| Sidebar: Now you may be thinking. "Oh, yeah? Well,
I've read a lot of other estimates and they are different from yours. How do I know
yours is right?
Two reasons:
Reason 1: Arithmetic
Simple enough. I calculated a spreadsheet with the likelihood of
every hit streak from zero to 139, and then balanced. I didn't round
anything. Everything double-checked. The number of streaks adds up to
the right number of strings for every number. (Counting every 56 game
streak as two 55s , three 54's, etc, it produces the right number of
strings of each length.) Everything adds back as it should. Everything that should balance to 100% or
reconcile to zero, does do so. I'm pretty sure this is on the money.
Reason 2: Some researchers actually played these million seasons! And they got the results I
predicted.
Two authors, Bob Brown and Peter Goodrich, writing in the Baseball
Research Journal number 32 in the Spring of 2004, used a computer
simulation to run a million seasons
very similar to DiMaggio's 1941 season. They used 139 games each year,
precisely matching DiMaggio's 1941 total, but their simulation differed from the 1941 performance
level
by having
DiMaggio hit in 81.7% of the games rather than 81.1%. (They used a
composite of DiMaggio's achievements in a five year period to formulate
their simulation number of .817, and then they used exactly 817
chances out of 1000 to make the simulation simpler.)
They reported the precise results of their first two runs of 50,000
seasons each.
It is a simple matter to plug their exact assumptions into the model. The model's prediction for 50,000 seasons of
139 games in length, with hits in
exactly 81.7% of the games, is shown in the table below, alongside the
two simulation runs of 50,000 seasons reported by Brown and Goodrich.
| |
|
Brown-Goodrich |
Brown-Goodrich |
| |
Prediction |
First Run |
Second Run |
| 31-40 |
1735 |
1724 |
1754 |
| 41-55 |
229 |
232 |
237 |
| 56 or more |
10 |
15 |
8 |
.
|