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Astros’ Pythag Luck and the Bullpen

Keeping the bullpen fortified is important in order to avoid under-performance of expected W-L record.

MLB: ALCS-Texas Rangers at Houston Astros
Reliever Bryan Abreu pitches in Game 7 of the ALCS.
Erik Williams-USA TODAY Sports

Looking back at the 2023 regular season, we know that the Astros’ under-performed their win percent by about three wins. The Astros faced substantial headwinds during the 2023 season—most notably injuries on both offense and defense. But, even with those injuries, the Astros’ W/L record was below what is expected for the runs they scored (RS) and the runs their pitching staff allowed (RA).

Why do I said that? The Pythagorean W-L record (or “Pythag” for short) is used to estimate the Win Percent that results from a given RS and RA. According to the traditional Pythag at Baseball-Reference, the Astros’ 90 win season in 2023 fell three wins short of the Pythagorean Record of 93 wins.

What causes a team to under- or over-perform its Pythag? Sabermetrics has pursued this question—almost Captain Ahab-like—without much in the way of satisfactory answers. One theory is that the manager’s in-game decisions are responsible for results better or worse than expected. But that is difficult to prove or disprove. And, I am skeptical of this theory because it’s hard to explain how a manager’s decisions cause a given RS and RA to produce more or less wins. The quality of a team’s bullpen is often considered a leading suspect for under-performing the Pythag record. The relief corps is a major factor in the team’s ability to win 1 or 2 run games. And there is some statistical evidence that high leverage relievers are correlated with under- or over-performing the Pythag Record.

And this may be more than an academic question. The Astros have several relievers who are now free agents, and the team has to decide how much resources to devote to the bullpen. (And I’m using “resources” broadly—not just the player payroll, but also the resources and effort required to identify “diamonds in the rough” and enable the analytics for pitching improvement.) At the margin, the bullpen is critical to a team in a very competitive division. Over the past six years, the Astros have under-performed their pythag by as much as six wins in a season. Given the stronger competition in the AL West, six wins is an enormous difference on the margin. Under- or over-performing the Pythag W-L record can be the deciding factor for playing in the post-season or not.

Bullpen Vs. Pythag “Luck”

In order to explore the relationship between the bullpen and Pythagorean “luck,” I downloaded data from Baseball-Reference’s “Detailed Standings for 2023”, and compared it with various measures of team relief pitcher performance on the Fangraphs leaderboards. My review indicated that general reliever measures like SIERA and WHIP are not significantly correlated with Pythagorean Luck (as represented by teams’ + or - wins over the Pythag). However, the win probability measures for the bullpen are more relevant to the Pythag Luck. Arguably, the win probabllity measures incorporate some degree of luck, themselves, but that’s a discussion for another day. The two most correlated measures: Win Probability Added (WPA) for teams’ bullpens and Shutdowns (SD) for a teams’ relief corps.

SD is a special form of WPA, inasmuch as it measures each time a relief pitcher’s appearance increased WPA by more than 0.6 win probability. As such, it’s not surprising that SD has a stronger relationship to Pythag Luck than WPA.

  • The R-square statistic measures how much variation is “explained” by the test variable. The R-square for SD and WPA (reliever) is 0.336 and 0.226, respectively, meaning that they explain 34% and 23% of the variation in Pythag Luck among MLB teams. Since we know that many factors affect Pythag Luck, this test demonstrates how the bullpen may affect the difference between actual W-L record and the Pythag record.
  • We would expect that the bullpen’s efficacy in close one run games plays a significant role. The teams’ records in 1-run games is notably associated with Pythag Luck (0.39 R-square). Similarly, the Shutdown statistic, in turn, is associated with performance in 1-run games (O.29 R-square).
  • Teams’ records in extra inning games also affects how much their Pythag departs from the actual W-L record. Extra inning records explain 24% of the variation in Pythag Luck. The Shutdown stat has a measurable, though weaker, relationship with extra inning records (R-square 0.177). It’s worth noting that the teams Win% for extra inning games was particularly low during 2023 and 2020—both Pythag under-performance seasons. In 2023 the extra-inning Win Percent record was 0.111 and in 2020, 0.211.

Astros’ Recent Pythag Performance

Over the past six years, the Astros’ under-performed the Pythag in 4 years and posted a record exactly equal to the Pythag in 2 years. The table below summarizes those seasons.

Astros’ Pythagorean Record 2018-2023
  • Although the comparison isn’t perfectly consistent, in general the Bullpen SD and WPA rankings (within MLB) for the Astros is lower in the “under-performance” seasons than for the two seasons equal to the Pythag Record. The 2022 season stands out as a season when the bullpen was particularly important.
  • The line for 1 run games calculates the number of 1 run wins minus 1 run losses. In the two years which were equal to the Pythag, the Astros performed quite well in one run games. The comparison for under-performing seasons is inconclusive, but in general the Astros’ performance in 1 run games appears to be weaker.
  • The Astros’ bullpen was particularly stout in 2022—a season that culminated in a World Series championship. (For example, the 2022 bullpen was No. 1 in ERA and No. 3 in SIERA.) Undoubtedly, the bullpen was at least partly responsible for the 12 net wins in 1 run games.


In my view, the strength of the bullpen is an important determinant of the team’s ability to avoid under-performance of the Pythag. As explained previously, the AL West race is likely to be closely competitive, and any under-performance of the Pythagorean Record could prove costly in the future.

I will admit to apprehension about a strategy that completely foregoes the free agent market for relief pitchers. It may well turn out that the Astros’ financial constraints prevent the team from signing a proven free agent. I previously published an article discussing some of the available free agent relievers; the article provides examples of experienced relief options who possess exceptional “stuff.” Re-signing one or more of their own free agent relievers is another possibile option for the Astros.

Developing and improving minor league relief options is an important facet of the Astros’ bullpen strategy. I can’t disagree with pursuing that approach. But if the Astros steer clear of signing any free agent relievers, that strategy could place excessive pressure and reliance upon the more unpredictable approach to developing “under the radar” options.