Author Archive

A New Way to Look at Sample Size: Math Supplement

This article is co-authored by Jonah Pemstein and Sean Dolinar.

For the introductory, less math-y post that explains more about what this project is, click here.

The concept of reliability comes from the classical test theory designed for psychological, research, and educational tests. The classical test theory uses the model of a true score, error (or noise) and observed score. [2]

CTT_EQUATION_diagram

To adapt this to baseball, the true “score” would be the true talent level we are seeking to find, and observed “score” is the actual production of a player. Unfortunately, the true talent level can’t be directly measured. There are several methods to estimate true talent by accounting for different factors. This is, to an extent, what projection systems try to do. For our purposes we are defining the true talent level as the actual talent level and not the value the player provides adjusted to park, competition, etc. The observed score is easy to measure, of course — it’s the recorded outcomes from the games the player in question has played. It’s the stat you see on our leaderboards.

The error term contains everything that can affect cause a discrepancy between the true score and the observed score. It contains almost everything that affects the observed outcome in the stat: weather, pitcher, defenses, park factors, injuries, and so on. This analysis isn’t interested in accounting for those factors but rather measuring the noise those factors in aggregate impart to our observed stat.

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Modeling Salary Arbitration: Stat Components

This post is part of an ongoing arbitration research project and is coauthored by Alex Chamberlain and Sean Dolinar.

April 24: Modeling Salary Arbitration: Introduction

Feb. 25: 2015 MLB Arbitration Visualized

* * *

A couple of weeks ago, we introduced a couple of regressions that modeled arbitration results using a basic formulae predicated on wins above replacement (WAR). Ultimately, the models estimated that an arbitration-eligible pitcher could expect his salary to increase by 14 percent, and his raise in salary to increase by 56 percent, for each additional WAR. A hitter could expect increases of 13 percent and 46 percent, respectively.

The models, however, were incomplete: they did not incorporate any other stats aside from WAR. This was by design, as we wanted to introduce simple one-variable equations for the sake of demonstration. WAR is, conveniently, a comprehensive variable that attempts to summarize a player’s worth in one easily digestible number. But what about the effects of a player’s age or arbitration year?

Moreover, the r-squared statistic — a quick-and-easy check of a model’s validity — for each specification is not especially strong, clocking in anywhere between .30 and .56. This is partly a result of specifying only one explanatory variable, so including more variables — which we have done in this post — should improve the goodness of fit of the models, assuming the variables are relevant.

With that said, we have new-and-improved models to share with you: one comprised of composite statistics and another comprised of traditional statistics. They are all vanilla, linear ordinary least squares (OLS) regression models, and it is important to remember that the values for each stat can only be used in the context of that specific model.

Non-Traditional Statistics

For each player, we specify…

  • a composite statistic, such as wins above replacement (WAR) for batters and RA9-WAR for pitchers, to measure overall performance (RA9-WAR uses runs allowed per nine innings rather than FIP);
  • a service statistic, such as plate appearances (PA) and innings pitched (IP), to measure playing time;
  • a “glory” statistic, such as home runs (HR) and saves (SV), to account for baseball’s affinity for traditional statistics and social constructs;
  • arbitration year (for pitchers*), indicating a player’s total service time;
  • and his age (for hitters*), to measure as best we can the number of years for which he has inhabited the earth.

We identify these particular stats not only to cover as much analytical ground as possible but also minimize the use of stats that have high correlation among themselves (multicollinearity). We want to isolate different aspects of player performance or value as best we can.

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A Visual Look at Defensive Metrics

As we move into May and people start to check our WAR leaderboards, there will inevitably be a discussion about why certain players rank highly, especially if they aren’t putting up big offensive numbers. Most of the time, that discussion revolves around the player’s defensive value; For example, last August, Alex Gordon sat on top of our WAR leaderboards, which generated a fair amount of controversy at the time.

Here at FanGraphs, we use Ultimate Zone Rating (UZR) as the fielding component of WAR. UZR is one of two defensive run estimators we host here on the site, the other being Defensive Runs Saved (DRS). Both metrics go beyond traditional fielding stats using the same Baseball Information Solutions (BIS) data set to assign runs to players by dividing the field into different areas and then comparing each play to a league average. At FanGraphs, we don’t have UZR values for catchers or pitchers, so those positions are simply removed from any data visualizations in this post. We also have great library entries that go over the minutiae of the metrics better than I can in this post.

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A Look at Statcast’s Broadcast Debut

Last night’s broadcast of the Cardinals and Nationals game debuted live, in-game Statcast enhanced graphics and replays. Statcast is the next-generation player tracking technology that combines both optical and radar measurements promising to create new ways to quantify previously unmeasurable aspects of baseball. The hype leading up to this game was billed as historic, and here at FanGraphs, we even had a special edition of the After Dark Live chat to cover this momentous occasion.

If you were expecting something earth-shattering from Statcast, once you began to watch the game you were probably disappointed at the slow start. If you were unable to watch the broadcast, no need to worry, because all the important replays from the broadcast were posted on Major League Baseball’s site, and I’m about to review and critique the different elements of the Statcast presentation.

First, before analyzing specific images and gifs from the game, MLB Network appeared to treat this as a normal broadcast using Statcast to augment their broadcast, not define it. 90% of the broadcast contained traditional camera angles, graphics, replays, and other broadcast elements. When Statcast was used, it was to produce enhanced replays and player positioning. There weren’t graphical overlays over live-game action aside from a few pre-pitch positioning graphics. ESPN currently has more detailed graphics for live-action pitch tracking with their K-Zone graphical overlay.

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Investigating the Idea of Scarce Right-Handed Power

I want to put to rest the discussion about the lack of right-handed power in Major League Baseball today. There has been a lot of anecdotal commentary about how scarce right-handed power has become, but there haven’t been too many analytical articles supporting this idea. If anything, the handful of articles that have been written question if the problem even exists in the first place. There are two different arguments about this topic: the first is that right-handed power is scarce — that is to say left-hand power is bountiful — but right-hand power is not, while the second argument, which I won’t address today, is that relative to left-handed power hitters, right-handed power hitters have declined in number.

In a hypothetical choice between players of equal talent, you would almost always prefer a left-handed power hitter to a right-handed power hitter, since the lefty will have the platoon advantage more often and should be more productive as a result. There are valid arguments concerning rounding out line-ups, but right-handed batters are not scarce; good left-handed hitters are actually the scarce commodity.

For reference, the general population is estimated at having a left-handed rate of 10%, while baseball has a left-handed rate among batters is about 33%; lefties are overrepresented in baseball.

This is a box plot of the various player-seasons from 2010 until 2014. I’ve chosen this time span since it’s recent and it falls after the implementation of PITCHf/x, which improved the measurement of the strike zone. I’ve excluded switch hitters for simplicity, and set a floor at 200 plate appearances.

2010-2014 Single Season HR

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BABIP and Year-to-Year Offensive Fluctuations

As we anticipate the start of the 2015 Major League Baseball season, we begin to speculate about player performance in the upcoming season. While most players are somewhat consistent year-to-year, there are some who have either breakout years or terrible seasons. These extreme years are a confluence of events throughout the season such as player health, skills peaking, and luck — which can be partially captured by BABIP.

To find the seasons with the greatest offensive output changes, I calculated year-to-year changes for players from 2000-2014 in a handful of offensive statistics: WAR, OPS, BABIP, and HR. Since playing time can fluctuate because of injury or being a rookie, I eliminated comparisons of seasons that a player had a high discrepancy in plate appearances.

To visually compare the seasons, I used slope graphs to show the year-to-year changes in the various statistics. Each graph is limited to players in the sample who had the largest changes in both the positive and negative directions. The left end of the line represents the player’s statistic in one year with the right end of the line representing the following year. A steeper the slope indicates the largest change between two years.
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Off-Season Twitter Usage Among MLB Teams

The original graphics and text omitted the Brewers, Cardinals, and Yankees. They have since been corrected.

If you’re on Twitter, you’ve probably noticed the current hashtag contest, #FaceofMLB, being run by MLB Network or the RBI Baseball advertising campaign. Social media has become an important platform that Major League Baseball teams use to communicate with their fans, especially during the off-season when there aren’t baseball games to watch or attend.  Twitter has also been touted for allowing teams or players to interact directly with fans, removing the need for an intermediary.  To measure that interaction, I gathered the timelines and favorited tweets from all 30 MLB clubs’ official Twitter accounts from November 1, 2014 until February 10, 2015 and ran an engagement analysis.

This particular analysis looks at how much effort each MLB team makes to interact with its fans, and not simply which team has the most followers. I’m looking at engagement three different ways: volume of tweets, media sharing and fan interaction. First, let’s look at volume of tweets.

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