To best estimate the probability of this event, the following data for Hamilton during each of the past four seasons at the Rangers were retrieved:
| Year | At Bat | Home Run |
| 2008 | 624 | 32 |
| 2009 | 336 | 10 |
| 2010 | 518 | 32 |
| 2011 | 487 | 25 |
| Sum | 1965 | 99 |
Since Hamilton hit 99 home-runs in 1965 at-bats during the past four seasons, let's assume that the probability of hitting a home-run is 99/1965 = 5.038%. On Wednesday night, Hamilton had 5 at-bats, and hit 4 home-runs. The probability of hitting 4 home-runs in a game with 5 at-bats will be the product of the following terms:
- nCr(5,4) to indicate the number of combinations
- (5.038%) ^ 4 to indicate the 4 home-runs
- (1-5.038%) to indicate the 1 non-HR at-bat
To put in perspective, each season is 162 games. During each game across the league, there are 30 teams and 9 players who come to bat. That is 30*162*9 = 43,740 total player-performances in a season, assuming uniformity. Already that number is greater than 32,688. This means that if every player in MLB had the HR-hitting probability as Hamilton, the league should expect to see occurrence like Tuesday night's every season. However, clearly that isn't the case. Four-HR games are more rarer than perfect games or no-hitters. In baseball, only 20-K games and unassisted triple players have been less frequent.
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