So, last week I introduced my statistic OARA and the concept of assigning blame for games to a pitcher or an opponent. In general, the idea was that we wanted to adjust the amount of runs a pitcher allows in a game for the quality of the offense that it faces.

While some writers here expressed some interest in this statistic for all pitchers, I'm still in the process of getting all the data necessary. So, in the meantime, I decided to apply this idea to expected wins.

The idea here is similar to the creation of OARA. We assign the result of each game, in terms of runs scored and runs allowed, to either the team that we're calculating expected wins for or their opponent with some probability. Once we have this probability, we can scale the actual number of runs scored to how many runs we'll "blame" the team for.

Before continuing further into the expected wins portion, allow me to say that this whole idea of adjusting for opponents abilities can be extended to any statistic. The hierarchy seen in the previous article can be applied to find a reasonably opponent-neutral version of the statistic.

Back to the expected wins. Now, as before, we assume the runs scored or allowed in a game is a mixture of two Poisson distributions, with λ values (Roughly the average runs per game) controlled by either the team of interest or the opponent. However, for the pitching team's λ, we need to account for the game's starter and then that team's bullpen. Why don't we account directly for the pitcher's used out of the bullpen? Mainly because there is the problem of when pitchers enter but do not record an out. They then wouldn't be included in the λ calculation. So, in the end we'll have

λ_{Pitching Team} = R_{Starter}*IP_{Starter}/IP + R_{Bullpen}*(IP-IP_{Starter})/IP

Where any R value is the R/9 value for either the starter or bullpen, and the IP_{Starter} is the innings pitched by the starter in that game.

We then apply our hierarchy to both runs scored and runs allowed in order to get the probability of blame for the game's result.

RA_{i}|z_{i} ~ z_{i} Pois(λ_{Team,i}) + (1-z_{i}) Pois(λ_{Opponent,i})

z_{i}|p ~ Bern(p)

p ~ Beta(1,1)

RS_{i}|z_{i} ~ z_{i} Pois(λ_{Team}) + (1-z_{i}) Pois(λ_{Opponent,i})

z_{i}|p ~ Bern(p)

p ~ Beta(1,1)

λ_{Team} ~ Γ(a_{P},b_{P})

From there, we calculate the Opponent Adjusted Runs Scored and Allowed for each team as follows.

Σ_{i} (RS_{i}-RS_{League})× P(z_{i}=1)+700

Σ_{i} (RA_{i}-RA_{League})× P(z_{i}=0)+700

Using this, we can calculate the Pythagorean Expectation as usually done. This calculated OAEW% (Opponent Adjusted Expected Win Percentage) could roughly be interpreted as how well you'd expect a team to do after the you adjust their runs scored/allowed for the opponent faced during the year.

### 2012: Baltimore and Cincinnati

So, of course, we want to test out this idea on the 2012 season. Again, due to data gathering complications, this hasn't been calculated for all 2012 teams. In this case, we're looking at only 2 teams from 2012: the Baltimore Orioles and Cincinnati Reds. In 2012, the Orioles scored 4.4 R/9 and allowed 4.35 R/9 for a Pythagorean Expectation of 82-80 (With a real record of 93-69). Cincinnati went 97-65 scored 4.13 R/9 and allowed 3.63 R/9, leading to a Pythagorean Expectation of 91-71.

However, Cincinnati's competition was a little worse than Baltimore. Baltimore's opponents (after taking starters faced into account) allowed an average of 4.25 R/9, while Cincinnati faced opponents with an average of 4.43. Further, Baltimore's opponents scored an average of 4.45 R/9, while Cincinnati's scored an average of 4.22. This isn't to knock the Reds. They are decidedly an excellent team, but Baltimore was also very good. Against neutral competition, they might be expected to have similar records.

The numbers appear to bear this out. After adjusting for opponent, Baltimore allowed 646.63 runs, while scoring 780.47. This leads to a Pythagorean Expectation of a .584 win percentage. Meanwhile, Cincinnati adjusts to 652.19 runs scored and 566 runs allowed, for a Pythagorean Expectation of .560. This might be a slightly extreme switch, but it reflect the difference in opponent for the two teams.

So, once again, it seems clear that adjusting for opponent can shed light on the ability of teams versus neutral competition. While it sometimes can have surprising results, it should be able to show us a truer, more opponent-neutral indication of how good a team is. As a side note, I plan on having my full OARA leaderboard for 2012 put together by next week.