrete baskets; a 100 m time is one person against the clock. The CV puts the numbers on a common scale, but the fairer comparison is still within an event: this sprinter against other sprinters, this guard against other guards.

The CV only works for quantities measured from a true zero, such as times, distances and counts. For a plus-minus rating or a score relative to par, where zero is an arbitrary reference point, a percentage of the mean is meaningless. Use the plain SD there.

Team consistency

The same measure works for teams. The SD of a team's points margin across a season says how predictable its games are: a team that wins by 3 to 8 points every night and one that alternates 25-point wins with 15-point losses can have the same average margin. Betting markets and power ratings care about this, because the SD of the margin sets how likely an upset is. If margins are roughly normal, a team whose average margin is +5 with an SD of 12 loses about a third of its games (a margin below zero is 0.42 SD under the mean); the same average with an SD of 4 loses about one game in ten (1.25 SD under).

Cautions before you rank players

Small samples are the main trap. Eight games or ten rounds give a rough SD at best, and a single injury-shortened game or a round in a storm can dominate it. Check for obvious one-off causes before concluding a player is erratic; our post on how outliers affect the standard deviation shows how much one extreme value moves the result.

Opportunity varies too. A player's points per game depend on minutes, which depend on the coach, so part of the SD is about playing time rather than skill. Per-minute or per-possession figures often give a cleaner view of consistency. For the general relationship between an average and its spread, see standard deviation vs mean; for how the SD is used across other fields, see the use cases page.