This is Chris Gauthier’s debut article for Bat Flips and Nerds. He’s a college student and a Mets fan.
If you’re a dedicated sports fan, chances are at one point or another, you’ve heard the term “sophomore slump,” referring to an apparent drop-off that second-year players face in terms of their on-field production.
Many believe it to be true; analysts and play-by-play commentators don’t fail to mention it if a player gets off to a slow start, and even the players themselves seem to acknowledge it when they’ve hit a snag in production.
While reading a textbook on statistics, I was interested to see the author used the idea of the sophomore slump to explain the concept of “regression to the mean.” Here is the exert that I found intriguing and ultimately inspired this article:
Regression to the mean refers to a phenomenon involving successive measurements on a given variable: extreme observations tend to be followed by more central ones….
… Sports fans are familiar with the “rookie of the year, sophomore slump phenomenon… Generally, this “rookie of the year” does not do as well in his second year…
Regression to the mean is a consequence of a particular form of selection bias. When we select the rookie with the best performance, skill and good luck are probably contributing. In his next season, the skill will still be there but, in most cases, the luck will not, so his performance will decline.
*From Practical Statistics for Data Scientists by Peter Bruce and Andrew Bruce
Any reasonable person with a baseline understanding of statistics would agree that this logic makes sense in theory, but does it hold up? I was curious, so I decided to analyze the production of the players who won Rookie of the Year awards from 2010 to 2018.
I first decided to do a simple analysis on some of the most important metrics used to evaluate production in today’s game. For the position players to win the award, I showed change in OPS+ and WAR per 100 PA (WAR from Baseball Reference). I put the players’ Wins Above Replacement in terms of 100 PAs to account for changes in the number of opportunities players got during each season.
In this group of 12 ROTY winners, only 3 improved on their OPS+ from their rookie season, with the same amount of improvements coming in WAR too.
For the pitchers to win the award, I showed change in ERA+ and WAR per 100 BF:
In this group of 6 ROTY winners, 2 improved on their ERA+ from their rookie season, with the same amount of improvements coming in WAR too.
We can also take a look at the average profile of these ROTY winners, both in their freshman and sophomore campaigns. For the hitters, I calculated the average triple slash-line, by season:
| Season | BA | OBP | SLG |
| Rookie Year | .293 | .370 | .538 |
| Sophomore Year | .282 | .368 | .492 |
For the hurlers, I calculated the average ERA, K%, and BB%, by season:
| Season | ERA | K% | BB% |
| Rookie Year | 2.66 | 24.0% | 8.2% |
| Sophomore Year | 2.85 | 23.9% | 6.8% |
There is a lot to unpack here.
First and foremost, these are simply averages, and averages can certainly be flawed when you introduce outliers. Within this pool of players, two in particular saw drastic changes in their performance from their first year to their second.
One was Craig Kimbrel, who, after making both the Cy Young ballot and Most Valuable Player ballot as a rookie reliever, preceded to throw 62.2 innings and give up only seven runs. You can tell he gets stingy with his run prevention when the rules of grammar force me to put the number of earned runs he gave up in word-form. His ERA+ in his second year: 399. That almost seems fake, doesn’t it?
The other outlier was Wil Myers, who unfortunately became an outlier in the negative sense. After winning the Rookie of the Year award, Wil Myers proceeded to put up a -0.9 WAR over 361 plate appearances his sophomore year. Yikes.
The point I’m making is that there can be extreme cases on both ends of the production spectrum that can affect these averages. Now, that isn’t to say that these profiles hold no value, as they seem to hold up the sophomore slump theory.
The main thing I take away from these average profiles is that statistics that players have better control over tend to stay more consistent. Out of the three proportions in the classic triple slash, the one that hitters have the greatest control over is On Base Percentage. This metric shows less variation because it includes walks, which are absent from the other two stats. A player’s ability to draw four balls, despite being viewed as a result of luck in past seasons, is understood now to be a feat of skill, one that remains more consistent than hits. Now, to dive down the rabbit hole that is the variation that comes into play when players record hits (and therefore, total bases) would be a hasty decision, so we will leave that conversation for another day.
On the opposite side of the battery, pitchers see virtually no change in their K%, what many analytics-nerds believe to be one of the most important pitching metrics out there (and isn’t that what we are?). On the flip side of that, this sample of pitchers actually improved on their BB%. And lastly, these pitchers saw an increase of .2 runs in their collective ERA.
Intuitively, these changes make sense; of the three metrics we analyze, the two that don’t bring in a pitcher’s defense into play are the ones that suggest no sort of regression in skill that “sophomore slump” might imply, and that is the point of this whole phenomenon. The reason these players make it to the peak of their rookie class is partially due to good luck that the other players might not have been so lucky to experience. The thing about luck is it isn’t specific to any one person, and in due time that luck runs out, hence the general drop in production. This isn’t to say that skill can be ignored, as many of the players in this pool are some of the game’s best to this day. It is to say, however, that it is better to be lucky and good than just plain good.