Monday, July 11, 2005

Yankees Lose!!!
The, THE, THE
Yankees Lose!!
*

It's the All Star break, which makes it a good time to take stock of the season so far. Here are the standings after Sunday night's games:

2005 American League Standings
 
EAST W L PCT GB RS RA
Boston 49 38 0.56322 0.0 473 429
Baltimore 47 40 0.54023 2.0 431 409
NY Yankees 46 40 0.53488 2.5 478 431
Toronto 44 44 0.50000 5.5 428 381
Tampa Bay 28 61 0.31461 22.0 399 553
 
CENTRAL W L PCT GB RS RA
Chicago Sox 57 29 0.66279 0.0 413 339
Minnesota 48 38 0.55814 9.0 396 360
Cleveland 47 41 0.53409 11.0 406 365
Detroit 42 44 0.48837 15.0 387 375
Kansas City 30 57 0.34483 27.5 376 485
 
WEST W L PCT GB RS RA
LA Angels 52 36 0.59091 0.0 420 355
Texas 46 40 0.53488 5.0 476 430
Oakland 44 43 0.50575 7.5 400 386
Seattle 39 48 0.44828 12.5 377 388
 
2005 National League Standings
EAST W L PCT GB RS RA
Washington 52 36 0.59091 0.0 357 361
Atlanta 50 39 0.56180 2.5 428 348
Florida 44 42 0.51163 7.0 383 368
Philadelphia 45 44 0.50562 7.5 410 417
NY Mets 44 44 0.50000 8.0 387 381
 
CENTRAL W L PCT GB RS RA
St. Louis 56 32 0.63636 0.0 447 340
Houston 44 43 0.50575 11.5 365 362
Chicago Cubs 43 44 0.49425 12.5 394 394
Milwaukee 42 46 0.47727 14.0 392 374
Pittsburgh 39 48 0.44828 16.5 365 403
Cincinnati 35 53 0.39773 21.0 434 518
 
WEST W L PCT GB RS RA
San Diego 48 41 0.53933 0.0 406 385
Arizona 43 47 0.47778 5.5 394 479
LA Dodgers 40 48 0.45455 7.5 384 422
San Francisco 37 50 0.42529 10.0 393 457
Colorado 31 56 0.35632 16.0 389 493

In the above table, "RS" and "RA" stand for "Runs Scored" and "Runs Allowed," respectively. More on that later.

From the standings, we see that there isn't any contest in either the AL or NL Central divisions, that the AL and NL West are, if not wrapped up, at least uninteresting for the moment, and that the most exciting baseball is being played in the AL East, closely followed by the NL East, where the Nationals are surprisingly in first place.

And "if the playoffs started tomorrow" we'd have Minnesota and Atlanta as the Wild Cards, and the Yankees would be out of the playoffs. (Yankees delenda est!)

Now one of the rules of baseball is that to win you have to score more runs than your opponent. If we look at the above table, you'll note that the Washington Nationals, though in first place in the NL East, have been outscored 361-357, even though they are 16 games over 0.500. What this means is that the Nationals are winning close games (except this last week) and losing blowouts. This is Not a Good Thing for Nats fans, because the winner of a one-run game is determined mostly by luck.

This is quantified by what is known as the the Pythagorean Method, which in its simplest form says that the fraction of games a team should win is related to RS and RA by the formula:

Pct. = RA2 /(RA2 + RS2)

So what would the Pythagorean rule say about this season? Let's calculate how the standings would look if each team won and lost according the to above equation:

2005 American League Standings
EAST RS RA PW PL Pct. PGB
Toronto 428 381 49.0953 38.9047 0.55790 0.0000
NY Yankees 478 431 47.4348 38.5652 0.55157 0.6605
Boston 473 429 47.7338 39.2662 0.54866 0.8615
Baltimore 431 409 45.7770 41.2230 0.52617 2.8183
Tampa Bay 399 553 30.4701 58.5299 0.34236 19.1252
 
CENTRAL RS RA PW PL Pct. PGB
Chicago Sox 413 339 51.3816 34.6184 0.59746 0.0000
Cleveland 406 365 48.6664 39.3336 0.55303 3.7152
Minnesota 396 360 47.0860 38.9140 0.54751 4.2956
Detroit 387 375 44.3540 41.6460 0.51574 7.0276
Kansas City 376 485 32.6598 54.3402 0.37540 19.2218
 
WEST RS RA PW PL Pct. PGB
LA Angels 420 355 51.3291 36.6709 0.58329 0.0000
Texas 476 430 47.3552 38.6448 0.55064 2.9739
Oakland 400 386 45.0491 41.9509 0.51781 5.7800
Seattle 377 388 42.2493 44.7507 0.48562 8.5798
 
2005 National League Standings
EAST RS RA PW PL Pct. PGB
Atlanta 428 348 53.5788 35.4212 0.60201 0.0000
Florida 383 368 44.7170 41.2830 0.51997 7.3617
NY Mets 387 381 44.6875 43.3125 0.50781 8.3913
Washington 357 361 43.5098 44.4902 0.49443 9.5690
Philadelphia 410 417 43.7467 45.2533 0.49154 9.8320
 
CENTRAL RS RA PW PL Pct. PGB
St. Louis 447 340 55.7473 32.2527 0.63349 0.0000
Milwaukee 392 374 46.0667 41.9333 0.52349 9.6805
Houston 365 362 43.8590 43.1410 0.50413 11.3883
Chicago Cubs 394 394 43.5000 43.5000 0.50000 11.7473
Pittsburgh 365 403 39.2058 47.7942 0.45064 16.0414
Cincinnati 434 518 36.2953 51.7047 0.41245 19.4520
 
WEST RS RA PW PL Pct. PGB
San Diego 406 385 46.8612 42.1388 0.52653 0.0000
LA Dodgers 384 422 39.8603 48.1397 0.45296 6.5008
San Francisco 393 457 36.9863 50.0137 0.42513 8.8748
Arizona 394 479 36.3194 53.6806 0.40355 11.0418
Colorado 389 493 33.3822 53.6178 0.38370 12.4790

Here "PW" and "PL" are the wins and losses as predicted by they Pythagorean rule, and yes, I've kept way to many decimal places. (You'll note that the total number of wins in this table isn't equal to the total number of losses. That's because the Pythagorean rule is applied on a per-team basis, so a win for one team isn't necessarily a loss for another team.)

For the Central and Western divisions of both leagues these results are essentially the same as the actual records. In the Easts, however, things are drastically different. For one thing, Toronto is actually a very good ballclub, ten games above 0.500. The Yankees aren't doing as badly as Mr. Steinbrenner thinks, they're in contention for the Wild Card. And in the NL, Atlanta is in its accustomed place, and Washington is at about 0.500.

Of course, what this tells us is that the Pythagorean rule isn't exact, and will have some discrepancies, especially over only a portion of a season. But it does suggest that the Nationals have been playing over their heads, as anyone who watched the games with the Mets and the Phillies will attest, and that the AL East is going to be very interesting.

OK, now for the fun part: Let's assume that for the rest of the year teams will win at their current Pythagorean rate, but, of course, keep the wins they already have. Then we get the following standings:

2005 American League Standings
EAST W L Pct. GB
Boston 90.1499 71.8501 0.55648 0.0000
NY Yankees 87.9191 74.0809 0.54271 2.2307
Baltimore 86.4629 75.5371 0.53372 3.6869
Toronto 85.2847 76.7153 0.52645 4.8652
Tampa Bay 52.9923 109.0077 0.32711 37.1575
 
CENTRAL W L Pct. GB
Chicago Sox 102.4070 59.5930 0.63214 0.0000
Minnesota 89.6109 72.3891 0.55315 12.7961
Cleveland 87.9241 74.0759 0.54274 14.4829
Detroit 81.1966 80.8034 0.50121 21.2104
Kansas City 58.1550 103.8450 0.35898 44.2520
 
WEST W L Pct. GB
LA Angels 95.1631 66.8369 0.58743 0.0000
Texas 87.8488 74.1512 0.54228 7.3143
Oakland 82.8355 79.1645 0.51133 12.3276
Seattle 75.4218 86.5782 0.46557 19.7413
 
2005 National League Standings
EAST W L Pct. GB
Atlanta 93.9466 68.0534 0.57992 0.0000
Washington 88.5878 73.4122 0.54684 5.3589
Florida 83.5174 78.4826 0.51554 10.4293
NY Mets 81.5781 80.4219 0.50357 12.3685
Philadelphia 80.8821 81.1179 0.49927 13.0645
 
CENTRAL W L Pct. GB
St. Louis 102.8784 59.1216 0.63505 0.0000
Houston 81.8095 80.1905 0.50500 21.0689
Milwaukee 80.7379 81.2621 0.49838 22.1404
Chicago Cubs 80.5000 81.5000 0.49691 22.3784
Pittsburgh 72.7981 89.2019 0.44937 30.0803
Cincinnati 65.5210 96.4790 0.40445 37.3574
 
WEST W L Pct. GB
San Diego 86.4367 75.5633 0.53356 0.0000
LA Dodgers 73.5189 88.4811 0.45382 12.9178
Arizona 72.0555 89.9445 0.44479 14.3812
San Francisco 68.8848 93.1152 0.42521 17.5519
Colorado 59.7777 102.2223 0.36900 26.6590

Based on these predictions, Atlanta will keep its accustomed first place in the NL East, Washington is a good shot for the Wild Card, just because they've won so many games in the first half of the season. And Boston and Minnesota will hold one to the AL East and the Wild Card to (yeah!) keep the Yankees out of the postseason.

Of course, these projections are just that, projections, and aren't a guarantee of anything. Don't even think about using these to place bets. At the end of the season we'll see how well these predictions stack up.


* I could not love baseball so much, did I not hate the Yankees more.

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