Have you ever watched a game where there was a batter on first or first and second and no outs and the manager calls for the next batter to bunt? Have you ever yelled at the T.V. when it happens something like, "What the hell are you thinking!" There is a fascinating Web page (http://www.users.nac.net/blacksaturn/rhoids2000/baseball/inningStateMatrix.htm) that gives a statistical overview of whether it's a good idea to bunt in certain situations. Here's a breakdown in plain English:

If there is a runner on first base and nobody out, then, according to the matrix set up on this Web page, there is an expectation of scoring 0.98 runs that inning. If you bunt that batter to second and now have one out, you have the exact same expectation (0.98)!

If you take the same scenario but this time making it first and second with no outs, there is an expectation of scoring 1.6 runs that inning. If you bunt the runners over to second and third and now have one out, there is an expectation of scoring 1.5 runs in that inning. So you've lost something there!

The above situations assume the bunt is successful. If in the first scenario, the bunt is unsuccessful and now there is a runner on first still but now with one out, the run expectation drops to 0.60. In the second scenario where the runners stay on first and second and now the bunt fails so there is one out, the run expectation drops back to 0.98 again. Fascinating!

I'm not smart enough to figure out all the writer is saying, but batting average does seem to play a part in the decision making process. According to the writer, the break even point for batting average: "Unless the batter when swinging away can achieve the singles outcome at least 29.2% (batting average = .292) the expected outcome favors bunting."

There is also another statistical nugget listed on the page that lists a success rate of 77% on stolen bases as the break even point on whether you should steal or not. Rickey Henderson was successful nearly 81% of his career so you can assume that his attempts were always helping the team. But the year he set the MLB record with 130 steals (1982 - 21 years ago!), he was thrown out 42 times for a success rate at a little over 75%. According to the statistical guru on the Web page, he didn't help his team that year. He did score 119 runs that season making his run expectation rate at 0.46 which seems to bear that out. Very interesting stuff if you like this sort of thing.

If you really are a mathematician and hunger for more of this stuff, see the following page: http://www.lunasoft.com/baseball/expectedruns.html

The bottom line for a Fan like me is that I'm happy as a cat in a tunafish factory if the stolen base or the bunt is successful and leads to runs and yell like anything at the manager if the opposite happens.