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Friday, June 29, 2007

FIRST TO THIRD 

Today in the Times Mike DiGiovanna looks at the Angels aggressiveness at going from first to third. Nothing you don't already know, really, but the article does report that the Angels have gone first-to-third 57 times this season, which leads the majors.

What it does not tell you is how many times the Angels have tried to do this, and have been thrown out, or how valuable going from first-to-third is.

Let's look at that second part first. Baseball Prospectus has the run expectancy matrix for 2007. You've seen these things, right?
RUNNERS EXP_R_OUTS_0 EXP_R_OUTS_1 EXP_R_OUTS_2
000 0.51922 0.27764 0.10591
003 1.42322 0.95287 0.42472
020 1.15109 0.70592 0.33828
023 2.04520 1.46536 0.57522
100 0.89761 0.52785 0.23109
103 1.83264 1.17478 0.50678
120 1.47430 0.85567 0.45846
123 2.31806 1.58758 0.82238
What this tells us is that an average team, with no one on and zero outs, will score .519 runs per inning. Two outs, make that .106 runs.

Now, this is for an average team, with average hitters and an average park, and against average pitchers. So it doesn't apply to every situation. But, it's a loose framework that can give us a guide.

Let's start by focusing on these situations:
RUNNERS EXP_R_OUTS_0 EXP_R_OUTS_1 EXP_R_OUTS_2
100 0.89761 0.52785 0.23109
120 1.47430 0.85567 0.45846
103 1.83264 1.17478 0.50678
No outs, a guy on first, you expect .898 runs. Make it first and second, you have 1.474 runs, a gain of .576. First and third, you've gained .935. But get thrown out going to third, and you lose .370 runs. Summarizing:
No Outs:
Gain from going 1st to 3rd instead of 1st to 2nd: .358
Loss from being thrown out going 1st to 3rd: -.946
Breakeven Point: 72.5%

One Out:
Gain from going 1st to 3rd instead of 1st to 2nd: .319
Loss from being thrown out going 1st to 3rd: -.944
Breakeven Point: 74.7%

Two Outs:
Gain from going 1st to 3rd instead of 1st to 2nd: .048
Loss from being thrown out going 1st to 3rd: -.458
Breakeven Point: 90.5%
You can see that some conventional wisdom is backed up by the empirical data; making the final out at third base is, obviously, awful, and if you're gonna go, you gotta be sure you can make it.

So far this season, the Angels have hit 121 singles with a runner on first base.

44 have been with no outs. 13 times, the runner has advanced to third base (I'm not including a time a bunt single and error led to such an advance); three of those times, the batter who hit the single ended up advancing to second on the throw. Only once has a runner been thrown out going for third.

So, 10 times 1st-and-3rd: 10 x .358
3 times 2nd-and-3rd: 3 x (2.045-1.474)
1 time 1st with 1 out: 1 x -.946

That's a total of 4.347 runs gained by trying to go 1st-to-3rd with no outs.

There are 43 singles with a guy on first and one out. Just skipping to the summary:

14 times 1st-and-3rd: 15 x .319
1 time 2nd-and-3rd: 1 x (1.456-.856)
1 time 1st with 2 outs: 1 x -.944
1 time 2nd with 2 outs: 1 x (.338-.856)

That's a total of 3.923 runs.

And with two outs, 34 singles:

10 times 1st-and-3rd: 10 x .048

A total of .48 runs.

So far, we've accounted for 39 first-to-thirds, and the team's up 8.75 runs. Let's look at other situations.

I'll spare you the details, but there's an additional 6 with 1st-and-3rd situations (4 with one out [4 x .319], 2 with two outs [2 x .048]) that add up to an additional 1.372 runs, getting us up to 10.122 runs; there are 8 with 1st-and-2nd, for which I'll assume the guy on second always either scores or tries to (2 with no outs [2 x .358, 2 with one out [2 x .319], 4 with two outs [4 x .048], 2 outs at third with one out [2 x -.944], 1 out at third with two outs [1 x -.458]) that add up to -.798 runs, getting us up to 9.324 runs; and 4 with the bases loaded (1 with no outs [1 x .358], 1 with one out [1 x .319], 2 with two outs [2 x .048]) that add up to an additional .773 runs, for a total of 10.097 runs.

So, there you go. Going first to third has added something close to a win to the Angels this year.

Now, there are things I'm missing; I didn't adjust for the quality of hitters on deck, I didn't look at the importance of the situation in the game (as I did for bunts this offseason a couple of times). But I think this is a good general approach. I think we'd have to look at other teams like this to see if the Angels are unique in this regard, but it does appear that aggressive baserunning, if executed efficiently, can really help out a team.

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Comments:
From my untutored observation it seems the Tigers are excellent at going first to third, but very conservative on second to home plays - I'd love to see the data on that.

Oh and RESPECT
 
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