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)


  1. Ming Jack Po:

    I can't say I'm a big fan of baseball, but Moneyball was a kickass book. Having spent some time at a hedge fund, the whole thing was just so brilliant to me....

  2. AustinContrarian:

    On bunting: The run expectancy goes down when you trade a base for an out. But the run expectancy is inflated by the prospect of multi-run innings. It doesn't necessarily follow that the chance for a single run goes down. I.e., your chance for a big inning goes down when you take that first out, but perhaps the chance for a single run goes up. Managers apparently believe that, because that's usually the only time they bunt (other than with pitchers in the NL) -- when they absolutely must have one run. I'd like to know whether that's true.

    BTW, Bill James has convinced me that stealing is usually a bad idea -- how many people consistently get caught less than 26% of the time? -- but Dave Roberts' steal in game 4 of the 2004 ALCS was one of the great moments in baseball, IMHO.

  3. JEH:

    Re: Exercise. I believe the .300 singles hitter has a .4938 run expectancy when leading off, the .258 doubles and singles hitter an expectancy of about .4865. So the singles hitter is a slight favorite.

  4. Steve:

    Damn, Austin Contrarian beat me to it. In the bottom of the 9th inning, tie game, 2 runs (or 11 runs) is no more valuable than one. Bunting may or may not make sense, but you need to look at the increased (or decreased) likelihood of scoring just one run from bunting. This is not that rare a situation. Basically, the closer and later the game, the more you're likely to play for one run. Also, the better the pitcher, the more likely you are to want to bunt.