What I've Been Up To

Hey all. Like I said before, I've sort of settled into the role of resident nerd over at http://thatballsouttahere.com/, a Phillies blog. I've been super busy producing a ton of content there, but here are a few of my statistics-heavy posts I've contributed:

Can Cliff Lee Throw Too Many Strikes?
A Look at Charlie Manuel's Decisions to Bunt in 2011
Looking at the Aces' Cutters
Who Has Accounted for the Phillies' Production?
Will Roy Halladay Reach 300 Wins?
Appreciating Ryan Madson's Dominant Years

Quick Update

If you've stumbled across this blog and want to read some more of my writing, I can now be found over at http://thatballsouttahere.com/ contributing Phillies-related statistical analysis on a regular basis. Thanks.

Context Matters: Why Fangraphs's Model for Valuing Free Agent Contracts is Wrong

Any time a star player signs a new free agent contract, fans and baseball writers alike naturally form an opinion of the signing. As Jose Reyes inked a new deal worth 6 years/$106 million last night, FanGraphs writer Dave Cameron applied a particular methodology to analyze the contract here. Before I move forward I would like to say that I think Dave, for the most part, is a fine baseball writer, and FanGraphs is an excellent resource for statistics. That being said, I find their model for valuing free agent contracts to be heftily flawed.

The basic framework for doing so seems to be:

• Determine a projection of the player's value for the life of the contract. Value is expressed in Wins Above Replacement and the player's decline is often expressed at a rate of 0.5 wins per year.
• Determine the "dollar amount per free agent win" in the first year, then account for inflation in this amount for the following years by using a 5% rate.
• By multiplying projected WAR by the projected dollar amount per WAR, determine the value that this player provides, expressed in a dollar amount.
• Compare this figure to the actual annual salary the player will be receiving in order to determine an opinion on the contract.

Below is Dave's chart that shows this methodology used to analyze Reye's contract.

Year	WAR	$/WAR	Value
2012	3.53	$5.00	$17.67
2013	3.37	$5.25	$17.67
2014	3.20	$5.51	$17.67
2015	3.05	$5.79	$17.67
2016	2.91	$6.08	$17.67
2017	2.77	$6.38	$17.67

Without saying anything about the rather arbitrary annual decline/inflation rates, the second step is where I believe this model truly fails. The "dollar amount per free agent win", also written as $/WAR, is the average amount that all teams spent per WAR on the free agent market. In other words, this is an aggregate figure resulting from hundreds of free agent contracts awarded by many different teams.  

The problem here lies in the fact that no two teams are in the same financial and/or competitive position. But why is that a problem? 

Chapter 5.2 of Baseball Prospectus's Baseball Between the Numbers illustrates a concept that can help begin to explain why this type of valuation is unsound. After confirming that reaching the postseason results in great financial gains, Nate Silver finds that not all marginal wins are of equal value, demonstrated by the density curve below (because of this financial incentive to reach October, a nearly identical curve can be extrapolated to show the marginal value of an additional win, expressed in monetary terms).

Consider this scenario: a 80-win team has about a 1.8% chance of making the postseason. If it adds a free agent who it believes will produce one additional win for the team (a 1 WAR player), it becomes an 81-win team and now has a 2.9% chance at reaching the postseason. The marginal postseason probability added is 1.1 percent: this player does not significantly affect this team's chances of receiving the huge financial benefits that are married with a postseason appearance. Now consider a second scenario. This same one-win player is signed by an 89-win team, thus making them a 90-win team. This move raises this team's chances of making the playoffs by over 11.4 percent. 

Which team does this player provide more value to? Quite clearly, the expected marginal revenue produced by this 1 WAR free agent is much greater for the second club. Since this player means more to the 89-win team, they would be willing to offer him a greater wage than the 80-win team would. This is what makes the FanGraphs model fall short. By assuming that each marginal win is worth a universal dollar amount (Dave used $5 million/WAR), the model states that revenue is a linear function of wins. This, however, is far from reality as linearity implies that context is not a factor. In this specific case, the FanGraphs methodology claims that both teams would be "rational" to offer this player a yearly salary of $5 million. Again, because of context, the offers from each team are not going to be equal, so two vastly different contracts could both be rational.

Of course, the amount of games a team can expect to win in an upcoming season is not the only matter that defines context. Other factors, such as market size, positional needs, new ballparks, and upcoming minor league talent all help define context. Each is taken into consideration by front offices when deciding how to value free agents. Again, a rigid $/WAR model is inherently incapable of realistically capturing the effects of such factors.

The $/WAR calculations that FanGraphs carries out tell us useful information about what the entire free agent market looks like as a whole--it shows that the average amount spent on each additional win is rising. But because it chooses to ignore a multitude of variables, I find it to be a futile tool for analyzing free agent contracts on an individual basis. To ignore context in such a way that strict $/WAR models do is a lazy and irresponsible excuse for analysis. 

What is the Marginal Benefit of an Additional Strikeout?

Not many would dispute that increasing a pitcher's strikeout rate is a good thing, all else held constant. A strikeout, in most situations, is the best way for a pitcher to record an out, and having the ability to miss bats is highly correlated to future success. In my never ending quest to quantify anything and everything, my question is then: just how much does an increase in strikeout rate benefit the pitcher? And what types of pitchers are better off from this given increase?

Starters and relievers are in many ways two separate beasts, so in choosing a sample I decided to work with starters only. I used every qualifying player-season since the expansion era (1961-present). Of course, different types of pitchers have different tendencies. High strikeout pitchers tend to also walk a fair amount of batters, while pitchers with great control don't usually see great K rates. Therefore, it is important to treat these types of pitchers differently. With this in mind, I segmented the sample into eight groups based on walk rate, providing a loose way to control for "pitcher type." This allows me to see how a given increase in strikeout rate affects different types of pitchers. Given that the primary objective of pitching is to prevent runs, I used ERA as a measure of pitcher success. Since I'm measuring the marginal impact of an increase in strikeout rate, K/9 is the independent variable and ERA is the dependent variable. 

I used linear regression to model the impact of an additional strikeout. I looked at a few other types of  regressions, yet none provided a substantial upgrade over the linear model. While it may not be entirely realistic to assume a linear relationship for a number of reasons, I feel that it is accurate enough for this evaluation. 

The following graphs detail the results, starting with low-walk pitchers and ending in high-walk pitchers. Since "marginal" refers to the derivative of a given function and we're working with a linear function, the slope of each regression line below represents the marginal impact of a one-unit increase, or in this case, an additional strikeout.

As expected, in every case a higher strikeout rate is associated with a lower ERA. However, each slope varies depending on type of pitcher. The chart below summarizes the marginal benefit (again, the slope of each regression) to each of these types.

An interesting pattern occurs here. Low-walk pitchers see a relatively large decrease in ERA from a one-unit increase in K/9. Then, in the next group, this marginal benefit drops nearly 5 percent. As walk rate increase, marginal benefit slowly increases then shoots up to for the group with the highest walk rate. In other words, it appears that the two groups that benefit the most from raising their K/9 are low-walk pitchers and high-walk pitchers. For instance, pitchers with average walk rates (around 3 BB/9) can decrease their ERA by about .12 with a one-unit increase in K/9. Yet this is roughly half of the benefit that a much wilder pitcher can receive with the same increase in strikeout rate. Simply put, this model finds that additional strikeouts are not created equal. 

Of course, these results must be looked at with a fair bit of caution. While low-walk and high-walk pitchers may benefit more from increasing their K/9 than everyone else, the margin in which they do so is around .05 to .1 of ERA. Over a full season, this is equivalent to about 2-3 runs, so the difference isn't exactly huge. Regardless, I find these results to be interesting and perhaps a beginning to a deeper investigation on the subject.

How do MVP Winners Perform in the Following Year?

The annual baseball awards aren't announced until next week, but as any fan knows, it's never too early to beginning discussing them. Yet I'm not interested in writing about the hackneyed debate of which player should win a given award, why they deserve it, and so forth. Rather, I want to look into a question that was recently posed to me: how well will a player perform in the season after he wins MVP?

Instinct as well as logic says, "worse." Above all, this hypothesis is backed by the fact that MVP seasons are usually driven by a player who, by some force, sees results that are above their true talent level. Thus, a trip back down to planet Earth is usually in order during the next season. It seems safe to say that players will likely perform worse in the year following an MVP campaign. This is not enough though, as I am concerned with testing this assumption against the hard data.

I took a sample of data from both leagues going back to 1980, omitting seasons in which a) pitchers were granted the award and b) the winner suffered a substantial injury the following season. The result is a sample of 56 player-seasons to work with. To evaluate performance, I utilized two metrics: OPS and FanGraphs WAR. For each winner, I recorded both statistics for the MVP season and for the season after. This allowed me to get an aggregate picture of how much players decline on average, expressed in a percentage. The results:

OPS	OPS After	OPS % Change	WAR	WAR After	WAR % Change
1.018	0.953	-6.37%	7.8	5.9	-24.31%

This is consistent with the assumed hypothesis that the league MVP's performance will decrease the following year. WAR, being an innately more volatile metric, sees a greater average decrease than OPS. Again, this makes sense as OPS is a rate statistic whereas WAR is a counting statistic.

If we multiply a given MVP season's results by the average rate of decline provided by this model,  we get an expected value for the season that follows; that is, how we can reasonably expect that player to perform. Comparing this expected value with the observed (actual) value is a way of looking at how well a given player-seasons fits the model. Most of the seasons from the "after" group fall very close to zero, indicating little error, as shown by the box plots below:

However, there are clearly some player-seasons which are substantially far from the expected value. Going back to the data for a closer look allows us to see at who produced these outliers. From that, we can deduce what types of players are more prone to deviating from the norm. 

On the negative end of the spectrum, it appears that the true "superstar" type players are likely to outperform their expected value. This phenomenon can be explain by the fact that great players are more likely to repeat MVP-caliber performances (opposed to a good player having a single great season). For instance, only one of Barry Bonds's six qualifying seasons saw a decrease in OPS that was greater than expected. In other words, because Bonds consistently performed at levels far beyond those of his peers, his numbers following an MVP season were less likely to diminish. In this area, Bonds is joined by other multiple-time MVPs such as Albert Pujols and Mike Schmidt. The other side, those who underperformed their expected values, is occupied by the likes of Willie McGee, George Bell, and others whose MVP seasons were significantly out of line with their career numbers. 

Another point worth noting: while it may seem reasonable to assume age plays a factor in explaining the performance following an MVP season, it has no apparent correlation here. Many younger players saw large drop-offs, and many older players who presumably passed their peak years followed up their MVP season with another strong year. Age probably does have some part in helping predict next season performance, but with the limited data available it's simply too difficult to extrapolate. 

All of the conclusions reached here may be, in some form or another, common sense. Superstars don't usually see great decreases in performance, "good" players do, and looking from an aggregate standpoint, a decline is expected. With a sample of only 56 player-seasons to it's difficult to reach a desirable level of precision, but the numbers certainly confirm the basic assumptions.

How will Derek Lowe Perform in Cleveland?

Groundball pitchers tend perform better when they have good defenders behind them. This is common sense—if more than half of balls in play are on the ground, it certainly helps to have a sturdy infield to convert them into outs. Owning modest a K/BB ratio and a career 63% GB rate, Derek Lowe is a classic example of an extreme groundballer. Two days ago, the Braves sent the 38-year-old to the Indians in return for a young pitching prospect. As a pitcher that lets his defense take care of making outs, how will Lowe fare as an Indian?

Lowe didn't particularly pitch well last season. In 34 starts, he posted a 5.05 ERA and significantly increased his walk rate which resulted in a sub-par 1.96 K/BB ratio. However, this doesn't fully explain the story considering that his FIP of 3.70 had a pretty significant discrepancy with the results he saw. This is not unlike his other two seasons in Atlanta—he underperformed his FIP by 0.11 and 0.61 in 2009 and 2010, respectively.

What is to be made of this disagreement? When predictive ERA estimators are off from what actually happens on the field, the causes usually include a combination of batted ball luck, random variation, and defense. In Lowe's case, I believe poor defense played a large role in his inflated ERA. Again, as a groundball pitcher, Lowe relies heavily on his infield for success, yet the Braves's infield has been pretty dismal in Lowe's days as a Brave. This is supported by the fact that Lowe's average BABIP as a Brave ballooned to .320, up from pre-Atlanta average of .291. If we look at each position individually, we see that Lowe wasn't exactly in the company of elite or even above average defenders. Below is a chart that quantifies this belief in the form of UZR data.

Year	1B	2B	SS	3B	Total
2009	3.0	3.1	0.9	-3.3	3.7
2010	-13.5	-4.9	6.3	-8.2	-20.3
2011	-12.6	-11.5	-2.2	-2.5	-28.8

As you can see, Lowe didn't have much help from his infield. Things got especially bad last season with UZR ranking the infield as being 28.8 runs worse than a hypothetical average infield. If we make the assumption that these "runs lost" were evenly distributed across Atlanta's entire season, we can calculate what his ERA should have been if he were given average defense. Lowe pitched 12.64 percent of all innings for the Braves this year, so by multiplying -28.8 by 0.1264, the infielders were worth -3.64 runs in innings that Lowe pitched. This would move his earned run total down to 101.36, giving him an ERA of 4.88, ceteris paribus. However oversimplfied, this model demonstrates that infielders have an impact on Lowe's results.

That brings us to the original question: how will he do in an Indians uniform? While it is hard to be precise in forecasting something with so many variables, I think there is sufficient evidence to believe that Lowe will likely perform poorly in Cleveland. The team has a below average infield which actually performed worse than Atlanta in 2011. As this article points out, they collectively posted a -34 UZR. With 60% of Lowe's balls in play coming towards them, it's hard to imagine Lowe being successful in Cleveland.

On Zach Britton's "Pitching To Contact" Comments

Over at FanGraphs, David Laurila recently conducted an interview with Zach Britton, the 23-year-old lefty who just finished up his rookie season with the Orioles. As a highly touted prospect, Britton didn't put up impressive strikeout totals, but his groundball-inducing heavy sinker allowed him to enjoy much success in the minors. When Laurila asked Britton for his thoughts on the his underwhelming major league 1.56 K/BB ratio, Britton responded with:

"I know that it could be better, obviously. I’m not going to be a guy who strikes out a ton of people; I’ll never lead the league in strikeouts. And with the movement I have, I’m going to walk guys. That’s something I can improve upon as I get older and more experienced, though. I can learn to make better adjustments...I pitch to contact. If I get a guy 0-2, I’m not necessarily looking to strike him out; I’m looking to get him to hit a ground ball. It’s a mindset. I’m not a huge believer in having to strike guys out in order to be successful. I’d rather keep my defense on their toes and get outs. Most times, when I strike guys out, it’s not on three or four pitches; it usually takes five, six or seven. Pitching to contact allows me to be more efficient."

My first instinct was to be a bit skeptical of the effectiveness of this "mindset."  Numerous studies have indicated that is issuing walks, not striking batters out, that ultimately increases pitch count to the point of being "inefficient." Yet in sabermetric analysis, it is not uncommon to find outliers in these aggregate models—some players simply don't fit the mold of generally accepted principles. Britton, after all, ought to know his own tendencies better than anyone else.

To test the validity of his statements, I looked at each of his 97 strikeouts this year and recorded how many pitches it took to retire the batter. The frequency for each amount of pitches was such:

On average, it took Britton 4.96 pitches to ring the batter up. This is on the lower side of his own anecdotal description of it usually taking, "five, six, or seven (pitches)." The league average amount of pitches it takes to record a strikeout hovers around 4.8 with a standard deviation of 0.15. Relative to his peers, Britton it appears is slightly less efficient, but not significantly so. 

This is not to say that Britton is wrong to have a "pitch to contact" approach, and this is by no means adequate grounds for concluding that he would be better off changing his mindset on the mound. His comments simply caught me off guard and I wanted to compare his words to the hard data. It does appear, however, that Britton is underestimating his ability to be efficient when striking batters out.