A new look at the TTOP, plus a mystery

I had the bright idea to look at the familiarity vs. fatigue TTOP debate, which has MGL on the familiarity side and Pizza Cutter on the fatigue side, by measuring performance based on the number of pitches the batter had seen previously and the number of pitches that the pitcher had thrown to other players in between the PAs in question.  After all, a fatigue effect on the TTOP shouldn’t be from “fatigue”, but “relative change in fatigue”, and that seemed like a cleaner line of inquiry than just total pitch count.  Not a perfect one, but one that should pick up a signal if it’s there.  Then I realized MGL had already done the first part of that experiment, which I’d somehow completely forgotten even though I’d read that article and the followup around the time they came out.  Oh well.  It never hurts to redo the occasional analysis to make sure conclusions still hold true.

I found a baseline 15 point PA1-PA2 increase as well as another 15 point PA2-PA3 increase.  I didn’t bother looking at PA4+ because the samples were tiny and usage is clearly changing.  In news that should be surprising to absolutely nobody reading this, PAs given to starters are on the decline overall and the number of PA4+ is absolutely imploding lately.

Season	Total PAs	1st TTO	2nd	3rd	4th	5th
2008	116960	42614	40249	30731	3359	7
2009	116963	42628	40186	30736	3406	7
2010	119130	42621	40457	32058	3990	4
2011	119462	42588	40458	32333	4080	3
2012	116637	42506	40336	30741	3050	4
2013	116872	42570	40422	31026	2851	3
2014	117325	42612	40618	31235	2856	4
2015	114797	42658	40245	29580	2314	0
2016	112480	42461	40128	28193	1698	0
2017	110195	42478	39912	26476	1329	0
2018	106051	42146	38797	24057	1051	0

Looking specifically at PA2 based on the number of pitches seen in PA1, I found a more muted effect than MGL did using 2008-2018 data with pitcher-batters and IBB/sac-bunt PAs removed.  My data set consisted of (game,starter,batter,pa1,pa2,pa3) rows where the batter had to face the starter at least twice, the batter wasn’t the pitcher, and any ibb/sac bunt PA in the first three trips disqualified the row (pitch counts do include pitches to non-qualified rows where relevant).  For a first pass, that seemed less reliant on individual batter-pitcher projections than allowing each set of PAs to be biased by crap hitters sac-bunting and good hitters getting IBBd would have been.

Pitches in PA 1	wOBA in PA 2	Expected**	n
1	0.338	0.336	39832
2	0.341	0.335	69761
3	0.336	0.335	79342
4	0.334	0.335	82847
5	0.339	0.337	74786
6	0.347	0.338	51374
7+	0.349	0.337	36713

MGL found a 15 point bonus for seeing 5+ pitches the first time up (on top of the baseline 10 he found), but I only get about an 11 point bonus on 6+ pitches and 3 points of that are from increased batter/worse pitcher quality (“Expected” is just a batter/pitcher quality measure, not an actual 2nd TTO prediction). The SD of each bucket is on the order of .002, so it’s extremely likely that this effect is real, and also likely that it’s legitimately smaller than it was in MGL’s dataset, assuming I’m using a similar enough sampling/exclusion method, which I think I am.  It’s not clear to me that that has to be an actual familiarity effect, because I would naively expect to see more of a monotonic increase throughout the number of pitches seen instead of the J-curve, but the buckets have just enough noise that the J-curve might simply be an artifact anyway, and short PAs are an odd animal in their own right as we’ll see later.

Doing the new part of the analysis, looking at the wOBA difference in PA2-PA1 based on the number of intervening pitches to other batters, I wasn’t sure I was going to find much fatigue evidence early in the game, but as it turns out, the relationship is clear and huge.

intervening pitches	wOBA PA2-PA1	vs base .015 TTOP	n
<=20	-0.021	-0.036	9476
21	-0.005	-0.020	5983
22	-0.005	-0.020	8652
23	0.004	-0.011	11945
24	0.000	-0.015	15683
25	0.004	-0.011	19592
26	0.001	-0.014	23057
27	0.005	-0.010	26504
28	0.009	-0.006	29690
29	0.015	0.000	31453
30	0.021	0.006	32356
31	0.014	-0.001	32250
32	0.020	0.005	30723
33	0.018	0.003	28390
34	0.027	0.012	25745
35	0.028	0.013	22407
36	0.023	0.008	18860
37	0.030	0.015	15429
38	0.025	0.010	12420
39	0.012	-0.003	9558
40	0.045	0.030	7362
41-42	0.032	0.017	9241
43+	0.027	0.012	7879

That’s a monster effect, 2 points of TTOP wOBA per intervening pitch with an unmistakable trend.  Jackpot.  Hareeb’s a genius.  That’s big enough that it should result in actionable game situations all the time.  Let’s look at it in terms of actual 2nd time wOBAs (quality-adjusted).

intervening pitches	PA2 wOBA (adj)
<=20	0.339
21	0.346
22	0.343
23	0.344
24	0.340
25	0.341
26	0.339
27	0.339
28	0.337
29	0.340
30	0.341
31	0.338
32	0.347
33	0.336
34	0.345
35	0.344
36	0.336
37	0.340
38	0.328
39	0.335
40	0.340
41-42	0.338
43+	0.344

Wait what??!?!? Those look almost the same everywhere.  If you look closely, the higher-pitch-count PA2 wOBAs even average out to be a tad (4-5 points) *lower* than the low-pitch-count ones (and the same for PA1-PA3, though that needs a closer look). If I didn’t screw anything up, that can only mean..

intervening pitches	PA1 wOBA (adj)
<=20	0.361
21	0.351
22	0.348
23	0.339
24	0.340
25	0.336
26	0.338
27	0.335
28	0.327
29	0.325
30	0.320
31	0.325
32	0.326
33	0.319
34	0.318
35	0.316
36	0.312
37	0.311
38	0.303
39	0.323
40	0.295
41-42	0.306
43+	0.318

Yup.  The number of intervening pitches TO OTHER BATTERS between somebody’s first and second PA has a monster “effect on” the PA1 wOBA.  I started hand-checking more rows of pitch counts and PA results, you name it.  I couldn’t believe this was possibly real.  I asked one of my friends to verify that for me, and he did, and I mentioned the “effect” to Tango and he also observed the same pattern.  This is actually real.  It also works the same way between PA2 and PA3. I couldn’t keep looking at other TTOP stuff with this staring me in the face, so the rest of this post is going down this rabbit hole showing my path to figuring out what was going on.  If you want to stop here and try to work it out for yourself, or just think about it for awhile before reading on, I thought it was an interesting puzzle.

It’s conventional sabermetric wisdom that the box-score-level outcome of one PA doesn’t impart giant predictive effects, but let’s make sure that still holds up.

Reached base safely in PA1	PA2 wOBA (adj)	Batter quality	Pitcher quality
Yes	0.348	0.338	0.339
No	0.336	0.334	0.336

That’s a 12 point effect, but 7 of it is immediately explained by talent differences, and given the plethora of other factors I didn’t control for, all of which will also skew hitter-friendly like the batter and pitcher quality did, there’s just nothing of any significance here.    Maybe the effect is shorter-term than that?

Reached base safely in PA1	Next batter wOBA (adj)	Next batter quality	Pitcher quality
Yes	0.330	0.337	0.339
No	0.323	0.335	0.336

A 7 point effect where 5 is immediately explained by talent.  Also nothing here.  Maybe there’s some effect on intervening pitch count somehow?

Reached base safely in PA1	Average intervening pitches	intervening wOBA (adj)
Yes	30.58	0.3282
No	30.85	0.3276

Barely, and the intervening batters don’t even hit quite as well as expected given that we know the average pitcher is 3 points worse in the Yes group.  Alrighty then.  There’s a big “effect” from intervening pitch count on PA1 wOBA, but PA1 wOBA has minimal to no effect on intervening pitch count, intervening wOBA, PA2 wOBA, or the very next hitter’s wOBA.  That’s… something.

In another curious note to this effect,

intervening pitches	intervening wOBA (adj)
<=20	0.381
21	0.373
22	0.363
23	0.358
24	0.351
25	0.344
26	0.343
27	0.335
28	0.333
29	0.328
30	0.324
31	0.322
32	0.319
33	0.316
34	0.316
35	0.312
36	0.310
37	0.310
38	0.307
39	0.311
40	0.308
41-42	0.309
43+	0.311

Another monster correlation, but that one has a much simpler explanation: short PAs show better results for hitters

Pitches in PA	wOBA (adj)	n
1	0.401	133230
2	0.383	195614
3	0.317	215141
4	0.293	220169
5	0.313	198238
6	0.328	133841
7	0.347	57396
8+	0.369	37135

Throw a bunch of shorter PAs together and you get the higher aggregate wOBA seen in the table right above this one. It seems like the PA length effect has to be a key.  Maybe there’s a difference in the next batter’s pitch distribution depending on PA1?

Pitches in PA	Fraction of PA after reached base	Fraction of PA  after out	wOBA after reached base	wOBA after out	OBP after reached base	OBP after out
1	0.109	0.089	0.394	0.402	0.362	0.359
2	0.164	0.158	0.375	0.376	0.348	0.343
3	0.183	0.182	0.308	0.303	0.284	0.278
4	0.186	0.191	0.289	0.276	0.299	0.281
5	0.165	0.174	0.311	0.301	0.339	0.323
6	0.112	0.120	0.323	0.32	0.367	0.360
7	0.049	0.052	0.346	0.339	0.393	0.386
8+	0.032	0.034	0.356	0.36	0.401	0.405

Now we’re cooking with gas.  That’s a huge likelihood ratio difference for 1-pitch PAs, and using our PA1 OBP of about .324, we’d expect to see a PA1 OBP of .370 given a 1-pitch PA followup, which is exactly what we get, and the longer PAs are more weighted to previous outs because of the odds ratio favoring outs after we get to 4 pitches.

Next PA pitches	This PA1 OBP	This PA1 wOBA
1	0.370	0.373
2	0.333	0.332
3	0.326	0.325
4	0.319	0.318
5	0.313	0.313
6	0.311	0.313
7	0.314	0.310
8	0.313	0.309

It seems like this should be a big cause of the observed effect. I used the 2nd/6th and 3rd/7th columns from two tables up to create a process that would “play through” the next 8 PAs starting after an out or a successful PA, deciding on the number of pitches and then whether it was an out or not based on the average values.  Then I calculated the expected OBP for PA1 based on the likelihood ratios of each number of total pitches to happen (the same way I got .370 from the odds ratio for a 1-pitch followup PA).

As it turns out, that effect alone can reproduce the shape and a little over half the spread

intervening pitches	PA1 OBP (adj)	model PA1 OBP
<=20	0.366	0.340
21	0.351	0.336
22	0.349	0.329
23	0.339	0.338
24	0.343	0.332
25	0.336	0.328
26	0.335	0.327
27	0.335	0.328
28	0.328	0.328
29	0.325	0.326
30	0.320	0.326
31	0.324	0.323
32	0.324	0.323
33	0.318	0.321
34	0.318	0.324
35	0.317	0.323
36	0.312	0.317
37	0.313	0.318
38	0.307	0.320
39	0.320	0.310
40	0.300	0.317
41-42	0.308	0.309
43+	0.320	0.317

and that simple model is deficient at a number of things (correlations longer than 1 pa, different batters, base-out states, etc).  I don’t know everything that’s causing the effect, but I have a good chunk of it, and that reverse pitch count selection bias isn’t something I’ve ever seen mentioned before.  This is also a caution to any kind of analysis involving pitch counts to be very careful to avoid walking into this effect.