SkyKing162's Baseblog

A fan of the Yankees, Red Sox, and large sample sizes.


This post is motivated by a quick conversation I had with a dude that's played Strat since 1967. His number one strategy tip was to get guys in scoring position, and then always send them home if given the opportunity. In the few games I've actually played on the computer, that little box pop-up box always presents a condundrum...

"The runner on third has a chance to score. The probabiliy of success is XX%. Try for home?"

I know the break-even point for stealing second. I know not to ever try for third with 0 or 2 outs. But I don't intuitively or mathematically know when it's smart to send guys home. So, I thought I'd figure it out.

First, I borrowed a run expectancy chart from a recent article about stolen bases over at Baseball Prospectus. It's a real good article explaining why stolen bases are overrated.

Bases Outs
0 1 2
empty 0.5219 0.2783 0.1083
1st 0.9116 0.5348 0.2349
2nd 1.1811 0.7125 0.3407
1st 2nd 1.5384 0.9092 0.4430
3rd 1.3734 1.0303 0.3848
1st 3rd 1.8807 1.2043 0.5223
2nd 3rd 2.0356 1.4105 0.5515
1st 2nd 3rd 2.4366 1.5250 0.7932
There are a number of circumstances you might find yourself in, when trying for home. There might be no other runners on base, or there might be other runners on first, on second, or on first and second. There might be no outs, one out, or two outs. I took each of the twelve possibilities, and computed the break-even percentage for sending a runner home. Here's the equation I started with. It basically states that the number of runs you expect to score without trying for home should be the same as the number of runs you'd expect to score if you tried for home.

ExpRuns w/o Attempt = %Succes*(ExpRuns/success) - %Failure*(ExpRuns/failure)

Noting that %Success = 1 - %Failure, you can rearrange to solve for %Success:

%Success = (ExpRuns w/o Attempt + ExpRuns/failure)/(ExpRuns/success + ExpRuns/Failure)

Since all of the run expectancies are in the previous chart (adding one run to the cases where the attempt succeeds, of course), I had Excel compute the break-even percentages, summarized in the chart below:

Bases Outs
0 1 2
3rd 92% 82% 35%
1st 3rd 99% 81% 42%
2nd 3rd 95% 85% 41%
1st 2nd 3rd 97% 84% 55%

* The first thing that I noticed was that the probabilities were very similar when grouped by the number of outs.

* With no outs, you really shouldn't try for home unless you're guaranteed of making it. In Strat, no matter how fast the runner and how poor the outfield throwing arm, there's always a 1/20 chance of getting thrown out. So unless the one run is important (late innings, down by one or tied), let your guy stay on third, and reap the potential benefits of a bigger inning.

* With one out, you better have more than an 80% chance of success. In Strat's magical world of 5% increments, go on 85% or higher. Again, unless you really need the one run and are willing to sacrifice more to get it.

* With two outs, you better damn well get the run before you use up all your outs. Unless the bases are loaded, go for home with only a 40% chance or higher. If the bases or loaded, it's about a 50/50 proposition. The reason for that is that even though you have a very small chance of scoring with two outs, if you do score, you'll probably score a lot.

I guess that in addition to the "don't make the first or last out at third base" mantra, we need to add a "never make the first out at home" baseball proverb. Spread the gospel.

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