Applying Hitter Volatility Research to Fantasy

Over the years, Bill Petti has done some fascinating research on hitter volatility. He recently updated that work at the new Hardball Times. I strongly recommend taking a look. You can follow Petti on Twitter @BillPetti. Hopefully he’ll now forgive me for shamelessly stealing his work for fantasy purposes.

Before we dive into Petti’s work and how it applies to fantasy baseball, let’s define volatility. In finance, volatility refers to variation in price over a period of time. A stock that sees frequent fluctuation of price is considered to be more volatile than a stock with very little price fluctuation. In fantasy baseball, we can replace price with category production or points. Player A is more volatile than Player B if his day-to-day performance is more varied.

Petti’s research is in day-to-day volatility, which differs from streakiness. As fantasy owners, we know that Jay Bruce is one streaky mofo guy. He’ll put up 20 excellent games followed by 30 atrocious games and he’s been doing it since the day he entered the majors. By Petti’s measure, Bruce is only four percent more volatile than league average over the last three years. That’s (probably) because he’s not measuring these long term fluctuations.

Generally speaking, power hitters are more volatile than contact hitters, with some notable exceptions. Petti’s stat, indexed volatility, is about as predictive year-to-year as batting average or batting average on balls in play, so one year of data has to be heavily regressed towards league average. For more detail, I once again recommend that you read his research linked above.

So how do we use this research to our advantage in fantasy baseball? In roto and points formats, volatility isn’t much of an issue. Hypothetically, if you know a hitter is volatile and he produces a few good games, you can try to sell high. But day-to-day volatility won’t affect your draft price or preseason projection. Generally, you don’t care how the player gets to his final numbers as long as they are good.

It’s a different story in head-to-head formats. A player’s volatility could affect a team’s performance. Returning to the example of Bruce, he’s capable of sealing a victory in his best weeks, but he can also ruin otherwise good performance when he’s playing poorly. Depending on the timing of Bruce’s streaks relative to the performance of your other players, streakiness could be a very good or very bad thing. Basically, your entire roster takes on a higher range of possible results due to one player’s volatility. While Petti’s volatility stat doesn’t account for this streakiness factor, it makes sense that volatile players are probably more prone to streaks.

It’s long been theorized that volatility is a bad thing in H2H leagues. I am unaware of any specific research proving this assumption. As I noted above, volatility probably increases the range of expected outcomes, but not the mean expected outcome. Depending on the construction of your roster, that could be good or bad. That’s my disclaimer, now let’s get into Petti’s results.

Here is a link to Petti’s spreadsheet with his VOL- statistic for the past three seasons. VOL- is simply volatility with league average set at 100, just like FIP-. So a 95 VOL- is five percent less volatile than league average.

We can use Petti’s research as is to get a general sense of who is and isn’t volatile. However, it’s not very useful to us as fantasy owners to know that Marco Scutaro, Skip Schumaker, and Alberto Callaspo are not volatile. It would be better if we interacted performance with volatility. That way, we would have an idea of the most stable players who are also fantasy assets. After all, a down day for Miguel Cabrera is still better than many of Scutaro’s best days, so there must be a point where raw performance overwhelms volatility.

I have taken Petti’s tables and added a column called Sharpe Ratio, which divides weighted Runs Created plus by VOL-. Credit for the idea to use a Sharpe Ratio goes to commenter Brandon. The Sharpe Ratio lets us find the best combination of high performance and low risk/volatility. You can find the full data in the updated spreadsheet here. Nothing has been done to adjust the Sharpe Ratio to a friendly scale. Higher numbers are better than low.

Below is a table of the top 30 hitters over the past three seasons by Sharpe Ratio. These players have featured the best combination of performance and volatility. Three year data is ostensibly more predictive than a single season of data, although I have done no testing to confirm this with VOL-.

Hitter	VOL-	STD VOL-	Sharpe Ratio
Miguel Cabrera	94%	0.10	189
Joey Votto	91%	0.02	178
Matt Holliday	92%	0.03	161
David Ortiz	100%	0.07	158
Shin-Soo Choo	85%	0.03	157
Prince Fielder	94%	0.04	156
Jose Bautista	99%	0.03	155
Andrew McCutchen	97%	0.06	151
Chase Headley	86%	0.03	149
David Wright	93%	0.03	148
Aramis Ramirez	94%	0.01	144
Giancarlo Stanton	100%	0.02	144
Robinson Cano	99%	0.03	143
Joe Mauer	93%	0.03	142
Jacoby Ellsbury	88%	0.03	141
Dustin Pedroia	86%	0.04	140
Mike Napoli	101%	0.08	139
Carlos Beltran	99%	0.06	139
Edwin Encarnacion	100%	0.07	137
Jose Reyes	89%	0.05	137
Alex Gordon	89%	0.01	136
Evan Longoria	101%	0.04	136
Josh Willingham	91%	0.06	136
Carlos Quentin	101%	0.07	136
Carlos Santana	95%	0.06	134
Yadier Molina	100%	0.02	133
Freddie Freeman	97%	0.03	133
Chase Utley	89%	0.05	133
Adrian Beltre	103%	0.00	133
Jayson Werth	96%	0.06	132

Unsurprisingly, Cabrera tops the list as the best combination of performance and volatility over the past three seasons. In volatility, he’s just six percent below league average, but the sheer weight of his performance outdoes his closest competition, which is Votto. As we can see, players like Ortiz, Stanton, and Encarnacion rank as some of the best values despite league average volatility. Beltre is three percent above league average. The take away is that overall production probably can overwhelm the value of consistency.

Freeman’s inclusion on the back end of the list caught my attention. Excluding 24 plate appearances in 2010, Freeman is the only player who made the list in his first three big league seasons. The Braves recently signed Freeman to an eight-year, $135 million extension. Given the financial constraints facing the club, this extension might mean that Jason Heyward, Craig Kimbrel, and Justin Upton will reach free agency.

Research shows that steady production is good for real-world teams. Whether consciously or unconsciously, Freeman’s combination of non-volatility and production may have been a contributing factor in the decision to extend him. He’s currently being drafted as the 24th pick and sixth first baseman off the board this season, which seems about right for strong four category production. Owners looking for steady production may want to target him if they miss out on the top tier of first baseman.

For H2H league owners who want to build a lineup that features consistent production week-to-week, this list is probably a great place to start. Every position is represented, and generally speaking the players range from the second (Cabrera) to 318th pick (Quentin). Expand the list a bit past 30 and you can probably build an entire roster of players who combine production with stability.

What about players who didn’t qualify for the above list? I have also included the 2013 season on a separate page of the spreadsheet, since only 154 batters qualified for the three-year table. I’ve limited the list to only players with at least 300 plate appearances and have presented the top 30 below. Bear in mind, this is much like a list of hitter BABIP. Just because Hanley Ramirez topped the list last season doesn’t mean he’ll do the same next season. VOL is Petti’s raw measure of volatility, which is used to derive VOL-.

Hitter	VOL-	VOL	Sharpe Ratio
Hanley Ramirez	91%	0.432	210
Mike Trout	86%	0.406	205
Miguel Cabrera	99%	0.468	194
Shin-Soo Choo	85%	0.405	177
Andrew McCutchen	89%	0.423	174
Joey Votto	90%	0.426	174
Matt Carpenter	86%	0.409	170
Matt Holliday	88%	0.418	168
Paul Goldschmidt	97%	0.458	161
David Ortiz	94%	0.447	161
Yasiel Puig	99%	0.471	161
Freddie Freeman	94%	0.444	160
David Wright	97%	0.461	159
Carlos Quentin	91%	0.432	157
Michael Cuddyer	89%	0.423	157
Marlon Byrd	87%	0.411	157
Jayson Werth	102%	0.484	157
Joe Mauer	92%	0.436	157
Chris Davis	111%	0.524	151
Josh Donaldson	100%	0.472	149
Carlos Santana	91%	0.431	148
Allen Craig	92%	0.436	147
Chase Utley	86%	0.407	147
Starling Marte	82%	0.391	147
Jhonny Peralta	85%	0.402	145
Edwin Encarnacion	101%	0.480	143
Carlos Beltran	92%	0.437	143
Brandon Belt	97%	0.462	143
Aramis Ramirez	93%	0.443	141
Dustin Pedroia	81%	0.386	141

We see some new names appear like Trout, Carpenter, Goldschmidt, and Donaldson to name a few. These are players that we can probably expect to make the three year list once they qualify. By restricting ourselves to one season, we’re cutting into the reliability of the VOL- statistic. We’re also seeing just one season of wRC+ performance, which is less informative. The one year sheet is probably best used to form a list of new players who might eventually find a ranking on the three-year list, like Trout.

I did not expect to find Byrd on the 2013 list with a VOL- 13 percent below league average (87% VOL-). If I had to bet on any one player on this list being a fluke, it would be Byrd. As a point in his favor, he was even less volatile in 2012. Of course, that was part of a miserable 153 plate appearance campaign that included a PED suspension. Last season included career highs in home runs, isolated slugging, and swinging strike rate. It would seem natural for a high swinging strike rate to coincide with high volatility. His 2011 season featured roughly league average volatility, which is more in line with what we probably should expect from him. In short, I wouldn’t add him to my short list of low volatility players based on his 2013 season.

Take It One Step Further

Enterprising owners in points leagues (especially points H2H formats) can further customize these lists. Substitute projected points for wRC+ and then divide by VOL-. The resulting list should give you a ROUGH idea of which players have the best combination of performance and stability in your points format. Just remember, the Sharpe Ratio you calculate will look like a points total, but it’s not. It can only be used to form a rough list. Statistically, there’s all kinds of things wrong with this approach, but the resulting output should be close to correct.

If you’re very enterprising, you could also try to project VOL and then calculate your own projected VOL-. Petti described the formula in his article, but it’s basically the standard deviation of daily wOBA divided by yearly wOBA raised to the .52 power. You could try taking a player’s past standard deviation regressed some amount to league average and then divide by his wOBA projection. Then take projected points divided by projected VOL-. That sounds terrible to me, I would never attempt it, but it should be possible.