Regressed WAR: An Introduction

In case you haven’t already heard, baseball is a game of numbers. Some curmudgeons like to say that baseball isn’t all about statistics, and to some extent, that’s true. However, the point of playing baseball is to win baseball games, and the number of wins a team has is a statistic. So in that sense, it’s all about statistics. I think I speak for all baseball fans, though, when I say that statistics aren’t the reason why we watch the game. We watch because we love to see home runs rocket off of bats, curve balls magically break into the dirt, and soft line drives find the gloves of diving defenders. The statistics come into play when we want to know something more about what it is we’re watching. As Crash Davis famously explained, the difference in a chump and a champ is one more dying quail a week. Our brains won’t notice one more dying quail a week, so we need some sort of statistic to make sense of it, to be able to separate the good from the bad.

If we could identify the main reasons for fans’ use of statistics, it’s to give an overall idea of how valuable a player has been to his team and what that player’s true talent level is. For the former, there is nothing better than Wins Above Replacement (WAR). I’m not going to defend this, because if you dispute it you’re just being willfully ignorant. For the latter, projection systems are the way to go. Whether you prefer the ZiPS, Steamer, or just the simple Marcel system, projection systems do a great job at nailing down how good a player actually is. The thing is, I’m often asking a question somewhere in the middle of those two. What I often want to know is simply how well a guy has played. Take away all the outcomes and luck and randomness that is inherent to baseball, and tell me how well he has performed his job. WAR doesn’t answer this question, because as far as WAR is concerned, a dying quail and a hard hit line drive to center field are the same thing if they both become a single, but the guy who hit the latter obviously played better than he who hit the former. Projection systems don’t answer it, as current-season data is a notoriously poor predictor of future performance, even if it’s not just due to luck. In order to nail down the answer of this question, I propose we start doing some regression. At this point I should mention that the rest of this article is going to involve math and technical terms. If you’re down with that, read on. If not, just know that I made a statistic that perfectly answers the question I posed and the link to the leaderboard is found below and I’m awesome and you should trust these numbers 100 percent because I made them with all of my genius. Got it? Here we go.

For those who don’t wanna read this long write up, the link at the bottom of the page is a leaderboard for Regressed WAR: a version of WAR that attempts to show how well a player has performed, adjusting for randomness and luck.


Creating Regressed WAR involved doing two simple things: regressing a player’s defensive value and regressing his offensive value. To do this for defense, I regressed his current season’s UZR toward his running 3 year average UZR. I set it up so that if a guy had played in 0 games, it would be regressed completely to his 3 year average, and if he had played in 162 games, it would be regressed 50 percent toward the 3 year average. If the player did not have at least 3000 innings in the 3 year sample, I regressed toward both his 3 year running average and toward zero. For example, if a guy had accumulated 6 UZR in 2000 career innings and had played in 81 games this season, we would regress his numbers 75% x 2/3 toward 6 and 75% x 1/3 toward 0. If the guy was a rookie, I regressed his numbers solely toward zero. The Excel statement for this part can be found here.

To take care of the offense, I regressed a player’s BABIP toward his xBABIP. As above, I regressed his BABIP 100 percent toward his xBABIP after 0 games and 50 percent toward his xBABIP after 162 games. I then used this new BABIP, his current home run total, and his career 2B and 3B per hit rates to calculate his regressed wRAA, in the same way I outlined here. If you want access to that Excel sheet and what’s going on with it just send me a message on twitter w/ your email address, and I’ll send you the file. At some point I’m going to use xHR instead of HR, but I haven’t gotten around to it. Here’s a picture of a Word document that explains the formulas I used:



Anyway, without further ado, here are the regWAR leaderboards. As always, let me know if you have any suggestions, potential improvements, criticisms of methodology, etc. I’m presenting this for it to be useful, so any suggestions you have to make it more useful are always appreciated. Remember though that this is more of a fun thought experiment than anything else. It’s in no way perfect and in no way claims to be. It’s simply putting some rough numbers to things I already think about in my head. Enjoy!

Note: I haven’t updated these numbers since Thursday, July 24th. I’ll try to update them every Thursday. I’d do it more often, but I don’t know how often people will look at this.

Stephen came up with the idea for this blog shortly after graduating from Tech. Realizing that life is ephemeral, he decided to put (metaphorical) pen to paper and catalogue his thoughts. His thoughts are series of numbers and spreadsheets, casually categorized as “research,” and said research is usually conducted on the margins of what is both relevant and socially acceptable.

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2 comments on “Regressed WAR: An Introduction
  1. Kevin J. Jamison says:

    Good work, I like it!

    I don’t quite understand how this is different from a projection system though. Don’t projection systems use multiple years worth of data and try to remove outliers?

    I think the next steps would be to optimize the variables that you assigned arbitrary values to (like using three years worth of data, weighing the years equally, weighing the current system up to 50%, using 3000 innings as a breakpoint, etc). I think a lot of good work can be build on this framework.

    • srbrown70 says:

      The main difference in this and a projection system is the much greater dependence upon this year’s results. If a guy has a 25% line drive rate this year, regWAR gives him credit for it, while a projection system may not that it’s unsustainable and predict it to be maybe around 20% next year. Essentially, a projection system is regressing process, but this is regressing results. If that makes sense.

      I completely agree with everything in the second part of your response. Those numbers were kind of used to just throw the thing together based on things I’d read about the reliability of UZR, BABIP, and xBABIP. I’m not sure how to really nail down what the constants need to be yet, so I’ll have to do some more research into this sort of thing.

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  1. […] with is what I’m calling Regressed WAR. Some of you may remember that I already tried this once, but my original methods were overly complicated so I thought it best to give it another […]

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