MASTER NOTES: Variation on a Theme of Regression

I was talking recently with a friend of mine about the trade value of CHW relief pitcher Alex Colome. Colome is a hottish topic these days because he might be traded, which would open a slot for a new closer on the South Side of Chicago. (And wouldn’t it be great if the new closer were named Leroy Brown?)

Anyway, as part of the discussion, my friend made the point that Colome might lose the closer job even if he isn’t traded, because of his poor skills metrics—a Dom rate of just 7.0 K/9, a Cmd ratio of 2.50 K/bb, both numbers which are well short of closer-level.

Then my friend also raised the point that Colome has been unusually lucky, with a Strand Rate of almost 80% and an absurdly low Hit Rate of 13% (a .130 BABIP, if you prefer). BaseballHQ analyst Bob Berger made much the same point about Colome’s luck in early July, when his Hit Rate was even lower, at 12%.

My friend then said something I think could be dangerous for fantasy owners. He said that Colome’s Hit Rate was “bound to rise back to his normal 29% or so” (Colome’s pre-2019 Hit Rate was 29%). This was subtly but crucially different from what Bob said, which was, “Colome has been incredibly lucky with his H%, and owners cannot expect that to continue.”

These two opinions might seem the same, but they aren’t. Bob said the expectation was that Colome’s lucky Hit Rate could not continue, which allows for the possibility that his luck might continue, because, well, baseball players have lucky streaks. That is, we might not expect it to continue, but it darn well might. It might even get lower.

That’s a different point than my friend's assertion, which said not only that the increase was bound to happen, but that Colome’s rate would go up to 29%.

This is an improved version of the “Gambler’s Fallacy,” which says, incorrectly, that matters of luck will even out in the short run: that a run of coin-tosses coming up heads make it more likely that the next toss will be a tail. In Colome’s case, a run of 36 games at 13% would inevitably be offset by 36 games at 43%, to even the scales at the established 28% mark.

To be fair, my friend did not say this. His point was that Colome’s true level is 29% and that was what it would be the rest of the season.

Better, but still not right, for two reasons.

First, the season was about 60% over when we were talking, so Colome was not likely to add another 36 appearances to the 36 he had when the comment was made. Algebra says it’ll be more like 24 more appearances.

That leads to the second issue: Even if we believe that a pitcher will revert exactly to "normal," what does “normal” even mean? What is "normal" for a Colome over 24 appearacnes?

The fact that Colome himself has had an unusually fortunate run over his 36 appearances so far surely proves that a highly fortunate run can happen over a short run of games, and therefore that any such run has to be thought of as “normal” for a pitcher with that package of skills, especially over an even shorter run of games to come.

That, in turn, got me wondering about what a “normal” range would look like. So I went to and searched for relief pitchers whose skills have been like Colome’s over the last season and a half:

  • Dominance 7.0-8.0 K/9
  • Command 2.4-2.6 K/bb
  • HR/9 under 1.0
  • and Hit Rate between 27% and 30%

The screen returned two relievers: Sam Dyson of SF and Adam Cimber of CLE.

I used the two pitchers’ b-r game logs from the start of 2018 to calculate their Hit Rates over all their 24-appearance spans. Dyson had 98 such spans, and Cimber had 91.

Both pitchers’ median Hit Rates over the spans were 28 and 27%, which is in line with also right around their career norms (a little over 27% for Dyson, a little under 29% for Cimber). And both pitchers showed similar variation from those medians. Dyson’s lowest Hit Rate over a 24-game span was 19%, about nine points less than “normal,” while his highest Hit Rate was 32%, about four points higher. Cimber’s numbers were a 21% low (six points lower than "normal") and 38% (11 points higher).

What does all of this mean? Well, to me, anyway, it means that from now to the end of the season, Dyson or Cimber—or Colome—could toss up a Hit Rate of anywhere from 19% to 38%, and that hit rate would be normal for him, given the relatively short 24-game span. And outliers are also possible: as noted, Colome posted that 13% mark earlier this year over 36 appearances, so clearly we have to include that outcome within the range of possibilities.

Now, this analysis does not take into account some other variables. Colome probably benefits from the quality of opponents’ hitting in the AL Central, but is probably stung by the park and his team’s defensive chops. Then there are purely random effects like the weather.

The takeaway, though is the same: What has happened is not a guarantee of what will happen. Regression to the mean is going to happen, but only if given a long enough stretch of activity. In the short run, much more is possible, and we have to understand that “normal” means “within a range of outcomes that gets wider as the number of events gets smaller.”

* * *

Speaking of random weirdness...

In Wednesday’s game between BOS and TAM, I saw something I hadn’t seen, well, ever.

You might have read about it. In the bottom of the eighth, with TAM clinging to a 3-2 lead, Rays manager Kevin Cash pulled an unusual switcheroo. He had brought in LHRP Adam Kolarek to open the inning against Jackie Bradley Jr., and BOS manager Alex Cora countered by pinch-hitting with RHH Sam Travis. Kolarek induced Travis to pop up to 1B Ji-Man Choi for the first out.

The next BOS hitter due was RHH Mookie Betts.

Complicating matters, on deck was the red-hot Rafael Devers, a LHH who has a big platoon edge—he’s OPSing 1.016 vs righties and just .742 vs LHP.

This sets up Weird Item #1. The easiest step for Cash would have been to just let the lefty Kolarek pitch to Betts, and then stay in against Devers. For his career, Betts has no platoon split to exploit: a .882 OPS vs RHP, and an .897 vs LHP. And this year, his platoon splits are actually reversed: .937 vs RHP, .683 vs. LHP, with 14 HR vs RHP and only one against LHP, although 25% of his PAs have been against southpaws.

As well, Cash didn’t have a lefty to throw at Devers. His other bullpen lefty, Colin Poche, pitched each of the last two days, and the other lefty, “opener” Ryan Yarbrough, had a 75-pitch, six-inning start on Saturday.

Despite the reverse-platoon disadvantage, and the righty-crushing Devers looming in the on-deck circle, Cash called upon RHP Chaz Roe to face Betts. And to solve the Devers side of the problem, Weird Item #2: After the lefty Kolarek got Travis to open the inning, Cash left him in the game, playing first base! Incumbent Ji-Man Choi left the game.

Now came Weird Item #3: BOS manager Alex Cora came out of the dugout and got very worked up arguing with home plate ump Angel Hernandez (go figure). Nobody knew what was going on, but the speculation was that Cora was arguing that Cash had erred in changing his batting order by putting Kolarek into Choi’s batting-order slot when he took over at first base, when by rule a pitcher joining the game as a position player must replace the DH. The new pitcher Roe should have taken Choi’s slot.

After 20 minutes of inspired beefing by Cora and uninspired “whadda we do now?” looks from Hernandez and the umpiring crew, they decided to put on the headsets and let the MLB replay center decide.

When the dust settled, Roe got Betts on a fly to left then left the game. Kolarek came back from first to pitch to Devers, with Nate Lowe taking over at first.

According to the official box score, the Rays’ moves were kosher. Kolarek had replaced DH Austin Meadows and Roe had indeed taken Choi’s spot.

Nonetheless, Weird Item #4: Cora had announced that the Sox were continuing the game under protest, so whatever happened (including a much-needed save from Emilio Pagan of my Tout-AL team) might yet un-happen, if MLB upholds the protest, say if Cash’s initial lineup changes were incorrect.

Anyway, Kolarek pitched to Devers, who grounded out into Weird Item #5: The putout went from Lowe to ... Kolarek, covering the bag on a right-side grounder. So the final out went from a first baseman who had replaced a pitcher to a pitcher who had replaced the first baseman!

Baseball, man. You gotta love it.


Click here to subscribe

  For more information about the terms used in this article, see our Glossary Primer.