## Saturday, April 28, 2012

### wOBA As A Measure of Success

Weighted On-Base Average (wOBA) is a metric that attempts to measure all the offensive things that can lead to success and boil them down to a number that we recognize, something like a batting average or on-base percentage. You can read more about how it is calculated either here or here, but it boils down to the same basic thing as every other baseball stat--how much did a given activity lead to run production, and ultimately to wins?

I'll take a step back and describe Bill James' Pythagorean Wins formula, which is simply (runs^2)/(runs^2+runs allowed^2), which reduces to a number similar to a winning percentage. All statistical number crunching is working at determining what leads to runs being scored, since no matter what era, if a team scores more runs than its opponents, it will have greater success. If a team averages 4 runs a game and gives up 3.5, the PW formula suggests a winning percentage of (based on a 162-game season) of .533, or a 86-76 record--respectable, perhaps even good enough for a wild card (or, like the 2006 Cardinals, a World Series championship). If a team averages 4 runs a game and gives up 4.5, or a .471 winning percentage, or the exact opposite record--76-86. The following chart shows how well the PW formula matches up with winning percentage for the years 1980-2010--winning percentage was used to smooth out the oddities of the 1981, 1994 and 1995 seasons, all strike-shortened to one degree or another:

Assuming that my chart is in correct proportion along both axes (and I did try), that sure looks like a pretty linear relationship. Another way to explain it would be to state that the greater the run differential (either plus OR minus), the greater the winning (or losing) percentage. It's a pretty easy number to visualize, calculate, and it appears to hold up well with the numbers as they come in.

wOBA uses the following formula (based on the 2010 season, the last for which weights were available:
((uBB*.7+(HBP*.73+(1B*.89)+(2B*1.27+(3B*1.61)+(HR*2.07)+(.25*SB)-(CS*.5))/PA
Using the 2010 Arizona Diamondbacks as an example:
589 BB-45 IBB=518 uBB*.7=380.8
39 HBP*.73=                             28.5
851 1B*.89=                           757.4
301 2B*1.27=                         382.3
34 3B*1.61=                             54.7
180 HR*2.07=                        372.6
86 SB*.25=                               21.5
41 CS*.5=                                 20.5
TOTAL                                   1977.3/6183 PA=.320

You can find this number on FanGraphs (it's not on baseball-reference.com, and there's probably a pretty simple explanation for that), but what you CAN'T find on FanGraphs is the mirror image of this number, the wOBA of the opponents. It's not that hard to derive when the primary data is obtained, and so, in abbreviated form, accept that for the Arizona Diamondbacks, the opponent's wOBA was .340--Diamondback pitchers gave up 510 unintentional walks, 58 HBP, 977 1B, 284 2B, 32 3B and 210 HR, 115 SB and 36 CS in 6260 PA, or a -.020 differential between wOBA and opponent's wOBA. How would THIS stack up in a graph?

Pretty spooky, but also completely logical when you consider it--if a team is giving up more walks and hits than it is creates, it's going to be difficult to win. When you think about it, both these metrics are telling the same story, with wOBA adding some of the context to the PW formula. In the end, it's to the extent that a team can score more runs that it gives up that will determine their ultimate success. Of course, it's totally useless when looking at an individual game or even one postseason series, but it helps us understand how the various parts of the game tie into winning.