# The "toughest out" study, redux

I never expected the “toughest out” study to be much of anything.

### 7 Responses to The "toughest out" study, redux

1. tangotiger says:

Cool stuff. Can you list the results in a table: out/actual/expected/diff/SD
Assuming about 7000 PA per out-slot, the random diff should be .0057. (SD above is diff/.0057). For the 17th out, you are reporting a diff of .017, meaning 3.0 SD from the mean. It’s possible this is evidence of a tiring pitcher (17th out would mean around the 26th batter, which is right around when pitchers are pulled).
When I looked at it by PA (not out), there was a definite tiring pattern (the OBP goes up, the more batters a pitcher faces). It’s in The Book if you want to reference it.
Anyway, the 17 point difference is more like a 9 point difference after reflecting the tiring aspect, turning the 3 SD into 1.5 SD.
You’ll probably find that after you apply a “tiring/starter” effect, that the differences are random, as you’ve suspected.

2. tangotiger says:

I should have added that if you take the SD of the (adjusted) SD, that you’ll probably get something very close to 1.00 (i.e., random).

3. Pizza Cutter says:

Hopefully this works formatting-wise…
Out Actual Expected Diff
17.00 .3614 .3441 .0173
9.00 .3608 .3484 .0125
12.00 .3439 .3327 .0111
14.00 .3450 .3363 .0087
21.00 .3506 .3425 .0081
10.00 .3555 .3493 .0063
18.00 .3461 .3412 .0049
8.00 .3434 .3391 .0044
11.00 .3441 .3403 .0038
13.00 .3357 .3343 .0013
16.00 .3453 .3440 .0013
20.00 .3408 .3400 .0008
27.00 .3282 .3279 .0003
4.00 .3449 .3449 .0001
23.00 .3416 .3417 -.0001
1.00 .3551 .3556 -.0004
6.00 .3192 .3207 -.0015
15.00 .3364 .3380 -.0016
22.00 .3402 .3429 -.0026
24.00 .3363 .3408 -.0046
2.00 .3554 .3630 -.0076
26.00 .3214 .3304 -.0090
19.00 .3331 .3426 -.0094
7.00 .3166 .3262 -.0097
5.00 .3174 .3291 -.0117
3.00 .3518 .3639 -.0120
25.00 .3071 .3325 -.0254

4. gdog says:

interesting…let’s sort that again
Out Actual Expected Diff
1.00 .3551 .3556 -.0004
2.00 .3554 .3630 -.0076
3.00 .3518 .3639 -.0120
4.00 .3449 .3449 .0001
5.00 .3174 .3291 -.0117
6.00 .3192 .3207 -.0015
7.00 .3166 .3262 -.0097
8.00 .3434 .3391 .0044
9.00 .3608 .3484 .0125
10.00 .3555 .3493 .0063
11.00 .3441 .3403 .0038
12.00 .3439 .3327 .0111
13.00 .3357 .3343 .0013
14.00 .3450 .3363 .0087
15.00 .3364 .3380 -.0016
16.00 .3453 .3440 .0013
17.00 .3614 .3441 .0173
18.00 .3461 .3412 .0049
19.00 .3331 .3426 -.0094
20.00 .3408 .3400 .0008
21.00 .3506 .3425 .0081
22.00 .3402 .3429 -.0026
23.00 .3416 .3417 -.0001
24.00 .3363 .3408 -.0046
25.00 .3071 .3325 -.0254
26.00 .3214 .3304 -.0090
27.00 .3282 .3279 .0003

5. tangotiger says:

If I take the standard deviation of the SD, I get 1.59 which is very significant. If I only do it to the first 18 outs (6 innings, basically the starter), I get an SD of 1.45.
If I stick with the first 18 outs, and adjust the first 7 outs diff upward by 6 OBP points, and the other 11 outs down by 6 OBP points (as a way to handle the tiring pitcher and/or advantage of batter in facing same pitcher multiple times), the SD is 0.95. That is, random.
Trying to do the same with the final 9 outs, and it becomes readily apparent that the easiest out, more than can be explained by chance, is the 25th out, as pizza has pointed out. The reason here is likely that it’s the first out of the 9th inning, and you have a “fresh” pitcher.
Otherwise, all other outs are within the realm of chance.

6. Steve Schramm says:

but, but, but, hang on here. if you’ve eliminated all the home team come from behind wins, does that affect the probabilities on outs 25, 26 & 27 in a statistically significant way?? Aren’t there a bunch of ABs for those outs that just got thrown out of the study? Or is it not enough to matter? Seems like I’m always seeing this on SportsCenter, but then again, it’s not much fun seeing the home team go down 1-2-3 9th (unless it’s your team as visitors, of course).

7. Pizza Cutter says:

A small mis-understanding. I did an earlier version of the study in which I had eliminated all come-from-behind wins. This post addressed that problem (and others) from the initial study.