Statistics
Batting average calculator
Batting average is hits divided by at-bats. Enter both to get the average in box-score form, plus a standard error that shows how much of it could be luck over that many at-bats.
Show the working, step by step
Divide hits by official at-bats. Walks, hit-by-pitches, sacrifices and catcher's interference are not at-bats, so they do not count either way.
AVG = H ÷ AB = 152 ÷ 541 = 0.280961
Round to three decimals and drop the leading zero, the way box scores print it.
AVG = .281
Each at-bat is a hit (1) or not (0), so the average is the mean of those 0s and 1s, and its luck component is a binomial standard error.
SD of one at-bat = √(p(1 − p)) = 0.4495 SE = √(0.281 × 0.719 ÷ 541) = 0.01932
Over 541 at-bats, a true .281 hitter would land anywhere from about .243 to .319 (±1.96 SE) by chance alone.
The formula
AVG = H / AB
H counts singles, doubles, triples and home runs alike. AB is official at-bats: plate appearances minus walks, hit-by-pitches, sacrifice bunts, sacrifice flies and times reaching on catcher's interference. Those events are left out of both the top and the bottom, so they neither help nor hurt the average. Reaching on an error or a fielder's choice is an at-bat without a hit, so it lowers the average.
By convention the result is rounded to three decimals and written without the leading zero: .281, said "two-eighty-one". A perfect 1.000 is the only average that keeps its leading digit.
A worked example
A player finishes the season with 152 hits in 541 at-bats. These are the numbers loaded above.
- AVG = 152 ÷ 541 = 0.280961.
- Rounded to three decimals: .281.
- To reach .300 in the same 541 at-bats, 0.300 × 541 = 162.3 means 163 hits, so 11 more of those outs would have had to be hits.
How much of an average is luck
Each at-bat either produces a hit or doesn't, so a batting average is a proportion. It has a standard error like any other sample statistic:
SE = √( AVG × (1 − AVG) / AB )
For the .281 hitter above, SE = √(0.281 × 0.719 ÷ 541) = 0.0193. A hitter whose true ability is .281 would finish anywhere from about .243 to .319 over 541 at-bats through chance alone. The spread is much wider over short stretches. For a true .300 hitter:
| At-bats | Standard error | Range by chance (±1.96 SE) |
|---|---|---|
| 50 | .065 | .173 to .427 |
| 100 | .046 | .210 to .390 |
| 300 | .026 | .248 to .352 |
| 600 | .019 | .263 to .337 |
That is why a hot April says little: over 50 at-bats a .300 hitter can look like a .180 hitter or a .420 one without anything having changed. The model treats every at-bat as an independent trial with the same chance of a hit. Real at-bats vary by pitcher, park and situation, but the model gives a fair sense of how much noise there is.
Combining averages
To combine two stretches, add the hits and add the at-bats. Don't average the two averages. A .400 month over 20 at-bats (8 hits) and a .250 month over 100 at-bats (25 hits) make 33 hits in 120 at-bats, or .275. The simple mean of .400 and .250 would be .325, which gives the short month far too much say. The weighted average calculator gives the same .275 if you weight each average by its at-bats.
What batting average leaves out
- Walks. A patient hitter who walks often gets no credit. On-base percentage adds walks and hit-by-pitches.
- Power. A home run and a single count the same. Slugging percentage weights hits by total bases.
- Sample size. Over fewer than a few hundred at-bats, most of the difference between two hitters' averages can be chance, as the table shows.
Related calculators
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Mean calculator
A batting average is the mean of 1s and 0s, one per at-bat.
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Binomial distribution
The chance of k hits in n at-bats for a given true average.
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Standard error
How precisely a sample average pins down the true one.
-
Weighted average
Combine averages from seasons with different numbers of at-bats.
Common questions
How do you calculate a batting average?
Divide hits by official at-bats: AVG = H / AB. Round to three decimal places
and drop the leading zero, so 152 hits in 541 at-bats is 0.280961, printed as .281.
Do walks count against a batting average?
No. Walks, hit-by-pitches, sacrifice bunts, sacrifice flies and catcher's interference are plate appearances but not at-bats, so they leave the average unchanged. That is why on-base percentage, which does count walks, is a separate statistic.
What is a good batting average?
In Major League Baseball, .300 over a full season has long been the mark of a very good hitter, and below about .200 is poor. League-wide averages have mostly sat in the .240s and .250s in recent seasons. Youth and amateur averages run higher, so compare within the level you play.
How much of a batting average is luck?
More than it looks. Treating each at-bat as a hit-or-not trial, a true .300 hitter's average has a standard error of about .046 over 100 at-bats and .019 over 600. Over a month, a .300 hitter can easily show .210 or .390 by chance alone. The calculator reports that range for the numbers you enter.
Is a batting average the same as a mean?
Yes. Score each at-bat 1 for a hit and 0 for anything else, and the batting average is the mean of those values. You can paste a game-by-game list of 1s and 0s into the mean calculator and get the same number.