Goatriders of the Apocalypse

Introducing WAR for hitters

There are a lot of various sabermetric stats that attempt to boil a player's value down to a single number, namely his value to the team in wins. Baseball Prospectus uses Wins Above Replacement Level, or WARP, invented by Clay Davenport. The Hardball Times publishes Win Shares Above Bench, invented by Bill James. Here at Goatriders, we use Wins Above Replacement, invented by Tom M. Tango. Lemme splain, and then I'll give you the goods.


There are plenty of ways to measure a player's offense, but since we're interested in comparing it with things that aren't hitting, we need to convert it to something else - sort of like how you exchange your currency when you travel abroad. We'll convert it to the universal currency of baseball, runs - and we'll use linear weights. Linear weights comes in many flavors; I use wOBA, another invention of Tango's. wOBA is a "rate" stat, which in this case means it measures run generation per plate appearance. It's designed to work on the same scale as OBP, hence the name - .330 is (roughly) average. You can easily convert wOBA to runs, but in this instance we'll let Excel handle that work for us.


When it comes to measuring defense, I generally use flavors of zone rating. First, you divide the field into zones:


Then, "stringers" in the press box record what zone each ball is fielded in. Each fielder is responsible for plays in certain zones - every time they make a play on a ball in their zone, they are credited with a play and and opportunity. Each time a ball passes through the zone without a play being made, they are credited with an opportunity. Their zone rating is:

Plays divided by opportunities

(Different zone rating systems have different ways of handling plays made outside of assigned zones. BIS Zone Rating, which is published by the Hardball Times, simply lists OOZ plays separately.) We can then convert zone rating into runs saved or allowed compared to the average player at that position.

Converting to Wins

We have run values for hitting and defense now. But how do we relate runs to winning?

Bill James invented something called the Pythagorean Theorem, based upon its resemblance to the Pythagorean equation for a triangle. He discovered that you can find a good approximation of a team's win-loss record through the following equation:

Runs Scored squared divided by Runs Scored squared plus Runs Allowed squared

There have been plenty of refinements to the Pythagorean formula over the years, increasing its accuracy (this will come up when we get to talking about pitchers). We can take a shortcut here, though - for an average team, ten runs is equal to one win, using Pythag. So we divide everything by 10. (10.5, actually, if you want to quibble.)

Replacement Level and Positional Adjustment

What we lack is a way to readily compare offense and defense between positions. We could simply use positional averages, but there are problems. Certain positions are more valuable than others - the average second baseman simply isn't as valuable to a team as the average third baseman, because third basemen tend to be better baseball players than second basemen. And an average defensive first baseman is nowhere near as valuable as the average defensive shortstop.

There's another issue with using average - there is plenty of value with simply being an average baseball player, and we don't want to understate that. There are fewer average baseball players than there are below-average baseball players, because baseball talent is not normally distributed - it doesn't follow a bell-shaped curve. When you start talking about below-average baseball players, the worse a player gets, the more likely it is that there's a guy at AA or AAA that could perform just as well as him.

That's where the concept of replacement level comes in. A replacement player is, generally speaking, the sort of player that can be acquired for very little. Nate Silver of Baseball Prospectus calls it "freely available talent" - minor league journeymen and free agents, Rule V draft picks, players on waivers, free agents making the league minimum or close to it.

(As aside - sabermetricians don't usually agree on precisely where the replacement level is, because they don't precisely agree on the definition of replacement players. So if you go comparing my numbers with WARP or WSAB and they look radically different, well, that's because we're all using different replacement levels. Nobody's wrong - well, Baseball Prospectus is probably wrong, but let's save that argument for another day, shall we?)

Some things to note about replacement level:

  1. You will sometimes hear people talking about replacement level hitting; it doesn't exist. Replacement level is a function of a player's total value, hitting and pitching.
  2. That said, you can get away with it because - on average - replacement players are average fielders for their position. It makes sense - teams will only play a player far out of position if they do something else well enough to compensate; poor defensive shortstops either hit well or they're not in baseball.

For our purposes, replacement level is set at two wins below average. But we also want to adjust for position, and so we give tougher defensive positions a "bonus" and easier defensive positions a "minus." Those numbers are derived by looking at the performance of players defensively that played multiple positions - a player who played shortstop and second base in the same season was generally about five runs better defensively at second than he was at shortstop, for example.

The full list of defensive adjustments, measured in wins:

+1.0 C
+0.5 SS/CF
+0.0 2B/3B
-0.5 LF/RF/PH
-1.0 1B
-1.5 DH

Those numbers are over a full season, and are pro-rated to playing time in the chart below. Speaking of which...

Cubs WAR to date

Here's the chart:


Some notes:

  1. I don't have zone rating data for catchers - I do have SB% and wild pitch/passed ball data, which at some point I could try to figure defensive translations for. But right now, Soto and Blanco aren't given any credit for their defense.
  2. Speaking of Soto - dear lord he's a monster. He's just wandering through Tokyo breathing radioactive fire wherever he pleases. He's Godzilla, man.
  3. WAR_650 is WAR extrapolated out to 650 plate appearances. That's not a projection, just a way of comparing players with different playing time. WAR_650 could be skewed by a player having an unusually large or small number of defensive opportunities compared to his number of plate appearances.
  4. For players who have played multiple positions so far, defense is only from their primary position. It's something I'd like to improve upon for the future.
  5. As much as I like to say bad things about Mike Fontenot, he comes off looking pretty good in this analysis. We can discuss sustainability of this performance, but so far he's played well in the opportunities he's had.
  6. You can talk about Soriano; I won't. Let's simply leave it at, "He's a good candidate to improve."
  7. Less likely to improve are our center field tandem of Pie and Johnson. Pie has the edge defensively and is the better hitter against righties (albeit only slightly) and so should probably see the bulk of the playing time going forward. But if he can't improve his hitting, we are looking at a gaping hole at the center field position going forward.
  8. Ryan Theriot is playing like Derek Jeter right now - great offensively, poor defensively. If he stops hitting well enough to paper over his shoddy defense, shortstop could also be a problem position. (Or his defense could improve and he could keep hitting like Jeter, I suppose. You decide what you think is most likely.)
  9. Ronny Cedeno isn't exactly flashing the leather, either - all I can tell you is that it's hard to gauge a player's defense on 21 chances. (All of these numbers, in fact, bear great big flashing "small sample size" caveats. It's a big reason I've waited this long to publish my WAR chart.)
  10. We were promised excellent defense from Fukudome, and so far he's delivered.
  11. Did I mention that Soto is bloody fantastic? Wow. Just... wow.

I'll try and get an odds and ends post up later, but no promises - this took a lot out of me, I'm not gonna lie. And if you liked it, hated it, or just have a question or an argument - please comment. I'd much rather have a conversation than a lecture.

Also - and someone hold me to this, please - at some point this weekend I hope to publish a WAR chart for pitchers as well.

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