I suspect many researchers and writers have their own white whale or unicorn; an idea or concept that they are always chasing, regardless of how fruitless or costly that search may ultimately be.
My unicorn is the concept of volatility. I spent a large part of my tenure at Beyond the Box Score exploring the topic for both hitters and pitchers. I even looked at the concept in relation to team performance earlier this year at FanGraphs and other outlets.
Essentially, the idea is to understand whether there are appreciable differences in how players distribute their daily performances over the course of a season. For example, if you have two hitters that are roughly equal in terms of overall skill (i.e. both are 25% better offensively than the league average) is there a difference in terms of how much each is likely to vary from their overall performance on a game to game basis? Is one hitter more consistent day in and day out, while the other mixes in phenomenal performances with countless 0-4 days?
My initial work had some problematic issues (as most initial work does), but thanks to some great feedback from readers and colleagues alike I am ready to roll out the new and improved version of Volatility (VOL), starting with hitters.
The biggest issue with my initial formulation was that it assumed that hitters daily performances (measured by weighted on-base average — wOBA) were normally distributed.
As with team run scoring, it turns out that is not the case. To illustrate, here is the distribution of all daily performances for 2012 (note that I am including stolen bases and caught stealing in the wOBA calculation since I want overall offensive production, not just what hitters do at the plate):
This meant that simply looking at something like the standard deviation of daily performances risked creating a metric that was biased against hitters with a higher seasonal wOBA. I tried a few different things, but I still ended up with metrics that were highly correlated with seasonal wOBA.
Enter colleague and mathematical wizard Matt Swartz. Matt suggested an approach that he used in an older study on team-level run scoring where he transformed a team’s seasonal run scoring average exponentially until the correlation between run scoring and the new variable was close to zero.
Using this technique I managed to come up with a metric that only has a .005 correlation to a player’s seasonal wOBA:
VOL = STD(daily_wOBA)/Yearly_wOBA^.52
VOL = volatility
STD(daily_wOBA) = the standard deviation of a player’s daily batting performance, measured by wOBA
Yearly_wOBA^.52 = a player’s yearly wOBA raised to the .52 power
Armed with this new metric we can now ask a whole slew of questions. I’ll start with some basic descriptive data and get into more inferential analysis in future articles.
Here are the players with the 25 lowest VOL scores for 2012 (min >= 300 plate appearances); VOL- is simply VOL indexed so that league average is 100 (not park adjusted):
|Name||Plate Appearances||Yearly wOBA*||VOL||VOL-|
|Alejandro De Aza||585||0.327||0.411||82|
The least volatile player in 2012 was Derek Jeter. This shouldn’t be surprising, since it turns out that Jeter is the least volatile player since 1974 for hitters with at least ten seasons with >= 300 plate appearances in those seasons. Over 17 seasons, Jeter posted an average .397 VOL, four points better than Brett Butler (.401 – 14 seasons).
For reference, here’s the 30 least volatile hitters since 1974 (min 10 seasons with >= 300 PAs):
|Rank||Name||# Seasons||Ave VOL||Ave wOBA*|
Joey Votto logged a little less than 500 plate appearances, but posted a .409 VOL. That’s incredible when you think about the fact that he had a .448 wOBA for the season. Basically, he was just as consistent as Denard Span, but with a wOBA that was 35% higher than Span’s.
The leader board should illustrate the general point that consistent doesn’t always mean better. For example, Michael Young was 17% more consistent that the league average last year, but he was abysmal at the plate overall. In his case, greater consistency meant that the Rangers didn’t benefit from as many “boom” type games as a less consistent hitter might have provided.
For completeness, here’s the 25 most volatile hitters from 2012:
|NAME||Plate Appearances||Yearly wOBA||VOL||VOL-|
The one bit of inferential analysis I’ve completed was a look at the year to year correlation of VOL. Turns out, this new formulation has a higher correlation year to year than my previous one (.39 vs. .23). Overall, it’s still low — basically, it’s as reliable year to year as batting average — but there is a decent relationship and we do see evidence in the data that, like BABIP, over the course of a career players will sort by generally higher or lower VOL. For example, the correlation between a hitter’s average VOL for years one and two and a hitter’s volatility in year 3 is .42. This is something that definitely needs to be examined further, which brings me to next steps.
Well, there is a lot to do.
First, I want to look at what traits might lead a hitter to be more or less volatile. From my earlier research, and observations from others, my initial guess is high on-base, low strikeout, solid contact hitters will tend to have lower volatility. From the initial leader boards I am seeing these might still be the most significant variables, but of course it needs to be verified empirically.
Second, there is the larger question of whether the volatility of hitters matters all that much. How does it factor in to team construction? There is evidence that more consistent offenses tend to perform better over the course of the year (i.e. beat their pythagorean expectation in terms of wins), but the relationship between individual-level volatility and team-level volatility still needs to be addressed.
I’ll turn to these questions (and I’m sure a few more) in the coming months. Until then, comments and suggestions are welcome.
Oh, and here’s the complete VOL and VOL- leader board for 2012 (min >= 300 PAs) — you may need to refresh the page to see it. And, yes, you are welcome, Eno Sarris:
*I used average constants from 2002-2012 in order to conduct some of the year to year correlational analysis. Also, as I mentioned earlier in the article I included stolen bases and caught stealing.