Tuesday, January 09, 2024
Explaining WAR simply
In the 1987 Baseball Abstract, Bill James invented WAR. He didn't call it that, and it was not WAR per se, but it was 90% of the WAR game. His idea was ridiculously simple, simple enough that you can put it in a tweet. It went like this:
- WAR = IP/9 * (lgERA + 1 - ERA) / 10
He actually didn't have that divideby-10, so it's really RAR (runs above replacement) that he introduced.
A few years earlier, Pete Palmer introduced WAA (wins above average). It was even simpler:
- WAA = IP/9 * (lgERA - ERA) / 10
Notice the difference? That "plus 1"? Yes, the entire dispute in the 1980s and 1990s between Bill James and Pete Palmer was that plus 1. Most of you who weren't around may not have realized that my heroes, the friendly group that started sabermetrics to begin with, could not see eye to eye here.
The solution that would have put them on the same page would have been to turn their WAR and WAA creations into Individualized Won Loss Records. Had they done that, they would have not only been on the same page, they could have likely co-authored books. But alas, it was not meant to be. Their dispute basically opened up the doors for the rest of us to fill in the gap.
Anyway, where was I? Oh, yes, explaining WAR simply. First, let's explain Wins Above Average. So, I said this:
- WAA = IP/9 * (lgERA - ERA) / 10
Let's break that down. What is IP/9? That is simply number of games. Throw 9 innings, and that counts as 1 full game. Throw 90 innings, and that's the equivalent to 10 full games. 180 innings is 20 games, and 225 innings is 25 games. We don't really care if 225 innings is spread out over 25 actual games or 35 actual games. We're just interested in full-time equivalent games. Ok, so, that's IP/9.
What is lgERA - ERA? Well, ERA is earned runs allowed per 9 innings (or per full-time equivalent game). lgERA is the League ERA. So, lgERA minus ERA is how much better a pitcher's ERA is compared to the league. If the league ERA is 4.00 and the pitcher's ERA is 2.50, then the pitcher is +1.50 ERA better than the league, or +1.5 runs per game better than the league.
So, when we multiply IP/9 (or number of games) by lgERA - ERA (or runs above average per game), we are left with total runs above average. A pitcher with 180 innings (or 20 games) with a 2.5 ERA in a 4.00 league (or +1.5 runs per game) is worth 20 x 1.5 = 30 runs above average.
Finally that divide by 10 is to convert runs into wins. Being 30 runs above average is equivalent to 3 wins above average. Or 3 WAA.
Now, you might see the problem with WAA. Actually, it's not a problem, but a limitation. When you are below average, but still eating innings, you will have a negative number. And the more innings you eat, the more negative your number. Given that teams pay alot of money for an average pitcher, and still a substantial amount for a below average pitcher, showing a negative number in the form of WAA for a pitcher who is actively contributing seems odd. That was Bill's point.
Pete chose league average as his "zero" point. That's how it works when you compare to average. But, we want zero to represent something else: no value. And to do that, you have to figure out the point at which a pitcher is so bad that he is actually not contributing anything. And that's where that "plus 1" in Bill's version comes into play.
Pete had this:
- (lgERA - ERA)
Bill proposed this:
- (lgERA + 1 - ERA)
So, instead of comparing a pitcher to the league average, he is being compared to 1 run above the league average. Our 2.50 ERA pitcher, instead of being compared to the 4.00 league ERA is instead compared to the 5.00 "zero baseline" ERA, or the replacement-level ERA. He is now +2.5 runs above replacement. Times those 20 games, and he is +50 runs above replacement (RAR), or 5 WAR.
A league average pitcher with 180 innings would have a 0 WAA and a 2 WAR. How did I get to 2 WAR? 180 innings is 20 games. And his 4.00 ERA, which matches league average, is +1 runs better than replacement. 20 times 1 is 20 RAR, or 2 WAR.
That's it! 90% of WAR can be explained by this:
- WAR = IP/9 * (lgERA + 1 - ERA) / 10
Next time, I'll show you the core basics of WAR as you see it on Baseball Reference, and creating separate standards for starting and relief pitchers. (Update: click here for part 2.)
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