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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