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Below are the top 5 relief staffs in MLB. This was computed by adding up all relievers listed for each team and adding their WAAs and innings pitched. WAAs are additive amongst any set of players. The sum of all WAAs for an entire team must and always does (because the formulae have proofs) add up to the W-L delta for a team according to the Pythagorean Expectation derived formula that converts runs into winning percentage.
In this case we chose as our set of players all relievers for each team.
| TeamID | WAA | IP |
| SDN | 8.7 | 339.6 |
| SEA | 7.3 | 351.4 |
| OAK | 7.1 | 375.9 |
| SFN | 6.6 | 352.3 |
| WAS | 6.0 | 307.9 |
Although San Diego doesn’t have a very good team this year, their relief squad stands out as best in MLB. First let’s do a Winning Percentage calculation for SDN as shown in the previous two posts:
Win% = 0.5*WAA/(number of games played) + 0.5
number of games played = 339.6/9 = 37.7
Winning % = 0.5*(8.7)/(37.7) + 0.5 = 0.615
Here are all relievers registered to having played for SDN this season:
| Rank | WAA | IP | ERA | G | W | L | Name_Tm | Pos |
|---|---|---|---|---|---|---|---|---|
| 1 | 2.2 | 33.0 | 1.09 | 33 | 1 | 0 | Huston_Street_SDN | PITCH |
| 2 | 2.0 | 43.0 | 1.88 | 42 | 4 | 2 | Joaquin_Benoit_SDN | PITCH |
| 3 | 2.0 | 45.0 | 2.00 | 49 | 3 | 3 | Dale_Thayer_SDN | PITCH |
| 4 | 1.5 | 40.0 | 2.25 | 48 | 1 | 0 | Alex_Torres_SDN | PITCH |
| 5 | 1.0 | 32.0 | 2.53 | 34 | 1 | 2 | Kevin_Quackenbush_SDN | PITCH |
| 6 | 0.9 | 21.0 | 2.14 | 17 | 0 | 0 | Blaine_Boyer_SDN | PITCH |
| 7 | 0.7 | 10.3 | 0.87 | 3 | 0 | 1 | Jason_Lane_SDN | PITCH |
| 8 | 0.2 | 7.3 | 2.45 | 8 | 0 | 0 | Troy_Patton_SDN | PITCH |
| 9 | -0.0 | 2.0 | 4.50 | 1 | 0 | 0 | Hector_Ambriz_SDN | PITCH |
| 10 | -0.2 | 43.0 | 3.98 | 28 | 2 | 2 | Tim_Stauffer_SDN | PITCH |
| 11 | -0.7 | 32.7 | 4.68 | 36 | 0 | 2 | Nick_Vincent_SDN | PITCH |
| 12 | -0.7 | 30.3 | 4.75 | 16 | 1 | 0 | Donn_Roach_SDN | PITCH |
Perhaps the biggest advantage the WAA weighting has over any other measure in baseball Sabermetrics is its ability to accurately compare not only individual players but sets of players; in this case each team’s relief staff.
In the last few posts we showed how to calculate winning % for a starting pitcher, an entire relief staff backing him up, and a batting lineup. We can take a harmonic mean of 2/3 starting pitcher to 1/3 relief staff winning percentages to get a pitching component percentage. Then we can take a harmonic mean of pitching and batting (lineup) components to get an overall winning percentage for a particular day. Compare this with the winning percentage derived for an opposing team and it’s possible to estimate a winning probability for each team where:
P(home team) + P(away team) = 1
But this is fodder for a future post. The WAA weighting value derived from this data model makes it possible to make these kinds of calculations.
Update 8/22/2018: We’re from the future to correct the above. It was unclear when the above was written how to take relief value, lineup value, and starter value to compute a probability. The above is not how it’s done. If was attempted but it could never pass the historical test against a past lines dataset. WinPct is included to provide context for the WAA value used for ranking.