Starter rest absorption: the rotation day is flat, and the reference forecast already carries it
Across 52078 MLB team-starts from 2010 to 2021 the starting pitcher's rotation day barely moves the win frequency: 0.5027 on four days rest (n=24333) against 0.5023 on five (n=18222) and 0.4999 on six or more (n=9014), a...
How to read this figure
Each cell reports n_starts first, then the observed win frequency and its game-cluster bootstrap interval, then the mean reference forecast and the gap between them with its own interval. The contrast panel subtracts the four-days bucket on the same resample, so its interval is paired. A gap whose interval contains zero means the recorded closing forecast and the observed frequency agree within noise for that cell.
Published panels
52,078 team-starts across 12 seasons (2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021).
27,983 games with recorded starters and a recorded closing reference forecast.
Honest null
Recorded as a null. Over 52078 team-starts the win frequency is flat across the rotation day; 0 of 3 paired contrasts against a standard four days have an interval that excludes zero, and none of the 4 rest buckets separate from zero against the recorded closing reference forecast. Holding that forecast roughly fixed does not change it: 0 of the 10 reference-forecast band by load cells separate from zero, and across 12 seasons the short-rest residual sits above the long-rest residual in 5 of them rather than holding one sign. The doubleheader nightcap, a second schedule state known before the first pitch, tells the same story: its gap of 0.0345 sits inside a [-0.014, 0.0849] interval on 358 games. The corpus rules out a large effect, not a small one -- the short-rest bucket carries only 509 starts and its frequency interval is 0.0858 wide.
| Rest cell | Starts (n) | Win frequency | 95 percent interval | Mean reference forecast | Observed minus reference | 95 percent interval | Masked |
|---|---|---|---|---|---|---|---|
| 3 or fewer | 509 | 0.4754 | 0.4312 to 0.5170 | 0.4848 | -0.0093 | -0.0528 to 0.0325 | no |
| 4 | 24,333 | 0.5027 | 0.4984 to 0.5069 | 0.5046 | -0.0019 | -0.0061 to 0.0023 | no |
| 5 | 18,222 | 0.5023 | 0.4970 to 0.5077 | 0.5025 | -0.0003 | -0.0054 to 0.0051 | no |
| 6 or more | 9,014 | 0.4999 | 0.4914 to 0.5079 | 0.4917 | 0.0082 | 0.0000 to 0.0163 | no |
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Each row reports the team-start count, observed frequency, its game-cluster interval, the mean recorded reference forecast, and observed minus reference with its interval.
| Rest cell | Starts (n) | Difference vs 4 days | 95 percent interval | Excludes zero | Masked |
|---|---|---|---|---|---|
| 3 or fewer | 509 | -0.0272 | -0.0717 to 0.0159 | no | no |
| 5 | 18,222 | -0.0004 | -0.0090 to 0.0082 | no | no |
| 6 or more | 9,014 | -0.0028 | -0.0141 to 0.0076 | no | no |
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Each difference is paired against the 4-day rest cell on the same bootstrap resample.
| Rest cell | Starts (n) | Win frequency | 95 percent interval | Mean reference forecast | Observed minus reference | 95 percent interval | Masked |
|---|---|---|---|---|---|---|---|
| under 0.42 / short rest (4 or fewer) | 4,806 | 0.3656 | 0.3526 to 0.3792 | 0.3697 | -0.0041 | -0.0171 to 0.0095 | no |
| under 0.42 / long rest (5 or more) | 5,879 | 0.3676 | 0.3550 to 0.3801 | 0.3677 | -0.0001 | -0.0126 to 0.0121 | no |
| 0.42 to 0.48 / short rest (4 or fewer) | 4,902 | 0.4425 | 0.4285 to 0.4560 | 0.4507 | -0.0082 | -0.0220 to 0.0055 | no |
| 0.42 to 0.48 / long rest (5 or more) | 5,581 | 0.4505 | 0.4372 to 0.4643 | 0.4506 | -0.0002 | -0.0135 to 0.0137 | no |
| 0.48 to 0.52 / short rest (4 or fewer) | 4,498 | 0.4951 | 0.4858 to 0.5047 | 0.5000 | -0.0049 | -0.0143 to 0.0047 | no |
| 0.48 to 0.52 / long rest (5 or more) | 4,608 | 0.5054 | 0.4960 to 0.5142 | 0.5000 | 0.0054 | -0.0040 to 0.0142 | no |
| 0.52 to 0.58 / short rest (4 or fewer) | 5,230 | 0.5539 | 0.5399 to 0.5668 | 0.5498 | 0.0042 | -0.0099 to 0.0169 | no |
| 0.52 to 0.58 / long rest (5 or more) | 5,426 | 0.5553 | 0.5416 to 0.5681 | 0.5491 | 0.0062 | -0.0074 to 0.0192 | no |
| over 0.58 / short rest (4 or fewer) | 5,406 | 0.6332 | 0.6211 to 0.6463 | 0.6316 | 0.0016 | -0.0106 to 0.0147 | no |
| over 0.58 / long rest (5 or more) | 5,742 | 0.6341 | 0.6219 to 0.6464 | 0.6320 | 0.0021 | -0.0101 to 0.0145 | no |
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five bands of the devigged closing reference forecast for that team: under 0.42, 0.42 to 0.48, 0.48 to 0.52, 0.52 to 0.58, over 0.58
| Season | Starts (n) | Short rest: n; frequency; interval | Long rest: n; frequency; interval | Gradient | Gradient sign |
|---|---|---|---|---|---|
| 2010 | 4,640 | 2,452; 0.4967; 0.4848 to 0.5082 | 2,188; 0.5078; 0.4953 to 0.5213 | -0.0203 | negative |
| 2011 | 4,659 | 2,372; 0.4933; 0.4807 to 0.5059 | 2,287; 0.5063; 0.4931 to 0.5194 | -0.0195 | negative |
| 2012 | 4,648 | 2,319; 0.5084; 0.4959 to 0.5202 | 2,329; 0.4968; 0.4852 to 0.5093 | 0.0085 | positive |
| 2013 | 4,636 | 2,401; 0.5065; 0.4940 to 0.5186 | 2,235; 0.4953; 0.4821 to 0.5080 | 0.0031 | positive |
| 2014 | 4,612 | 2,291; 0.4998; 0.4867 to 0.5126 | 2,321; 0.5037; 0.4911 to 0.5165 | -0.0111 | negative |
| 2015 | 4,612 | 2,306; 0.5017; 0.4889 to 0.5143 | 2,306; 0.5013; 0.4886 to 0.5140 | -0.0081 | negative |
| 2016 | 4,591 | 2,336; 0.5077; 0.4957 to 0.5207 | 2,255; 0.4918; 0.4782 to 0.5041 | 0.0138 | positive |
| 2017 | 4,590 | 2,220; 0.5063; 0.4920 to 0.5202 | 2,370; 0.4962; 0.4831 to 0.5095 | 0.0112 | positive |
| 2018 | 4,572 | 1,896; 0.5021; 0.4860 to 0.5177 | 2,676; 0.5026; 0.4918 to 0.5141 | -0.0135 | negative |
| 2019 | 4,537 | 1,973; 0.5084; 0.4930 to 0.5241 | 2,564; 0.4984; 0.4866 to 0.5102 | 0.0101 | positive |
| 2020 | 1,459 | 675; 0.4963; 0.4700 to 0.5246 | 784; 0.5064; 0.4825 to 0.5298 | -0.0140 | negative |
| 2021 | 4,522 | 1,601; 0.4922; 0.4734 to 0.5115 | 2,921; 0.5118; 0.5015 to 0.5221 | -0.0219 | negative |
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The gradient is short rest minus long rest within each published season.
| Schedule slot | Games (n) | Home win frequency | 95 percent interval | Mean reference forecast | Observed minus reference | 95 percent interval | Masked |
|---|---|---|---|---|---|---|---|
| first game | 27,625 | 0.5361 | 0.5304 to 0.5417 | 0.5352 | 0.0009 | -0.0047 to 0.0062 | no |
| second game of a doubleheader | 358 | 0.5642 | 0.5142 to 0.6158 | 0.5297 | 0.0345 | -0.0140 to 0.0849 | no |
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game_seq as recorded in the source schedule: 1 for a single game or the opener, 2 for the nightcap. The unit in this panel is one game and the outcome is a home win, so n_starts counts games.
Checks
- Label cross-check: home_runs and away_runs in data/domains/mlb/games.parquet (27,983 games).
- Label agreement: 1.0000.
- Tied finals: 0.
- Starts dropped for missing starter: 118.
- Starts dropped for no prior start: 3,770.
- Maximum observed rest: 164 days.
What it means
A starting pitcher's rotation day, on its own, does not separate winners from losers in this corpus. Four days rest, five days and six or more all win close to half their starts, and the residual against the recorded closing reference forecast stays inside its interval in every bucket. The same holds inside narrow reference-forecast bands, where two teams carry almost the same forecast and differ mainly in rotation day.
Caveats and confounds
Descriptive conditional frequencies, not a forecast and not a causal estimate. The pitcher recorded is the one who actually started, so a rare late scratch would not have been known before the game; rest is confounded with rotation role, injury returns and the all-star break; and the reference forecast comes from a single archived source.