Tag Archives: wOBA

The Quality of Postseason Play

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Summary: I look at averages for hitters and pitchers in the postseason to see how their quality (relative to league average) has changed over time. Unsurprisingly, the gap between postseason and regular season average pitchers is larger than the comparable gap for hitters. The trend over time for pitchers is expected, with a decrease in quality relative to league average from the 1900s to mid-1970s and a slight increase since then that appears to be linked with the increased usage of relievers. The trend for hitters is more confusing, with a dip from 1950 to approximately 1985 and an increase since then. Overall, however, the average quality of both batters and pitchers in the postseason relative to league average is as high as it has been in the expansion era.

Quality of play in the postseason is a common trope of baseball discussion. Between concerns about optics (you want casual fans to watch high quality baseball) and rewarding the best teams, there was a certain amount of handwringing about the number of teams with comparatively poor records into the playoffs (e.g., the Giants and Royals made up the only pair of World Series teams ever without a 90 game winner). This prompted me to wonder about the quality of the average players in the postseason and how that’s changed over time with the many changes in the game—increased competitive balance, different workloads for pitchers, changes in the run environment, etc.

For pitchers, I looked at weighted league-adjusted RA9, which I computed as follows:

  1. For each pitcher in the postseason, compute their Runs Allowed per 9 IP during the regular season. Lower is better, obviously.
  2. Take the average for each pitcher, weighted by the number of batters faced.
  3. Divide that average by the major league average RA9 that year.

You can think of this as the expected result you would get if you chose a random plate appearance during the playoffs and looked at the pitcher’s RA9. Four caveats here:

  1. By using RA9, this is a combined pitching/defense metric that really measures how much the average playoff team is suppressing runs relative to league average.
  2. This doesn’t adjust for park factors, largely because I thought that adjustment was more trouble than it was worth. I’m pretty sure the only effect that this has on aggregate is injecting some noise, though I’m not positive.
  3. I considered using projected RA9 instead of actual RA9, but after playing around with the historical Marcel projections at Baseball Heat Maps, I didn’t see any meaningful differences on aggregate.
  4. For simplicity’s sake, I used major league average rather than individual league average, which could influence some of the numbers in the pre-interleague play era.

When I plot that number over time, I get the following graph. The black dots are observed values, and the ugly blue line is a smoothed rolling estimate (using LOESS). (The gray is the confidence interval for the LOESS estimate.)

Pitching

While I wouldn’t put too much weight in the LOESS estimate (these numbers should be subject to a large bit of randomness), it’s pretty easy to come up with a basic explanation of why the curve looks the way it does. For the first seventy years of that chart, the top pitchers pitched ever smaller shares of the overall innings (except for an uptick in the 1960s), ceding those innings to lesser starters and dropping the average quality. However, starting in the 1970s, relievers have covered larger portions of innings (covered in this FiveThirtyEight piece), and since relievers are typically more effective on a rate basis than starters, that’s a reasonable explanation for the shape of the overall pitcher trend.

What about hitters? I did the same calculations for them, using wOBA instead of RA9 and excluding pitchers from both postseason and league average calculations. (Specifically, I used the static version of wOBA that doesn’t have different coefficients each year. The coefficients used are the ones in The Book.) Again, this includes no park adjustments and rolls the two leagues together for the league average calculation. Here’s what the chart looks like:

Batting

Now, for this one I have no good explanation for the trend curve. There’s a dip in batter quality starting around integration and a recovery starting around 1985. If you have ideas about why this might be happening, leave them in the comments or Twitter. (It’s also quite possible that the LOESS estimate is picking up something that isn’t really there.)

What’s the upshot of all of this? This is an exploratory post, so there’s no major underlying point, but from the plots I’m inclined to conclude that, relative to average, the quality of the typical player (both batter and pitcher) in the playoffs is as good as it’s been since expansion. (To be clear, this mostly refers to the 8 team playoff era of 1995–2011; the last few years aren’t enough to conclude anything about letting two more wild cards in for a single game.) I suspect a reason for that is that, while the looser postseason restrictions have made it easier for flawed teams to make it in the playoffs, they’ve also made it harder for very good teams to be excluded because of bad luck, which lifts the overall quality, a point raised in this recent Baseball Prospectus article by Sam Miller.

Two miscellaneous tidbits from the preparation of this article:

  • I used data from the Lahman database and Fangraphs for this article, which means there may be slight inconsistencies. For instance, there’s apparently an error in Lahman’s accounting for HBP in postseason games the last 5 years or so, which should have a negligible but non-zero effect on the results.
  • I mentioned that the share of batters faced in the postseason by the top pitchers has decreased steadily over time. I assessed that using the Herfindahl-Hirschman index (which I also used in an old post about pitchers’ repertoires.) The chart of the HHI for batters faced is included below. I cut the chart off at 1968 to exclude the divisional play era, which by doubling the number of teams decreased the level of concentration substantially.  HHI
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Is There a Hit-by-Pitch Hangover?

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One of the things I’ve been curious about recently and have on my list of research questions is what the ramifications of a hit-by-pitch are in terms of injury risk—basically, how much of the value of an HBP does the batter give back through the increased injury risk? Today, though, I’m going to look at something vaguely similar but much simpler: Is an HBP associated with an immediate decrease in player productivity?

To assess this, I looked at how players performed in the plate appearance immediately following their HBP in the same game. (This obviously ignores players who are injured by their HBP and leave the game, but I’m looking for something subtler here.) To evaluate performance, I used wOBA, a rate stat that encapsulates a batter’s overall offensive contributions. There are, however, two obvious effects (and probably other more subtle ones) that mean we can’t only look at the post-HBP wOBA and compare it to league average.

The first is that, ceteris paribus, we expect that a pitcher will do worse the more times he sees a given batter (the so-called “trips through the order penalty”). Since in this context we will never include a batter’s first PA of a game because it couldn’t be preceded by an HBP, we need to adjust for this. The second adjustment is simple selection bias—not every batter has the same likelihood of being hit by a pitch, and if the average batter getting hit by a pitch is better or worse than the overall average batter, we will get a biased estimate of the effect of the HBP. If you don’t care about how I adjusted for this, skip to the next bold text.

I attempted to take those factors into account by computing the expected wOBA as follows. Using Retrosheet play-by-play data for 2004–2012 (the last year I had on hand), for each player with at least 350 PA in a season, I computed their wOBA over all PA that were not that player’s first PA in a given game. (I put the 350 PA condition in to make sure my average wasn’t swayed by low PA players with extreme wOBA values.) I then computed the average wOBA of those players weighted by the number of HBP they had and compared it to the actual post-HBP wOBA put up by this sample of players.

To get a sense of how likely or unlikely any discrepancy would be, I also ran a simulation where I chose random HBPs and then pulled a random plate appearance from the hit batter until I had the same number of post-HBP PA as actually occurred in my nine year sample, then computed the post-HBP wOBA in that simulated world. I ran 1000 simulations and so have some sense of how unlikely the observed post-HBP performance is under the null hypothesis that there’s no difference between post-HBP performance and other performance.

To be honest, though, those adjustments don’t make me super confident that I’ve covered all the necessary bases to find a clean effect—the numbers are still a bit wonky, and this is not such a simple thing to examine that I’m confident I’ve gotten all the noise out. For instance, it doesn’t filter out park or pitcher effects (i.e. selection bias due to facing a worse pitcher, or a pitcher having an off day), both of which play a meaningful role in these performance and probably lead to additional selection biases I don’t control for.

With all those caveats out of the way, what do we see? In the data, we have an expected post-HBP wOBA of .3464 and an actual post-HBP wOBA of .3423, for an observed difference of about 4 points of wOBA, which is a small but non-negligible difference. However, it’s in the 24th percentile of outcomes according to the simulation, which indicates there’s a hefty chance that it’s randomness. (Though league average wOBA changed noticeably over the time period I examined, I did some sensitivities and am fairly confident those changes aren’t covering up a real result.)

The main thing (beyond the aforementioned haziness in this analysis) that makes me believe there might be an effect is that the post-walk effect is actually a 2.7 point (i.e. 0.0027) increase in wOBA. If we think that boost is due to pitcher wildness then we would expect the same thing to pop up for the post-HBP plate appearances, and the absence of such an increase suggests that there is a hangover effect. However, to conclude from that that there is a post-HBP swoon seems to be an unreasonably baroque chain of logic given the rest of the evidence, so I’m content to let it go for now.

The main takeaway from all of this is that there’s an observed decrease in expected performance after an HBP, but it’s not particularly large and doesn’t seem likely to have any predictive value. I’m open to the idea that a more sophisticated simulator that includes pitcher and park effects could help detect this effect, but I expect that even if the post-HBP hangover is a real thing, it doesn’t have a major impact.