You Too Can Be Billy Beane
As a baseball fan, you may have heard something about Bill James, Billy Beane, and/or Sabremetrics, but were afraid all the math was too difficult. Well, you too can use simple numbers to out-manage most major league skippers. For today's introduction, you only need one simple table of numbers:
| RE 99-02 | 0 | 1 | 2 |
| Empty | 0.555 | 0.297 | 0.117 |
| 1st | 0.953 | 0.573 | 0.251 |
| 2nd | 1.189 | 0.725 | 0.344 |
| 3rd | 1.482 | 0.983 | 0.387 |
| 1st_2nd | 1.573 | 0.971 | 0.466 |
| 1st_3rd | 1.904 | 1.243 | 0.538 |
| 2nd_3rd | 2.052 | 1.467 | 0.634 |
| Loaded | 2.417 | 1.65 | 0.815 |
These are the run expectancy numbers, compiled from data in the 1999-2002 baseball season. Here is how to read the table: With a runner on 2nd (row three) and two outs (column three) a team on average can expect to score .344 runs the rest of that inning.
So, to test your understanding, how much does a leadoff double increase a team's chance of scoring? Well, the base run expectancy at the beginning of an inning is .555 runs. After a leadoff double, you are in the square for man on second, still no outs, which has a run expectancy of 1.189. On average, then, a leadoff double increases the scoring expectations for the inning by 0.634 runs, which is a lot. So here are a few simple sabremetric type conclusions you can reach just from this data:
- Outs are extraordinarily valuable. For example, man on first and third with two outs has a WORSE run expectancy than you have at the beginning of the inning, ie it is worse than nobody on and no outs.
- Bunting almost never makes sense. Assume a runner on first, no outs -- a typical bunting situation. After a succesful bunt, you have runner on second and one out. Notice that this has REDUCED the run expectancy from 0.953 to 0.725. The reason I say "almost" never is that an even worse outcome is a strikeout, which would take you to man on first and one out for a RE of .573. For batters highly likely to strike out or pop up in the infield (think: pitchers) bunting can make sense.
- You can actually calculate what percentage chance of success you need to justify stealing second. Lets again take man on first, no outs. The RE is 0.953. If he steals successfully, the RE goes to 1.189. If he gets thrown out, the RE goes to 0.297 (bases empty, one out). If X is the probability of stealing success, then 1.189X+0.297(1-X)>0.953. X must be about 74% or greater.
Exercise: You have two hitters. Assume they always lead off an inning. One hits .300 with all singles. The other hits .258 but a third of his hits are doubles, the rest singles. Which is more valuable (assuming they walk and strikeout at the same rate)
