The Division Series (Plural) / Goodbye Pythagoras

Thursday, October 07 2021 @ 07:00 AM EDT

Contributed by: Magpie

One Evil Empire was dispatched by another on Tuesday night, as Boston dismissed the Yankees in a somewhat ho-hum game. And last night the Dodgers got by the Cardinals in a tense, gripping affair that was only decided on the game's final pitch. Which took place four hours and fifteen minutes after the first pitch. It was wonderful, dramatic entertainment if you had the endurance required to stick with it to the end. But now we have an Elite Eight.

The ALDS kicks off this afternoon with the White Sox in Houston, two teams managed by guys even older than me. Cool. The Red Sox and Rays get underway in Tampa Bay later tonight. The Other League gets started on Friday.

So why don't I make a fool of myself and venture some predictions?

Boston-Tampa Bay
The Red Sox are irritating, streaky, and unpredictable. But the Rays are easily the best team in the league, and by a considerable margin. Rays in four

Chicago-Houston
Two ancient managers (who apparently don't like each other too much) will get a lot of the attention. But the real story is the classic clash between an irresistible force (the Houston offense, best in the league) and an immovable object (the White Sox pitching, also best in the league.) It's always interesting when that happens. Astros in five

Atlanta-Milwaukee
The Braves have a solid team but the main reason they're in this thing is because they're the only good team in their weak-ass division. They'll be in tough against what might be the most frightening pitching rotation in the post-season. It's one thing to win the NL East without your best player. This will be harder. Brewers in three

Dodgers-Giants
These teams have never met in actual post-season play, but they do have a history. Oh, they have a history. One than spans an entire continent and more than a century of baseball. And some of the most memorable parts of that history have indeed come after what supposed to be the last day of the regular season. There was a rather playoff famous series to settle a tie between these teams at the end of the 1951 season. There was another at the end of the 1962 season. The Giants were the winners on both occasions, and got to go to the World Series and get beat by the Yankees.  I think the Dodgers are the better team and they were unlucky to finish second. But the Giants are really good as well and the Dodgers are pretty banged up. Giants in five

Matchups!

Thursday
Chicago (Lynn 11-6, 2.69) at Houston (McCullers 13-5, 3.16)
Boston (Rodriguez 13-8, 4.74) at Tampa Bay (McClanahan 10-6, 3.43)

Friday
Chicago (Giolito 11-9, 3.53) at Houston (Valdez 11-6, 3.14)
Atlanta (Morton 14-6, 3.34) at Milwaukee (Burnes 11-5, 2.43)
Boston (Some Guy ?=?, ?.??) at Tampa Bay (Baz 2-0, 2.03)
Los Angeles (Buehler 16-4, 2.47) at San Francisco (Webb 11-3, 3.03)

And there will be more...

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I mentioned the other day that I had moved beyond Pythagoras when it came to evaluating a team's season, because I am so very, very progressive. So let me explain myself! (He never does anything else, they wearily murmur.)

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 we have come to call a team's Pythagorean W-L record. This is based entirely - entirely - on the relationship between totals 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. Please. 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, which I regard as as less important but still an issue, 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.

But I think that's a fairly minor matter. The other issue I think is much more important. And it's pretty obvious. And 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 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 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 game, the .450 teams will play something .480 ball in one-run games. And so on.

And so I developed a very, very simple formula to generate a team's projected record in one-run games. It's as consistent as I could hope for 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!)

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.

Repeat 29 times. Or do what I did, Copy and Paste the formula. (I had a blank cell waiting for this calculation in 2,789 other seasons. That would have been a lot of data entry.)

And these would be your modified standings. (The two Times columns near the end give the results of the two calculations carried out on the team's one-run games; the final pair gives their new fantasy record in those games.)
                       FANTASY                    REALITY            ONE RUN GAMES         OTHER GAMES (OG)  Times  Times    FANTASY ONE-RUN    
                  W    L    PCT    GBL          W    L    PCT        W    L    PCT         W    L    PCT       OG %  0.5        W    L
                                                                                        
Tampa Bay       106    56    .654     -       100    62   .617      20    25   .444       80   37   .684       30    22        26    19
Toronto          92    70    .568    14        91    71   .562      15    15   .500       76   56   .576       17    15        16    14
Boston           89    73    .549    17        92    70   .568      26    18   .591       66   52   .559       24    22        23    21
NY Yankees       89    73    .549    17        92    70   .568      28    20   .583       64   50   .561       26    24        25    23
Baltimore        54   108    .333    52        52   110   .321      13    24   .351       39   86   .312       11    18        14    23
                                                                                       
Chicago          98    64    .605     -        93    69   .574      18    24   .429       75   45   .625       26    21        23    19
Cleveland        82    80    .506    16        80    82   .494      17    22   .436       63   60   .512       19    19        19    20
Detroit          76    86    .469    22        77    85   .475      23    23   .500       54   62   .466       21    23        22    24
Kansas City      71    91    .438    27        74    88   .457      21    19   .525       53   69   .434       17    20        18    22
Minnesota        67    95    .414    31        73    89   .451      25    19   .568       48   70   .407       17    22        19    25
                                                                                        
Houston          96    66    .593     -        95    67   .586      21    19   .525       74   48   .607       24    20        22    18
Oakland          89    73    .549     7        86    76   .531      23    27   .460       63   49   .563       28    25        26    24
Seattle          83    79    .512    13        90    72   .556      33    19   .635       57   53   .518       26    26        26    26
LA Angels        69    93    .426    27        77    85   .475      25    14   .641       52   71   .423       16    19        17    22
Texas            58   104    .358    38        60   102   .370      18    21   .462       42   81   .341       13    19        16    23
                                                                                        
Atlanta          93    68    .578     -        88    73   .547      26    31   .456       62   42   .596       33    28        30    27
Philadelphia     79    83    .488    14.5      82    80   .506      30    25   .545       52   55   .486       26    27        26    29
NY Mets          78    84    .481    15.5      77    85   .475      31    35   .470       46   50   .479       31    33        32    34
Miami            68    94    .420    25.5      67    95   .414      21    29   .420       46   66   .411       20    25        22    28
Washington       64    98    .395    29.5      65    97   .401      22    26   .458       43   71   .377       18    24        21    27
                                                                                        
Milwaukee        93    69    .574     -        95    67   .586      21    15   .583       74   52   .587       21    18        19    17
St.Louis         87    75    .537     6        90    72   .556      26    19   .578       64   53   .547       24    22        23    22
Cincinnati       81    81    .500    12        83    79   .512      24    20   .545       59   59   .500       22    22        22    22
Chicago Cubs     70    92    .432    23        71    91   .438      24    27   .471       47   64   .423       21    25        23    28
Pittsburgh       58   104    .358    35        61   101   .377      20    22   .476       41   79   .342       14    21        17    25
                                                                                        
LA Dodgers      111    51    .685     -       106    56   .654      24    24   .500       82   32   .719       34    24        29    19
San Francisco   104    58    .642     7       107    55   .660      31    17   .646       76   38   .667       32    24        28    20
San Diego        81    81    .500    30        79    83   .488      21    26   .447       58   57   .504       23    23        23    24
Colorado         73    88    .453    37.5      74    87   .460      24    25   .490       50   62   .446       21    24        22    27
Arizona          59   103    .364    52        52   110   .321      10    31   .244       42   79   .347       14    20        17    24
This past season, eight of the 30 teams would see a change of more than five games in their W-L record.  As you can see, the AL East, the Al West, and the NL West all end up with a slightly different pecking order. Boston, New York, and San Francisco all did better in the one-run games played in the Real World, while the A's and Dodgers did worse. This was enough to vault the Giants past the Dodgers, the Red Sox and Yankees past the Blue Jays. Because in baseball, the real world is stranger than fantasy.  Otherwise, the Giants would have faced off with the Cardinals last night. Boston, New York, and Oakland would have had to fight among themselves to see who played Toronto in the AL Wild Card.

And Seattle finishes a respectable enough 83-79, slipping one spot to third place. The Mariners were in fact the team that really set me off on this adventure, this mad pursuit of an untamed fowl. Seattle's raw Runs Scored and Allowed aren't remotely impressive. If you just apply one of the Pythagorean formulae to it, the team ends up with a losing record. The one-run games were very good to them indeed - they played lots of them and they won 14 more of them than they lost. That was largely good luck, pure and simple. But the Mariners also won more games than they lost the rest of the time as well (57-53.)  Which may be why I have some trouble thinking of the 2021 Mariners as losers. They may not be a 90 win quality team. But losers? I think not.

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