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Wednesday, July 28, 2010
SABR 101 - Outs
When you make an out, and no one is on base when you make an out, there’s no direct change in base advancement. When you make the first or second out, the runners already on base, presuming they are not putout, also have no direct change in base advancement.
The direct change occurs on the third out, where all the runners on base are cleared off, and on putouts with less than two outs, like DP.
If you have a leadoff single (+1 base), the next two outs still leave that runner on base, but the third out removes it from the bases (-1 base), so that we are back to bases empty (and three outs).
In MLB, there are about 39 batters sent to bat each game, with 4.7 of those scoring a run, and 27 of them being putout, leaving 7.3 of them left on base (an average of 0.81 runners LOB per inning).
Where are these runners located? I wish I would have thought to check myself last night, but, I didn’t. I’ll take a guess that 0.35 were at 1B, 0.25 were at 2B and 0.21 were at 3B. I just made these numbers up for illustration purposes. So, the number of bases lost is 0.35 plus 2 x 0.25 plus 3 x 0.21 equals 1.48 bases. Treating each base as 0.25 runs (i.e., 4 bases = 1 run), and we have 0.37 runs wiped from the bases each inning. With 3 outs per inning, that’s -0.123 runs per out.
Basically, if you take the bases values for the events we’ve talked about:
5.40 HR
4.40 3B
3.22 2B
1.81 1B
1.42 BB
-1.48 innings
And apply that to how often each of those events occurred, and then divide by 4, you are going to get exactly, EXACTLY (*), the number of runs scored.
(*) Almost exactly. In the bottom of the ninth of games won by home teams, you will have runners left on base that are in limbo: not cleared out by the outs, and not reaching home plate. So, the “exactly” provision is true in 3-out innings.
I didn’t really test those numbers against any kind of real-life scenarios. I could just make one up to see what kind of environment I’ve been using. Say in a 9-inning game we have this:
1 HR
0 3B
2 2B
7 1B
3 BB
27 batting outs
We get 5.4 bases from the HR, 6.44 bases from the two doubles, 12.67 bases from the 7 singles, and 4.26 bases from the walks. We remove the 13.32 bases from the 27 outs (9 innings). Adding up all the bases is 15.45. Divide by 4, and we get 3.86 runs scored per game.
In fact though, some singles and doubles lead to outs, we also have outs on steal attempts, etc. It’s not as clean as all this.
But, that’s how bases and outs add up to total runs scored.
