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Jose Fernandez and regression to the mean

Miami Marlins fans should not expect a repeat performance of Jose Fernandez's stellar 2013 season, but not because of any "sophomore slump," but rather because no player should be expected to continue that type of performance.

Jonathan Ernst

Over the weekend, I spotted an article by Ryan Gaydos over at Rant Sports regarding Jose Fernandez and the expectations on him heading into the 2014 season. After the spectacular Rookie of the Year season Fernandez put up in 2013, it is natural for fans to expect more of the same or even improvement from such a young player. But Ryan says that those expectations would not be wise.

The best thing to do when dealing with Fernandez in 2014 is to hope that he has solid outings. You cannot expect him to be dominant again. You want him to save his shoulder a bit since he is only going to be 22-years-old by the end of July this year. A solid year is the best thing to expect from the youngster. There is always a chance of the unexpected happening.

This paragraph itself does not say much. Essentially, it says "hey, you never know what might happen to the guy, just hope he stays healthy!" Indeed, health is something the Marlins will continue to monitor as they manage a precious commodity in another meaningless Marlins season. Last year, the Fish held Fernandez's innings down in order to avoid injury, and while it is expected that the team will allow him to go all-out this year, they may cut him short a start or two to avoid the 200-inning mark and maintain a 20-inning increase from last year to this year. Given that the Fish have nothing at stake, this would not be a bad idea.

But the important thing to consider when you consider your expectations for Fernandez is not just health but a simple, ever-present concept: regression to the mean.

Jose Fernandez in 2013 was special. Jose Fernandez going forward may very well be special. Fernandez could be the next Felix Hernandez or Justin Verlander or another top-flight, guaranteed ace of the future. But with only one season down, it is hard to tell whether he really is that guy or whether he is any number of pitchers who have faltered for various reasons over their careers. That is why you have to have reasonable expectations as a fan of the Fish next year.

Felix Hernandez followed a 12-start stretch in 2005 during which he had a 2.67 ERA and 2.85 FIP with three years of a 3.96 ERA. Justin Verlander had two more mediocre 4.00 ERA years after his rookie season until he became the Verlander we all know now. And those were two of the very best pitchers of our most recent era of starters. It is not easy to maintain fantastic success.

And the reason why it is not easy is not just because of an injury or because the league has "figured out" a player. It is more likely that the player was never as good as the first measurement, and regression to the player's true talent or mean was the most expected result. Consider the example on the concept's Wikipedia page:

Consider a simple example: a class of students takes a 100-item true/false test on a subject. Suppose that all students choose randomly on all questions. Then, each student’s score would be a realization of one of a set of independent and identically distributed random variables, with a mean of 50. Naturally, some students will score substantially above 50 and some substantially below 50 just by chance. If one takes only the top scoring 10% of the students and gives them a second test on which they again choose randomly on all items, the mean score would again be expected to be close to 50. Thus the mean of these students would "regress" all the way back to the mean of all students who took the original test. No matter what a student scores on the original test, the best prediction of his score on the second test is 50.


Most realistic situations fall between these two extremes: for example, one might consider exam scores as a combination of skill and luck. In this case, the subset of students scoring above average would be composed of those who were skilled and had not especially bad luck, together with those who were unskilled, but were extremely lucky. On a retest of this subset, the unskilled will be unlikely to repeat their lucky break, while the skilled will have a second chance to have bad luck. Hence, those who did well previously are unlikely to do quite as well in the second test even if the original cannot be replicated.

Fernandez likely did well based on a combination of good fortune and skill. His strikeout rates have a lot to do with what he does with his amazing three-pitch arsenal. But his .240 BABIP implies some favorable bounces and some help from the defense behind him. Like all other pitchers, Fernandez is subject to luck's vacillations, and regression to the mean figures that, like the most talented students taking tests in the above classroom example, even the best pitchers are more likely to do worse following an excellent season.

You can look no further than the examples we displayed last week when we considered Fernandez's expectations. We talked about 15 of the best age-20 pitching seasons since the late 1970's, and we examined those pitchers and saw how well they did in seasons afterward. Each of those players posted age-20 seasons that were worth at least two FanGraphs Wins Above Replacement. Over the next three years, how many of them averaged, on a per season basis, better than their age-20 marks?

Seven of them. Essentially half of the players sampled.

Jose Fernandez could be Felix. He could be Fernando Valenzuela. Or he could just be another cautionary tale of great pitchers. Those 15 pitchers averaged 3.5 wins per year over the next three years as a group. After just one spectacular year, the possibilities lying ahead for Fernandez could still be anything. As we mentioned last week, Marlins fans need to temper their expectations, because a pitcher's career can veer many directions after just one year. The thing we know is that it is very likely that Fernandez is good, a well-above-average contributor going forward. Predicting stardom is no guarantee, and heading into next season, that is the mindset Marlins fans should have.