It’s a grumbling sort of common knowledge these days that Shelby Miller has rotten luck, as far as snatching up the Ws with which he could adorn the back of his baseball card. You can make the facts as pity-inducing as you’d like:
- Shelby Miller only has five "wins."
- Shelby Miller only has five "wins" despite a 2.48 ERA.
- Shelby Miller only has five "wins" despite the 11th-lowest ERA in baseball (starters, qualified for ERA title only).
- Shelby Miller has about four RA9-based wins, and only five "wins."
- Shelby Miller has the second-lowest overall run support, and lowest run support per innings pitched, of all qualified starters in baseball.
- Shelby Miller’s run support is the lowest since detailed statistics for run support have been tracked (early 00s), and manual confirmation indicates no one has received less support than him since 1985 (Jose DeLeon, 1985 Pirates).
- Shelby Miller hasn’t won a game since mid-May. He has eight "losses" and seven no-decisions since then; in that span, he’s shut the opposing team out once, allowed one run four times, allowed two runs three times, and allowed three runs three times.
- Shelby Miller is tied for the league lead in shutouts. His two shutouts are 40 percent of his "win" total.
- Anibal Sanchez has 10 "wins." His ERA is about double that of Shelby Miller’s (4.95).
- Nathan Eovaldi allowed seven hits, three walks, and four runs to the Indians in five innings yesterday, but still got the "win." Shelby Miller has yet to garner a "win" this season in a game where he allows more than two runs.
This uncanny streak got me thinking about whether there was anything particularly anomalous about the rest of the Braves when Miller starts. Specifically, I wondered about whether the Braves were inefficiently stacking their runs during those outings: after all, they’ve scored more than four runs a couple of times since his no-"win" streak started, and there have been a few three-run and two-run efforts as well. Meanwhile, Shelby’s kept the opposition to one run or fewer five times.
This then led to a broader question about whether the Braves have stacked their runs well. It’s no secret that their offense has been dismal this season: the team is scoring the third-fewest runs in baseball, and the team’s hitters have the 6th-worst wRC+ collectively at 93 (i.e., seven percent below league average). On top of that, the pitching has not been much of a revelation either, allowing something like the 9th-most runs per game, mostly due to the bullpen. (The rotation’s been average at run prevention, the bullpen has been horrid.)
To analyze this, I simply took the individual quantities of runs the Braves have scored in their games this season, and the individual quantities of runs they’ve allowed this season, and then drew one number from each group at random. Where the former was greater than the latter, I considered it a win, the opposite resulted in a loss. (Ties were simply not used.) I did this once for every game the Braves had played so far this season (114), and then repeated this experiment 10,000 times. The results were not all that surprising:
Given the team’s run-scoring and run-allowing patterns, we can see that they’ve actually stacked their runs pretty well so far. The most common outcome in the simulation was 49 wins; five discrete win totals over the 114-game period were more likely than the 51 wins the team has currently attained. On top of that, there’s a greater likelihood the team has 49 or fewer wins than 51 or more wins. It should also not come as a surprise that the expected value of this distribution, and the team’s runs-scored/runs-allowed pattern, is 49 wins, which, by the way, is the team’s expected win quantity using Pythagorean Expectation.
But this whole rumination came out of Shelby’s hard luck, so let’s look at his starts more closely. There’s one complication here: teams aren’t allowed to garner no-decisions, but pitchers can and do. Shelby has recorded a decision in 14 of his 23 starts. I have not done the research to determine whether we should expect him to have garnered more or fewer decisions than that, but I’m taking those numbers as a baseline, such that I model his win quantity over 14 decisions.
There are two things that jump out at me here. First, Shelby should probably be expected to have something like 6 wins at this point. He and the offense have combined to deny him a win he’s more likely to get than not. On top of that, there’s a considerably greater likelihood of him having six or more wins, as compared to five or fewer. And yet, that nickel figure is where he sits.
The second thing I found notable is that Miller hasn’t really suffered all that much from the unfortunate run-stacking sequence. Still assuming 14 decisions, 5-9 does not appear that much worse than 6-8, which is the expected value outcome. There’s a miniscule chance that Shelby Miller’s pattern of wins and losses over 14 decisions would reach something like 10-4 or 11-3; the run-stacking would have to be near-perfect for that to be the case. Given the runs given up and scored in his starts, something like 12-2 is pretty much out of the question.
Of course, this brings up a question a bit beyond the scope of this exercise. One is the bullpen: it’s possible for bad relief to rob a pitcher of a well-deserved “win,” and the Braves have bad relief in spades. But in Miller’s nine no-decisions so far, only one was the result of the bullpen blowing a lead. The remainder were cases where the offense either never woke up, or bailed Miller out of a potential loss (this latter outcome also happened rarely). So, even if we consider that Miller should have something like 15 or 17 decisions rather than 14, it’s still fairly unlikely that he’d have either an even record or more than seven wins. The offense, which has been paltry, is largely to blame. Again, “worst run support since 1985” shouldn’t be taken all too lightly.
To summarize: the Braves’ record is a little better than you’d expect given their offensive and pitching performances so far. However, Shelby Miller’s record is a smidge worse: even with his low levels of run support, he’s been a bit unlucky on when he’s been able and unable to come down with a pitcher win.
A couple of minor errata-esque things:
- The Braves have scored 2.73 runs per game in Miller’s starts, compared to 4.00 runs in the remainder of their games. Yep, that’s a disparity – a quick t-test indicates that these differences are significant at the five percent level. In aggregate, that’s 3.75 runs per game, but the offense has continuously scored less for Shelby than when someone else is on the bump.
- There some idea that some teams, or all teams, pitch or hit to the score, which would blow my methodology out of the water by mandating that allowing and scoring runs were “sticky” with one another in some way. However, there’s no evidence of this for the 2015 Braves, nor for Miller’s starts. There’s very little correlation between runs scored and runs allowed. Thinking through this issue, it makes sense that there would not necessarily be correlation: while some games are close contests featuring good starters and dominant bullpen arms and other games are high-scoring shootouts (hi Coors Field), there are also plenty of games where one team blows out another and both teams insert backups and mop-up guys, or something similar. The Braves are 8-15 in games decided by five or more runs this season, which explains a good chunk of why their record is better than their run differential, and why this exercise suggests that they’ve gotten a bit lucky in terms of how they’ve stacked their runs from game to game.
Miller toes the rubber again this Sunday. Hopefully the team scores a bunch for him.