The standings present multiple realities.
At the top, of course, there is the genuine reality, the bottom line, the real deal, terra firma: the actual wins and losses of each team. To a statistician, the actual results are just a little boring: they don’t necessarily reflect the likelihoods that this particular result would happen. The Indians, for instance, are 7-20, as of this morning. Ho-hum.
So the second reality, or the first alternate reality, is found by looking at how many games the team should have won, given how many runs they scored and allowed. There are plenty of ways to make that estimate–Rob Neyer, for one, regularly tracks the standings using Bill James’ “Pythagorean” theorem (in fact, Rob recently wrote an article on pretty much exactly what I’m doing here–and believe it or not, I didn’t read that article until after I’d finished drafting this. It must have been in the air). We’ll be just a little different.
The so-called “Pythagenport” method (I didn’t name it; I think you have to blame one of the Keiths) expands on James’ Pythagorean method by making the exponent a function of run scoring instead of a constant. In the range of run scoring that any team, even the Tigers, is going to see this year, the diference is trivial, although if you were ever considering applying them to your slow-pitch softball team it would make a much bigger difference. These projected wins are what we’ll call “first-order” wins. Looking at the Indians once more, they have scored 91 runs while giving up 132. The Pythagenport calculation says that should have produced 9 wins in 27 games, not seven; they have been a little unlucky (and yes, luck may have had nothing to do with it. As a shorthand explanation for the difference, “luck” is as good a label as any.)
The difference between projected wins and actual wins is only one type of apparently random fluctuation in baseball stats. A second alternate reality comes from substituting projected run scoring for actual runs. Now we’re going back to the basic statistical lines, for both the offensive and defensive sides, figuring how many runs you’d normally get from those, and using those runs in the Pythagenport calculation. These are the second-order wins. Consider those Indians again. They’ve scored 91 runs, but their stats say they should have been expected to score 106–a 15-run deficit that we’ll once again call bad luck. Their pitchers have allowed 132 runs, and should have allowed 135–so they get three runs of good luck back. Their projected run totals, 106 scored and 135 allowed, would suggest 10.5 wins in 27 decisions. Their inability to score as many runs as expected compounds their inability to win as often as expected, and now their luck deficit is up to 3.5 games.
But wait, as the Ronco ads say, there’s more. There’s another kind of luck that has nothing to do with meeting or failing to meet expectations: the luck of the schedule. Sure, your hitting may look awful, but if you’ve spent the year so far going up against the As and Royals and Yankees, while missing out on the Devil Rays and Rangers…then that’s hardly a surprise. Moreover, it isn’t something that will even out over the course of the year. Not having to face your own teammates makes it likely that Yankee pitchers will have faced a below-average cast of hitters when the season is said and done, and sharing a division with powerhouse offenses will hurt everybody in the AL West.
The final permutation we’ll put on these standings, then, is to adjust everybody’s quality of opposition up or down to average. Michael Wolverton did something similar to this, in the Rangers’ essay in Baseball Prospectus 2003, and now we’ll set it up to work every day. Using the Indians for our example once more, they have only played two games against a team who has been below average in pitching this year: seven games against the White Sox, who have held teams to a .239 EQA so far this year, six against KC (.233), six against Baltimore (.253), three each against Seattle (.249) and Oakland (.226), and two games against the Angels, who are below average by a sliver of a fraction, with a .260 EQA against.
All in all, Cleveland’s opponents have an average EQA allowed of .242. Yes, part of that is circular (they are pitching well because they have faced Cleveland, who’s poor hitting makes their pitching look good), but that part will even out as the season progresses. Now, if the Indians can score 106 runs against a set of .242 pitchers, it is easy to figure out how many they should score against a group of average, .260 pitchers – 106 * (260/242)^2.5 = 127 runs. When you do the same sort of analysis for their pitchers, there isn’t as much to change–Cleveland’s opponents have hit a nearly-average .259, so their runs allowed only gets adjusted from 135 to 137.
Our third alternate reality–and, mercifully, that’s as far as I’m going–comes from running the Pythagenport formula on the strength-of-schedule adjusted estimates of 127 runs scored and 137 allowed. In our alternative universe, the Indians win 12.5 and lose 14.5. They are a nearly .500 team, who have been bedeviled by bad luck at every step between our universe and the alternate one–in fact, they’ve been the unluckiest team in baseball to date.
Reality Alternative #1 Alternative #2
Team W L RS RA W1 L1 EQR EQRA W2 L2
----------------------------------------------------------------
Yankees 21 6 178 99 20.5 6.5 190 105 20.7 6.3
Red_Sox 18 9 159 144 14.9 12.1 156 140 14.9 12.1
Blue_Jays 10 18 153 186 11.2 16.8 153 188 11.0 17.0
Orioles 13 12 126 120 13.1 11.9 114 110 13.0 12.0
Devil_Rays 10 17 124 166 9.7 17.3 121 163 9.7 17.3
Reality Alternative #3 Differences
Team W L AEQR AEQRA W3 L3 D1 D2 D3
-----------------------------------------------------------
Yankees 21 6 172 107 19.4 7.6 0.5 0.3 1.6
Red_Sox 18 9 135 138 13.2 13.8 3.1 3.1 4.8
Blue_Jays 10 18 165 171 13.5 14.5 -1.2 -1.0 -3.5
Orioles 13 12 104 121 10.8 14.2 -0.1 0.0 2.2
Devil_Rays 10 17 126 148 11.4 15.6 0.3 0.3 -1.4
The Red Sox have been very lucky so far this season–the second luckiest team in the majors, who by the numbers should be below .500. Toronto is 8.5 games behind them, and the entire difference can be explained by the differences in luck, not baseline performance.
Team W L RS RA W1 L1 EQR EQRA W2 L2 ------------------------------------------------------------------ Royals 17 7 125 95 15.0 9.0 125 96 15.0 9.0 Twins 12 14 101 114 11.6 14.4 103 106 12.6 13.4 White_Sox 14 13 119 106 14.9 12.1 121 109 14.8 12.2 Indians 7 20 91 132 9.1 17.9 106 135 10.5 16.5 Tigers 3 21 55 127 4.4 19.6 51 127 4.0 20.0 Team W L AEQR AEQRA W3 L3 D1 D2 D3 ------------------------------------------------------------ Royals 17 7 122 119 12.4 11.6 2.0 2.0 4.6 Twins 12 14 99 107 12.1 13.9 0.4 -0.6 -0.1 White_Sox 14 13 129 138 12.6 14.4 -0.9 -0.8 1.4 Indians 7 20 127 137 12.5 14.5 -2.1 -3.5 -5.5 Tigers 3 21 63 136 4.8 19.2 -1.4 -1.0 -1.8
Kansas City’s luck has been shifting back towards average, what with blowing two ninth-inning leads this week, and they remain the only team in the Central who deserve a .500 record – but they still have had a lot of luck on their side. The objects in their rear view mirror are closer than they appear – except for the Tigers, who have been a little unlucky, but have been genuinely bad nonetheless.
Team W L RS RA W1 L1 EQR EQRA W2 L2 ----------------------------------------------------------------- Athletics 17 10 133 96 17.4 9.6 129 94 17.4 9.6 Angels 13 14 140 127 14.8 12.2 138 135 13.8 13.2 Mariners 17 10 132 104 16.4 10.6 132 112 15.6 11.4 Rangers 13 14 147 167 11.7 15.3 158 170 12.5 14.5 Team W L AEQR AEQRA W3 L3 D1 D2 D3 ------------------------------------------------------------ Athletics 17 10 125 97 16.6 10.4 -0.4 -0.4 0.4 Angels 13 14 144 122 15.6 11.4 -1.8 -0.8 -2.6 Mariners 17 10 135 114 15.6 11.4 0.6 1.4 1.4 Rangers 13 14 173 154 15.1 11.9 1.3 0.5 -2.1
Throw a towel in and everybody’s covered.
Team W L RS RA W1 L1 EQR EQRA W2 L2 ---------------------------------------------------------------- Braves 17 10 132 132 13.5 13.5 140 123 15.2 11.8 Phillies 16 12 147 105 18.3 9.7 131 110 16.2 11.8 Marlins 14 15 137 150 13.2 15.8 151 146 15.0 14.0 Expos 17 10 124 93 16.9 10.1 119 107 14.8 12.2 Mets 11 16 97 138 9.2 17.8 94 142 8.6 18.4 Team W L AEQR AEQRA W3 L3 D1 D2 D3 ------------------------------------------------------------- Braves 17 10 139 114 16.0 11.0 3.5 1.8 1.0 Phillies 16 12 126 103 16.5 11.5 -2.3 -0.2 -0.5 Marlins 14 15 144 141 14.8 14.2 0.8 -1.0 -0.8 Expos 17 10 110 111 13.4 13.6 0.1 2.2 3.6 Mets 11 16 101 138 9.6 17.4 1.8 2.4 1.4
The first-place Montreal Expos have been one of the luckier teams in the majors, especially with their runs allowed, but they are at least part of the peloton–unlike the Mets.
Team W L RS RA W1 L1 EQR EQRA W2 L2 ----------------------------------------------------------------- Cubs 15 12 150 109 17.5 9.5 134 91 18.1 8.9 Cardinals 13 12 156 114 16.3 8.7 159 124 15.6 9.4 Pirates 12 14 101 105 12.5 13.5 96 96 13.0 13.0 Astros 11 15 108 127 11.0 15.0 120 122 12.8 13.2 Brewers 9 18 109 150 9.5 17.5 117 157 9.7 17.3 Reds 11 16 132 187 8.9 18.1 121 172 8.9 18.1 Team W L AEQR AEQRA W3 L3 D1 D2 D3 ------------------------------------------------------------ Cubs 15 12 124 97 16.4 10.6 -2.5 -3.1 -1.4 Cardinals 13 12 144 124 14.4 10.6 -3.3 -2.6 -1.4 Pirates 12 14 92 94 12.8 13.2 -0.5 -1.0 -0.8 Astros 11 15 107 114 12.2 13.8 0.0 -1.8 -1.2 Brewers 9 18 119 145 10.9 16.1 -0.5 -0.7 -1.9 Reds 11 16 136 169 10.6 16.4 2.1 2.1 0.4
In the NL Central, everybody’s luck is pretty much even and its all bad (except for the Reds, but their bad luck has come in other guises).
Team W L RS RA W1 L1 EQR EQRA W2 L2 ---------------------------------------------------------------- Rockies 15 12 173 155 15.0 12.0 162 150 14.5 12.5 Giants 19 7 132 109 15.3 10.7 131 123 13.8 12.2 Dodgers 14 14 103 85 16.3 11.7 107 97 15.3 12.7 Diamondbacks 12 16 109 119 12.9 15.1 120 124 13.7 14.3 Padres 10 17 107 139 10.2 16.8 117 135 11.7 15.3 Team W L AEQR AEQRA W3 L3 D1 D2 D3 ----------------------------------------------------------- Rockies 15 12 160 147 14.7 12.3 0.0 0.5 0.3 Giants 19 7 135 127 13.7 12.3 3.7 5.2 5.3 Dodgers 14 14 101 96 14.6 13.4 -2.3 -1.3 -0.6 Diamondbacks 12 16 117 119 13.7 14.3 -0.9 -1.7 -1.7 Padres 10 17 119 129 12.5 14.5 -0.2 -1.7 -2.5
Where the Indians were the unluckiest team in baseball, the Giants have been the luckiest. While they’ve allowed 14 fewer runs than expected, tied with the Expos for best in that category, the largest component has been getting more wins for their runs.
Terms:
- W, L: Actual team wins and losses.
- RS, RA: Actual team runs scored and runs allowed.
- W1, L1 (“First-order wins”): Pythagenport expected wins and losses, based on RS and RA.
- EQR, EQRA: Equivalent Runs scored and equivalent runs allowed (equivalent runs, generated from the opponent’s batting line)
- W2, L2 (“Second-order wins”): Pythagenport wins and losses, based on EQR and EQRA.
- AEQR, AEQRA: EQR and EQRA, adjusted for the quality of their opponent’s pitching and hitting.
- W3, L3 (“Third-order wins”): Pythagenport wins and losses, based on AEQR and AEQRA.
- D1, D2, D3: Deltas between actual wins and W1, W2, and W3. Positive numbers
mean the team has won more games than expected from their statistics.
Thank you for reading
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