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March 31, 2006

Probability and Possibility

The Odds Report Tackles the 2006 Season

by Clay Davenport

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On Wednesday, Nate broke hearts, letting a cruel PECOTA loose to smack down the dreams and fantasies of fans across the country. There, there…Clay is here to make it all better.

PECOTA, you see, uses a "most likely" to set the value of all the players and teams. "Most likely," though, is very different from "only." For the last couple of years, we've been running a product called the Postseason Odds Report. We've used it to to evaluate a team at any point in mid-season, and to play out the remainder of schedule a million times, to estimate the likelihood that the team will make the playoffs.

It doesn't take a lot of brain power to realize that what can be done in mid-season can also be done in pre-season. It is also a pretty short leap to go from using Adjusted Standings to using the PECOTA-based estimate as a stand-in for them. What we find is that there is hope for everyone (even the Royals) when we apply some random numbers, and get to see the difference between probabilities and possibilities.

Average wins by position in AL Central: 103.1 91.3 81.7 72.6 60.8

AL East            W    L   Pct3  Avg W  Avg L  Champions  Wild Card   Playoffs
Yankees           94   68  0.580   94.2   67.8   43.28778   15.72260   59.01038
Red_Sox           93   69  0.574   93.3   68.7   39.77486   16.22681   56.00166
Blue_Jays         79   83  0.488   78.1   83.9    8.31576    6.89441   15.21017
Orioles           77   85  0.475   76.3   85.7    6.62935    5.73227   12.36162
Devil_Rays        69   93  0.426   67.6   94.4    1.99225    1.87677    3.86901
The "W" and "L" columns are the records Nate gave us yesterday. "Avg W" and "Avg L" are the results of the simulation, along with the percentage of the time the team won the division championship, or made the wild card, along with the combined playoff likelihood.

Yes, it is a ridiculous degree of precision. All it is is the actual number of times the team won in the million-run simulation. The Yankees won the title 432,877.8 times--yes, .8 times; sometimes, you finish in a tie, and that's why there's an extra decimal place. The Yankees and Red Sox are clearly favorites, but are hardly locks. It is interesting that even though no team is expected to average more than 94 wins, the winner of the division (whoever it might be) is expected to win over 100. That isn't as unreasonable as it sounds; the team that ends up winning is liable to be whichever team exceeds expectations, not just simply meets them.

Average wins by position in AL Central: 99.3 88.9 80.8 71.8 56.4

AL Central         W    L   Pct3  Avg W  Avg L  Champions  Wild Card   Playoffs
Indians           88   74  0.543   88.5   73.5   35.20064    8.78274   43.98338
Twins             84   78  0.519   84.2   77.8   23.49712    7.77191   31.26903
Tigers            83   79  0.512   83.1   78.9   21.08707    7.27850   28.36557
White_Sox         82   80  0.506   82.3   79.7   19.38250    6.92247   26.30498
Royals            61  101  0.377   59.2  102.8    0.83267    0.34850    1.18117
The AL Central is baseball's most even division--no other division can boast four teams with a 25% chance of making the playoffs. Yet believe it or not, the odds say that once every eighty-five years the Royals would be the team that stepped forward. There are a lot of ways a team can get lucky (as seen in the White Sox chapter of this year's book); players can play over their own heads, they can get lucky in converting hits into runs and runs into wins. KC not only needs all of those things to happen, but for the other four teams to play under their expectations. One time in 85, all of those things happen. The other 84 times, it's anybody's race.

Average wins by position in AL west: 99.0 86.6 77.2 66.1

AL West            W    L   Pct3  Avg W  Avg L  Champions  Wild Card   Playoffs
Athletics         93   69  0.574   93.2   68.8   56.29157    6.59269   62.88426
Angels            81   81  0.500   80.6   81.4   17.79706    6.24361   24.04066
Rangers           80   82  0.494   78.9   83.1   14.87564    5.44827   20.32391
Mariners          77   85  0.475   76.2   85.8   11.03572    4.15847   15.19420
The A's have the (un?)enviable position of entering the season as the biggest favorite--the only team that rates a 50% chance of winning their division. The other teams are all about even--their chances come from those simulations where the A's collapse. After all, somebody has to win the division, no matter what.

Average wins by position in NL East: 99.7 89.1 80.7 71.9 60.6

NL East            W    L   Pct3  Avg W  Avg L  Champions  Wild Card   Playoffs
Mets              88   74  0.543   88.7   73.3   34.87073    9.38327   44.25401
Phillies          86   76  0.531   86.7   75.3   29.17462    9.02598   38.20060
Braves            85   77  0.525   85.9   76.1   26.90155    8.85743   35.75898
Marlins           71   91  0.438   70.8   91.2    4.86164    2.14093    7.00258
Nationals         70   92  0.432   69.7   92.3    4.19146    1.88337    6.07483
Three teams pretty much split the pot, with scant (but non-zero!) chances for the remaining two. The Marlins and Nationals rank as the third- and fourth-worst teams in PECOTA's rankings; being in the same division makes it fairly likely that one of them (at least) will underperform and lose 100 games.

Average wins by position in NL Central: 100.5 91.5 85.2 79.3 73.0 64.0

NL Central         W    L   Pct3  Avg W  Avg L  Champions  Wild Card   Playoffs
Cardinals         86   76  0.531   86.8   75.2   25.60775   10.19374   35.80149
Cubs              85   77  0.525   84.8   77.2   20.92252    9.30203   30.22454
Brewers           84   78  0.519   84.3   77.7   19.73443    9.14919   28.88363
Astros            81   81  0.500   81.4   80.6   14.15639    7.53457   21.69096
Pirates           79   83  0.488   78.7   83.3   10.36314    6.04375   16.40689
Reds              78   84  0.481   77.5   84.5    9.21577    5.28132   14.49708
The NL Central features the major league's weakest favorite, the Cardinals, tipping the scales at not quite 36%. The range, just 2.5x from top to bottom, also makes this the tightest division, at least on the average; as you can see by the rankings, real life will probably stretch things out a bit.

Average wins by position in NL West: 97.4 87.2 79.7 72.3 62.4

NL West            W    L   Pct3  Avg W  Avg L  Champions  Wild Card   Playoffs
Dodgers           87   75  0.537   88.2   73.8   40.46942    5.97881   46.44822
Giants            80   82  0.494   80.4   81.6   19.46346    4.71041   24.17387
Padres            78   84  0.481   78.5   83.5   15.81572    4.09959   19.91531
Diamondbacks      77   85  0.475   77.6   84.4   14.40048    3.79279   18.19327
Rockies           74   88  0.457   74.2   87.8    9.85092    2.62281   12.47373
Out west, the Dodgers are set to be the favorite team in the National League. That doesn't mean they'll win, and it doesn't mean that they've choked if they don't. Life is a lot less deterministic than most of us think, a thought that is profoundly unsettling to many, and so we read meaning and make explanantions and dole out rewards, when the real reason is simply that breaks went their way at the proper time. Life is unpredictable, as are players, teams, and seasons.

And I'm glad they are.

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