Illustration of Simpson's paradox using batting averages for two prominent baseball players
| 1995 | 1996 | Combined | |||||||
|---|---|---|---|---|---|---|---|---|---|
| N hits | N at-bats | Batting average | N hits | N at-bats | Batting average | N hits | N at-bats | Batting average | |
| Derek Jeter | 12 | 48 | 0.250 | 183 | 582 | 0.314 | 195 | 630 | 0.310 |
| David Justice | 104 | 411 | 0.253 | 45 | 140 | 0.321 | 149 | 551 | 0.270 |
Example taken from Reference 11; statistics confirmed through http://www.baseball-reference.com/ (last accessed 25 Jun 2014). The example shows that David Justice had a higher batting average (the ratio of hits over ‘at-bats’) than Derek Jeter in both 1995 and 1996. Yet, when the 2 years are combined, Derek Jeter has the higher batting average. This paradoxical reversal of their batting averages results from the large difference in ‘at-bats’ in the 2 years.