So last night the twins lead off the game with 8 hits in row. What is the probability of that happening?
The easiest thing to do is take the batting averages of our first 8 players and multiply them together. I am not about to take the easiest route.....But I will take the second easiest route! If I take the average of the hitters batting averages and Madison Bumgarner's batting average against (.264 before last night, .284 after last night), I am at least acknowledging a hitters chance of success is not independent of who is pitching.
| Name | Real Average | Chance of hit against Bumgarner |
| B. Revere cf | 0.269 | 0.2665 |
| A. Casilla 2b | 0.268 | 0.266 |
| J. Mauer c | 0.22 | 0.242 |
| M. Cuddyer rf | 0.28 | 0.272 |
| D. Young lf | 0.254 | 0.259 |
| D. Valencia 3b | 0.221 | 0.2425 |
| L. Hughes 1b | 0.264 | 0.264 |
| T. Nishioka ss | 0.2 | 0.232 |
So,
The probability the twins lead off the game with 8 hits is 0.000018. On the flip side, the probability Madison Bumgarner throws a no-hitter last night is 0.00055
In other words, before the game started Madison Bumgarner was over 30 times more likely to throw a no hitter than the twins were to start the game with 8 straight hits.
So how rare was this feat. Well, the argument is the exact same as the three birthday problem in the Star trib last year. So if we forget about walks, the average number of real at-bats in game is about 34. That means the 27 at-bats are followed by at least 7 more at-bats. Each team plays 162 games a year so there are roughly 27*162= 4374 at-bats that could be the start of an 8 hit streak. Now, nearly all teams are better at hitting than the twins, but lets just stick with their probability. That means the expected number of 8-hit streaks in one year around the entire major leagues is around:
0.00001795009 * 4374 = 0.08
If all teams were as bad at hitting as the twins and Madison Bumgarner pitched every game for every team we would only expect to see this feat about once every 12.5 years! My guess is that if someone researched this, they would find 8 consecutive hits in game happens more often than every 12 years, but lets not sell the twins short.....That was a pretty cool accomplishment.
Also, I promise the next blog won't be about baseball.
If you were really good, you'd use batting average split stats - i.e. Bumgarner and the Twins' hitters averages against lefties and righties (whichever is applicable).
ReplyDeleteAlthough for guys like Revere and Nishioka, the sample size in the major leagues is probably too small, you'd have to use minor league (or Japanese league) stats, which can be tougher to find.