Getting Dirty With Stats – Linear Weights

Getting Dirty with StatsIntro | Batting 1 – Linear Weights | Batting 2 – wOBA and wRC+

Respeck. We’re back to our chat about stats and our first real topic: linear weights. As a refresher, I finished up the intro post with the some goals:

  • Figure out which baseball player is responsible for which baseball thing
  • Figure out how much that baseball thing helps that baseball player’s team win more baseball games

Lets focus first on batters, as they will be easier to deal with the first issue above.

We’ll start with things batters aren’t responsible for. They’re not responsible for the ballpark where they hit half of their games, so we’ll have to deal with that later. They’re also not responsible for the skill of the defenders or pitchers against them, though those defenders and pitchers rotate throughout the league as hitters play against different teams. So while not perfect, we can feel comfortable saying defender skill isn’t a big enough issue to deal with here. Finally, batters aren’t responsible for the number of baserunners when they come up to bat, so we won’t need to worry about them.

Batters are responsible for the types of hits and other outcomes of their plate appearance.

Towards the end of his 2013 campaign, Padre second basemen Jedd Gyorko saw a marketing push focusing on his 23 home runs, which lead rookies across all of baseball. A nice piece of trivia, but if you’re the kind of fan who wants your players helping the team win, the fact alone becomes less helpful considering all the other things a hitter must do successfully. Fans, including media analysts and guys getting in arguments in bars often face the difficult challenge of comparing one thing a hitter can do with all of the other things a hitter should also do.

I’m excited as I’m typing this, because I get to tell you about such a simple and beautiful method of measuring different outcomes of plate appearances. Say what you will about things that excite me (TWSS), but holy crap it’s awesome we’ve figured out the value for everything a batter does so specifically.

Baseball actions must lead to either scoring or preventing runs, so we’ll convert each action into the equal amount of “runs” it is worth. This allows us to compare the value of different things consistently, and in the form something that directly helps the team win. Here’s the run value of a few things thing a batter can do:

Home Run: 1.39 runs

Triple: 1.09 runs

Double: 0.77 runs

Single: 0.47 runs

Walk: 0.32 runs

Stolen Base: 0.16 runs

Pretty incredible huh? We call them linear weights, and they make some intuitive sense if you think about them. A home run, for example is guaranteed to be worth at least one run since the batter will always score. But there’s also a chance someone could be on base for the home run. So a home run is worth a little more than that, based on how often guys are on base in front of batters.

We can now say the Gyork Store’s 23 home runs were worth about 32 (23 x 1.39) runs. Yasiel Puig didn’t hit as many home runs as our boy Jedd, but he did enough other things to help the Dodgers on offense more than the Padres. Puig’s 19 home runs were worth about 26 runs, but his additional singles, triples, walks, and (oddly) hit by pitches unfortunately helped his team more.

This is all possible through the magic of the run expectancy matrix. It takes the 24 possible situations of men on base and the number of outs (bases empty no outs, man on second 2 outs, etc.) to figure out how many runs a team can expect to score. The run value of many other events can be found here. Then you can get really dirty with baseball legend Tom Tango if you’re into that sort of thing.

While calculating each of these items individually for every player ever sounds like a raging good time, we’re lucky enough to live in a world where someone has done the work for us. We’ll get into that in a future post.

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  • USMC53

    Why is an inside-the-park-HR worth more (1.45 runs) than a regular HR (1.39 runs)?

    • Change the Padres

      My initial guess is that an inside-the-park-HR occurs partially because the fielder attempts to make a play because there are runners on base which he can prevent from scoring. A regular homerun is independent of defensive alignment and effort.

    • Sac Bunt Melvin

      Probably related to what CTP said.

      If you scroll down on the list (http://www.insidethebook.com/ee/index.php/site/comments/run_values_of_events/) Tom Tango explains that the values are from actual events from one year, 2006. So theoretically they’re the same value, but in practice they’re slightly off since there aren’t many inside the parkers in one year which would skew things slightly. Plus, as mentioned, defenders are more likely to take risks with runners on base to prevent them from scoring which would create extra inside the parkers.

  • Patrick R.

    Great piece. I actually just checked out The Book from the San Diego Public Library. I love their SABR section. Tons of great stuff.

    • Sac Bunt Melvin

      Good idea, and thanks! I need to get down there soon.

      • Patrick R.

        Definitely worth it. They have some old Bill James abstracts and BP annuals. I was really impressed.