You may recall that around this time last year I explained to the world and everyone why I was Through With Pythagoras. I had long given serious attention to the teaching of the old desert sage, but those days were now behind me.
I shall now copy and paste for a while...
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We are more or less agreed that sometimes a team's W-L record doesn't tell their story clear and true. And when it doesn't, we know why. It's because the team's record in either one-run games or blowouts (or both) varies somehow from their performance the rest of the time.
These days even ESPN's home page includes Runs Scored and Allowed and Run Differential. As if that told the story (after all, a run differential of 100 runs in Dodger Stadium is very, very different from the same thing in Coors Field.)
From a team's Runs Scored and Allowed we extrapolate what we have come to call a team's Pythagorean W-L record. This is based entirely - entirely - on the relationship between total Runs Scored and Allowed. As I suppose is generally known, there are two fairly common methods of making that calculation: one involves squaring the numbers involved, while the other uses a component, often 1.83, instead. Whichever you use is entirely up to you. Let me hear no talk of accuracy. Whichever formula you choose generates a fiction, an imaginary W-L record. One fantasy is not more accurate than another. It's all a matter of which one you like best, or which one suits your needs. (As I was generally trying to identify real seasons that didn't tally closely with the actual results, I very much preferred the traditional formula that squared the numbers. If you're looking for seasons that deviate from one's reasonable expectations you don't want to use a method that generates those deviant seasons willy-nilly. Which is what using the component will do.)
Now there are two problems with using one of the Pythagorean formulae to generate a W-L record, as imaginary as it may be.
The first problem is with the blowout games that constitute a significant part of any team's season. It's not that it makes no difference at all whether you win by 6 runs or 12 - but I do suspect that this mostly tells you something about choices made by the losing team when a game gets out of hand rather than anything about the quality of either team. So I think that while a team's record in blowout games is very significant, I don't think a team's Runs Scored and Allowed in those games is nearly as important. And what this means is that the raw data - the Runs Scored and Allowed - that is being fed into the Pythagorean formula of your choice creates its own distortions right from the jump.
The other issue, which I think is much more important, is pretty obvious. Of course it involves my own Great White Whale. But nevertheless, here we go! Because baseball teams play lots of games that are decided by a single run. And even if you do believe that Run Differential and the Pythagorean formula will give you an accurate idea of a team's quality, you still can't apply it to one-run games. You simply can't do that.
Because that's not how one-run games work.
It just isn't. You can't apply a Pythagorean formula to those games. Because in one-run games, the impact of random chance is sufficient to overcome the impact of team quality. You may not be able to win a game by ten runs thanks to a lucky bounce. But you can definitely win by one-run.
This is why the effect of one-run games is to drag every team to the centre. It drags everyone towards .500 - it lifts the bad teams and it lowers the good teams. That's what it does. This is a Law.
This doesn't quite mean that we should set a .500 record in one-run games as a team's expected outcome. The better teams actually do play better in one-run games than the bad teams. It's just that any single season is much, much too short a sample for that result to manifest itself. It would be exactly like assessing a hitter's season on 30 random plate appearances. We need the whole season, we need the 700 plate appearances to have a decent idea. As it happens, that's about how many one-run games it takes for a team's quality to begin to consistently affect that team's record in one-run games.
And even when we have that many games (in truth, the number needed might be closer to 1,000 games) - a team's record in one-run games still isn't going to match whatever Pythagorean projection we had come up with. Because one-run games are still going to drag teams towards .500, however good or bad they may be. That's what they do. It's just that if you play enough of those games, the effect won't be as pronounced. Given enough games, an equilibrium between these two forces is eventually reached, between the the relentless pull towards .500 and the actual quality of the teams.
The effect is always present, and it's generally reliable. To state it very crudely, the .600 teams will play something like .550 ball in one run games, the .550 teams will play something like .530 ball in one-run games, the .450 teams will play something .480 ball in one-run games. There is a reasonable expectation that teams of a specific quality will provide a specific level of performance in one-run games. We know this because we have more than a century of data that tells us so. Here is the data (through 2015)
OVERALL ONE-RUN GAMES OTHER GAMES
Record No. of Teams GPL W L PCT GPL W L PCT GPL W L PCT
.700 plus 10 1,530 1,100 430 .719 393 256 137 .651 1,137 844 293 .742
.650-.699 43 6,556 4,394 2,162 .670 1,931 1,158 773 .600 4,760 3,236 1,389 .700
.625-.649 68 10,576 6,723 3,853 .636 3,106 1,837 1,269 .591 7,470 4,886 2,584 .654
.600-.624 133 20,686 12,651 8,035 .612 6,195 3,488 2,707 .563 14,491 9,163 5,328 .632
.575-.599 199 30,987 18,235 12,752 .588 9,305 5,230 4,075 .562 21,682 13,005 8,677 .600
.550-.574 233 36,253 20,401 15,852 .563 10,983 5,898 5,085 .537 25,270 14,503 10,767 .574
.525-.549 325 51,352 27,572 23,780 .537 15,589 8,103 7,486 .520 35,763 19,469 16,294 .544
.500-.524 258 40,532 20,677 19,855 .510 12,445 6,252 6,193 .502 28,085 14,425 13,662 .514
.475-.499 238 37,403 18,166 19,237 .486 11,472 5,655 5,817 .493 25,931 12,511 13,420 .482
.450-.474 256 39,927 18,439 21,488 .462 12,149 5,792 6,357 .477 27,778 12,647 15,131 .455
.425-.449 202 31,600 13,823 17,777 .437 9,746 4,529 5,217 .465 21,854 9,294 12,560 .425
.400-.424 173 27,129 11,166 15,963 .412 8,157 3,687 4,470 .452 18,972 7,479 11,493 .394
.375-.399 113 17,554 6,800 10,754 .387 5,320 2,253 3,067 .423 12,234 4,547 7,687 .372
.350-.374 62 9,520 3,446 6,074 .362 2,828 1,172 1,656 .414 6,692 2,274 4,418 .340
.300-.349 81 12,500 4,145 8,355 .332 3,712 1,479 2,233 .398 8,788 2,666 6,122 .303
.000-.299 20 3,057 843 2,214 .276 909 331 578 .364 2,148 512 1,636 .238
2414 377,162 188,581 188,581 .500 114,240 57,120 57,120 .500 263,055 131,461 131,461 0.500
As you can see, the pattern is pretty dependable. The only group that doesn't fit perfectly includes the 133 teams who played between .600 and .624 ball. Those teams had results in one-run games that were just a little bit worse than all this would lead you to expect. They played 6195 one run games, and I would have expected them to win about 3560 of them (roughly .575 ball) - they actually went 3488-2707, which is just .563 ball. How big a deal is that? Not all that much, actually - it's exactly the same as the difference between going 93-69 and going 91-71.
But I certainly didn't want to create a dozen different formulae, depending on a team's WL record, in order to derive expected outcomes in one-run games. That would be... extremely tedious. I wanted a nifty, catch-all that I could apply to everyone. And so I developed a very, very simple formula to generate a team's projected record in one-run games. I'm sure it's somewhat crude, but It's as consistent as I could hope it to be once the sample gets large enough. Once the sample gets large enough, the formula actually works (I can hardly believe it myself!) I don't need to worry about the blowouts. I don't even have to worry about total Runs Scored and Allowed. Simply adjusting the outcomes of one-run games turns out to be enough to make the actual results match up with the expected results.
Here's how it works (three calculations are involved!)
In 2021, Tampa Bay went 20-25 in their one-run games. They played .684 ball (80-37) the rest of the time. So:
1) Multiply their 45 one-run games by their .684 winning percentage in their Other Games. You get 30 (because I'm using the INTEGER function, I don't want to mess around with 30.7 - hey, you either win or you don't!)
2) Multiply those same 45 games by .500 - after all, dragging every team towards .500 is precisely what one-run games do. It's what they're for. This time we get 22 (the INTEGER function strikes again, lowering 22.5 to 22).
3) Add the two figures - 30 and 22 - and divide them by 2. Easy enough, it's 26.
Voila! Tampa Bay's expected W-L record in one-run games is 26-19 instead of the 20-25 inflicted on them by Cold Reality. We are free, if we like, to regard this as more reflective of that team's quality than What Actually Happened.
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I have, naturally, carried out the same operation on the season just concluded and I am ready - nay, I am eager - to tell everyone what You Just Saw!
This, I submit, is a better reflection of true team quality than the actual standings (or anything Pythagoras shoots out of his rear end.)
ADJUSTED RECORD NOT ONE-RUN GAMES ACTUAL ONE RUN GAMES ADJUSTED ONE RUN GAMES
W L PCT W L PCT W L PCT W L PCT
NY Yankees 102 60 .630 68 36 .654 31 27 .534 34 24 .586
Toronto 89 73 .549 62 50 .554 30 20 .600 27 23 .540
Tampa Bay 88 74 .543 59 49 .546 27 27 .500 29 25 .537
Baltimore 85 77 .525 60 55 .522 23 24 .489 25 22 .532
Boston 79 83 .488 54 58 .482 24 26 .480 25 25 .500
Cleveland 88 74 .543 64 53 .547 28 17 .622 24 21 .533
Minnesota 82 80 .506 58 56 .509 20 28 .417 24 24 .500
Chicago 75 87 .463 54 65 .454 27 16 .628 21 22 .488
Kansas City 65 97 .401 49 77 .389 16 20 .444 16 20 .444
Detroit 62 100 .383 44 76 .367 22 20 .524 18 24 .429
Houston 104 58 .642 78 40 .661 28 16 .636 26 18 .591
Seattle 85 77 .525 56 50 .528 34 22 .607 29 27 .518
Los Angeles 78 84 .481 55 61 .474 18 28 .391 23 23 .500
Texas 78 84 .481 53 59 .473 15 35 .300 25 25 .500
Oakland 61 101 .377 43 77 .358 17 25 .405 18 24 .429
NY Mets 101 61 .623 80 46 .635 21 15 .583 21 15 .583
Atlanta 100 62 .617 75 43 .636 26 18 .591 25 19 .568
Philadelphia 91 71 .562 65 50 .565 22 25 .468 26 21 .553
Miami 76 86 .469 45 53 .459 24 40 .375 31 33 .484
Washington 54 108 .333 38 85 .309 17 22 .436 16 23 .410
St Louis 94 68 .580 77 54 .588 16 15 .516 17 14 .548
Milwaukee 85 77 .525 58 53 .523 28 23 .549 27 24 .529
Chicago 73 89 .451 48 61 .440 26 27 .491 25 28 .472
Pittsburgh 62 100 .383 41 73 .360 21 27 .438 21 27 .438
Cincinnati 60 102 .370 41 77 .347 21 23 .477 19 25 .432
Los Angeles 114 48 .704 95 36 .725 16 15 .516 19 12 .613
San Francisco 85 77 .525 59 54 .522 22 27 .449 26 23 .531
San Diego 83 79 .512 59 56 .513 30 17 .638 24 23 .511
Arizona 80 82 .494 57 59 .491 17 29 .370 23 23 .500
Colorado 66 96 .407 45 70 .391 23 24 .489 21 26 .447
We would still have the same six teams meeting in the AL post-season, but the match-ups would be slightly different. Toronto would be hosting Tampa Bay in the fight to see who gets to play Houston. And Seattle (who edge out Baltimore with the tie-breaker) would be off to Cleveland.
The most interesting AL team, by a mile, is Texas. Normally the one-run games help losing teams - they drag their records up towards .500. But in the tiny sample that is any single season, literally anything can happen. Like the Rangers going 15-35 in one-run games. I think we all understand that this was simply karmic payback for their equally inexplicable record (36-11) in these games back in 2016, but poor Chris Woodward paid a terrible price for this random misfortune.
These adjustments really shake up the NL post-season. The Braves, by losing just one of their wins, end up as with a Wild Card berth instead of the division title. They will take on... San Francisco? Yup - the Padres fall to third place in the NL West and miss the post-season entirely. The Giants hold the tie-breaker over Milwaukee.
Gosh. The Astros and the Dodgers are the best teams in the game? Who knew?
