Pebble Hunting: Sim City 1000000

If PECOTA were a sentient Baseball Prospectus reader, I bet it would mostly ignore our projected team win totals. Putting a single number on a team’s upcoming season is antithetical to what PECOTA tries to do. It doesn’t actually see the Royals as a 75-win team, or the Cubs as a 94-win team; it sees them both as collections of players who are individually more likely to do some things than others, and who are collectively more likely to do some things than others. If forced—and, really, if you think about how many steps it takes us to get from Omar Infante’s individual projections to a one-number team projection for the Royals, “forced” might be exactly the word you’d use—PECOTA will give you a most likely number for the team. But that specific number is not that likely, and it's not what PECOTA wants you to take away from this.

The other day, talking to Jon Meoli of the Baltimore Sun, I used the word “hubristic” to describe how some PECOTA-scorning fans view the one-number projection. It’s hubris for us to think we can pin a team down to one number. In our defense: We don’t think that we can! We vastly prefer the Playoff Odds approach, whereby we recognize that a season could play out many, many ways—thousands, tens of thousands, or even, yes even, One Million Ways. If PECOTA were a sentient Baseball Prospectus reader, the Playoff Odds are what it would be into.

Today, we’re releasing our 2016 playoff odds (read all about them here, or look at them here), which are based on simulations of the season one million times. (We upped it this year from 50,000 because it sounds cooler.) On the surface the odds that we display, too, suffer from the one-number problem. But that one number embeds within it the recognition that this is a probabilities exercise, or rephrased in an explicitly non-hubristic way, an exercise in doubt. While you see the one number, within that number are literally one million different ways that the season can go, each as likely (and unlikely) as the next. PECOTA favors none of the million any more than any other; PECOTA watched the Royals win 95 games last year and nodded, because PECOTA totally called it in Sim #16,304*. PECOTA 100 percent believed in the Royals’ ability to win 95 games last year, just as it 100 percent believes in the Royals’ ability to win 106 games this year (Sim #644083). If the Royals win fewer than 106 games this year, don’t blame PECOTA for being just way too high on the Royals. It’s not PECOTA’s fault it loves the Royals! It’s our fault for not playing enough seasons.

Because there might be infinite universes, it is inevitable that in one of those universes—this one—I’m spending my day looking deep into the details of our million simulations. Henceforth: The individual sims in this year's playoff odds that made me sit up:

The Best Team Ever simulation: Sim #781143
If we play this season one million times, I can get a team to win 123 games—and that in a season that is, at least in the American League, defined by parity, and in an era that has overall been quite short on “great,” i.e. 100-win, teams. A 123-win season—123-39, to put how many wins that is in perspective—would mean a winning percentage of .759. The Blue Jays managed such a pace last year, in August. The Dodgers did it in July and August of 2013, when they had the best 50-game stretch in history. It basically happens over the course of a single month once per season, but if we run through the various scenarios 781,143 times we find a team that does it for an entire season. The team is:

The Mets! Good job, 781,143^rd version of the Mets.

The 1906 Cubs won 76.3 percent of their games, but baseball in 1906 was barely baseball. That was, in fact, the first year that the outcome of the World Series was even reported in west coast newspapers. No team during the Real Baseball Era has won 123 games—or won 76 percent of its games—because we’ve only tried 100 or so Real Baseball years. But how unlikely is it, really? The Mariners of 2001 won 116 games, the most ever. Are they really any better than the Mets? The Mariners won 91 games in 2000, and 93 in 2002. The Mets won 90 last year, playing half the year without Conforto, Cespedes, Syndergaard, Matz. Not hard to believe they're as good as those Mariners were, in true talent.

But of course those 2001 Mariners were seven wins short. All I’ve got to do to get them to 123 is:

• April 8, Mariners lose 5-4: John Olerud’s eighth-inning lineout to center field is a hit, instead. He scores on Mark McLemore’s home run; instead of 4-4 game, Mariners now lead 5-4. Seattle brings in Jeff Nelson to protect the lead instead of Jose Paniagua. Mariners win 5-4.
• May 19^th, Mariners lose 2-1 in extra innings: In ninth, Alfonso Soriano is thrown out stealing third instead of advancing safely. Ballgame ends before Derek Jeter’s game-tying hit, Mariners win 1-0.
• June 18^th, Mariners lose 4-3: Instead of 0-for-4, Ichiro—batting .352 on the year—goes 1-for-4. Steals a bag, scores a run, whatever. Mariners win.
• Aug. 5, Mariners lose 15-14 in extra innings: Instead of blowing a 14-2 seventh-inning lead, Mariners do literally anything else and win.
• Sept. 4, Mariners lose 8-3 in extra innings: Instead of allowing five runs in the 10^th, Jose Paniagua is never born. Mariners win.
• Oct. 7: Mariners lose 4-3: With the score tied late in the final game of the season, Edgar Martinez doesn’t get picked off at second, because seriously what was he even doing? Mariners win.

None of that would be remotely unusual, and collectively those six very usual things get us to 122. Now assume one thing weird happens in any of the other 40 games and boom, 123. Could have happened. Will happen. If we stay at it long enough.

The Worst Team Ever simulation, Sim #964264
Of course, the bad news for the Mets is that there’s also a sim (#964827) in which they lose 102 games. That’s a lot better than the Twins’ worst-case scenario: 39 wins, 123 losses. The exact inverse of the best season on sim-record.

Nothing about this season is odd. It isn’t as though volcanic eruptions worldwide are covering ballparks in ashen morbidity, or an outbreak of fleas has made it impossible to come set on the mound without balking. The rest of baseball is simply walking down the sidewalk, nothing out of the ordinary, while the Twins attempt to walk against traffic in the middle of the street. This wretchedness/normalcy dynamic results in the Twins finishing 38 games out of fourth place; they “win” the first pick in the 2017 draft by 23 games. In this scenario, the Indians would be favored at better than 6-to-1 in any individual game against the Twins.

What’s especially fun is that the Twins are not, generally speaking, hated by PECOTA. They’re projected to finish around .500, tied for third place, with a better record across all sims than at least 12 other teams. There’s a season where they win 106. And for the first 960,000 sims, the Twins were just going about their business, happily engaged in the dream so many of us wished for as children. And at the very end, something tragic happened. This is life. We’re all, each one of us, conclusively disproving the theory that everybody dies, up until the last second.

The Best and Worst Seasons for Every Team simulations

The Most Narrative-Busting Season simulation, Sim #706043
I alluded to the American League’s unusual parity earlier, but others have noted the National League’s unusual lack of parity, too. At least four teams were solidly sellers this offseason, and as many as seven seem barely to be trying. It’s practically impossible to imagine the Phillies, the Reds or the Rockies playing relevant games in September, let alone October.

And yet, in a million simulations there ought to be at least one where all three are good. In fact, there are four seasons where all three win their divisions.

It only takes us 25,064 to get to the first. The Phillies win 89 games to tie the Mets; the Rockies win 83 to tie the Padres (!); and the Reds, with 96, win what looks to be the toughest division in baseball by 17 games.

In Sim #167639, all three win their divisions outright, with exactly 87 wins in all three cases. In Sim #323469, the Reds win with just 81 games; the real drama of that season comes in the AL Central, where the Royals’ 91 wins narrowly edges the Indians’ 90, the Tigers’ 89 and the White Sox’ 88.

But it's Sim #706043 that gives us the most forceful refutation of the “no parity in the NL” narrative. The Rockies, with 87 wins, are the best team in the league. The Padres, at 85, are second best. The other three NL West teams all tie for third with 81. A six-game spread for the entire division. Meanwhile, the Phillies tie for the NL East crown with 84, and they end up with just a 10-game lead over the last-place Braves. And in the Central, the Reds tie the Cubs with 84, just five games better than the last-place Pirates. All 15 National League teams are bunched up in a 13-game mess; 14 are within 10 games of each other; and 10 are within five games of each other, winning 79 to 84. (And 12 of the 15 AL teams are between 77 and 87!)

The Most Not Even Predictably Unpredictable Season simulation, sim #315521
We can disagree about most things—the Mets or the Nationals seems like it’ll be a hot one, the Cardinals and Pirates each have strong cases against the other, the entire AL East and AL Central can go in any direction, and so on. But there’s one division where we all pretty much agree: The Dodgers are the best team, the Rockies are the worst, and the Giants, Diamondbacks and Padres are in the middle—and in that order. If I polled 100 of you, I suspect I might get 80 responses that had the division in exactly that order. You can’t predict baseball, but sometimes you can.

There are 61 seasons in which we get literally every one of those statements wrong. In these 61, the Rockies win the division, the Padres are second, then the Diamondbacks, then Giants, then Dodgers. As you might imagine, a lot of these are tightly bunched divisions where the Rockies’ best efforts are just barely enough to top the Dodgers and Giants’ worst: There are sims where the spread from first to last is just four games; seasons where all five teams are at or above .500, or all five teams are below. But there’s also Sim #315521,

where the Rockies beat the Dodgers by 18. Put your analyst self into the final week of that season and think about what this outcome would mean: The Rockies’ trade of Corey Dickerson for Jake McGee no longer looks like the pointlessly shortsighted trade of a long-term asset for a superfluous short-term closer, but like the final piece for a competitive team. The Dodgers’ decision to let themselves be outbid for Zack Greinke no longer looks like a strangely passive, small-market decision, but like a realistic acknowledgement of where this last-place team was on the win curve. These are the outlier seasons, obviously, but they're not even outliers that we're remotely considering when we think about where each team is heading into the season. Yet come late September, we’re going to find ourselves retroactively judging any number of moves based on the particular outlier Sim # that reality landed on. For instance, the 3,099 simulated seasons where the full-rebuild Braves miss the playoffs by one game. Would such a season make the Andrelton Simmons deal look better (“Wow, this team is going to be good even sooner than we thought!”) or worse (“Welp, there goes that realistic chance at a ring”) or neither (“this 83-win team is only an illusion anyway”)? Who knows! But we'll sure say something. All we can say now is that PECOTA saw it coming, eventually.

*The example used for the 2015 Royals is a made-up sim #. The rest are real. Indeed, you can see all one million of this year's simulations if you want: Just change the number at the end of this URL to anything from 1 to 1000000.

Thanks to Rob McQuown and Nick Wheatley-Schaller for heavy lifting.