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Our lives are ruled by probabilities. All things are possible, and the varying degrees of possibility of various things govern everything from our decisions to our dispositions. Often, we’re too preoccupied by our preoccupations to look forward very far, but the truth is that few events in our lives sneak up on us. Conscious or subconscious, perceptions of the likelihood of important events inform our mood, our priorities and our choices.

Sports fandom is a unique sliver of life, though, in which those probabilities aren’t floating whispers in the background. We’re constantly reevaluating them, recalculating and recalibrating them. Even in baseball, the sport of the long season, we look for significance in every win and every loss. We try to gauge the impact of everything we see, not only in the context of the game or the series at hand, but in the big picture. That’s why spirited fans so often seem to agonize over every pitch: it affects our perception of our team’s chances in the long run, and that affects our sense of well-being about our entire investment in the team. The effect of those small things is minute, compared to what we perceive it to be, but baseball is bedeviling. It lures us into the sense of constant cataclysm that characterizes the NFL, even though the moments that really matter as much as the outcome of any given NFL game happen perhaps once a month.

We’ve now come to the time of the baseball year during which the dissonance between how important games feel and how important they are is perhaps harder than ever to reconcile. Fans of struggling teams see a season slipping away. Fans of surprising teams start to shake off their skepticism and give themselves over to hope. The truth is, every game on the calendar carries the same weight in the standings, but when it comes to the likelihood of winning anything, that’s a little less true. Games against key rivals are more important than others. So are stretches of the season during which, for instance, a middling upstart has to fight not to be left in the dust by the flavor of the week. In not all that long, teams need to start making decisions about whether to make big changes, like firing managers and general managers or trading for reinforcement for the stretch run.

The Playoff Odds Report is so great. It provides tremendous relief from that strain, that feeling that what you’re seeing must be more important than the numbers say. Because these are the numbers, and to whatever extent one trusts PECOTA (and subscribes to just one or two assumptions, which we’ll get into shortly), they’re authoritative. They tell the story.

I’ve gone through the Playoff Odds on each Wednesday of the season to date, and noted where each team stood at the time. The graphic below shows all of those numbers, and to help see where real changes have happened, and where the only shift has been a subtle slide along the possibility curve, I’ve added a color scale. Red means your playoff hopes are on life support. Yellow means you’re very much in limbo. Green indicates a team with real cause to maintain, not just optimism, but high expectations.

Playoff Odds, April 8-May 20

We can use this to group some teams together, in terms of where their fans’ expectations might fairly have been coming into the season:

· Heavy Favorites: The Nationals, Dodgers and Angels entered the season with excellent chances to reach the playoffs. They were the clear class of their respective divisions. The goal for fans of these teams was to not sweat a single bead until October.

· Regional Favorites: The Red Sox, Cardinals and Tigers were also favorites to win their divisions coming in, but each had one or two reasonably threatening rivals with whom to deal. These fans had every right to start saving for playoff tickets, but would not have been able to turn down a role in their brother’s wedding just because it was scheduled for the second weekend of the Division Series.

· Contenders: The Cubs, Mariners and Rays weren’t technically likely to see the playoffs, but they were absolutely close enough to permit fans to have hope. Fans could reasonably schedule their summer work calendar around a road trip to see the team in August, and should have cleared July 31 on their schedule in order to obsessively refresh MLB Trade Rumors in the comfort of their own homes.

· Hopefuls: The Giants, Padres, Mets, A’s and Indians all had enough cause for optimism to make getting a dental cleaning out of the way before the All-Star break worthwhile, but none were so well-positioned as to make putting off graduate school by a semester rational.

· Blue Jays: As always, the Blue Jays were clearly not the worst team in the AL East, but with such a bizarre roster and the year-in, year-out instability of the team, there wasn’t much more that one could say for sure. It used to be that the Jays were clearly better than a fistful of playoff contenders from other AL divisions, but had no hope against the Northeast power corridor. These days, it feels like they just float between contender and pretender status, in a way no other team does.

· Dreamers: The Pirates, Yankees, Marlins, Orioles and Brewers entered the season with enough hope to keep turnstiles clicking, because baseball begins in the spring and everyone wants to believe that people can change and life can get better as the winter finally gives way. This is the first class of teams, though, for whom the playoffs were clearly a long shot, and who would need to meaningfully outrun their expected performance in order to become relevant.

· Lottery Ticket Buyers: The Reds, Astros, Royals and Rangers were something less even than those teams. They technically had a shot, but they lacked the usual tools necessary to ascend. One good turn couldn’t make them competitive. They would need multiple big breaks in order to break out.

· All But Hopeless: The Braves, Rockies, Twins, Phillies and Diamondbacks shared a fundamental losing identity. They stood so far apart from real contention that even making the playoffs wouldn’t really change what they were. They would merely be a team that got outrageously lucky. Fans should have made plans to go on international mission trips and serve suspended jail sentences from late summer through the end of the World Series.

Six weeks later, using the same dividing lines, we can re-categorize the league thusly:

· Heavy Favorites: Dodgers, Nationals, Cardinals

· Regional Favorites: Cubs, Tigers, Angels, Astros

· Contenders: Red Sox, Rays, Royals, Giants, Mets

· Hopefuls: Yankees, Mariners

· Blue Jays: Padres (You can raise an eyebrow if you want, but you have to admit, it still kind of makes sense)

· Dreamers: White Sox, Pirates, Twins

· Lottery Ticket Buyers: Blue Jays, Orioles, Indians

· All But Hopeless: Diamondbacks, Braves, Reds, Brewers, Phillies, Rangers, A’s, Marlins, Rockies

We see some of the typical stretching that happens as a season wears on. The hopes of the formerly faintly hopeful are being dashed. The rich and powerful are settling into their easy chairs.

Which teams’ fans have the right to feel that something real has changed, instead of (merely) that they’ve ridden the rising and falling tide of probability in gentle cycles?

· Astros, Royals: Before the season, they were buying lottery tickets. Those tickets aren’t totally scratched off, but the winning numbers are showing through so far. Both teams looked like good defensive clubs coming in, but both have been better than good. Ditto for each bullpen. They’re not fakes, and now, they’re serious contenders.

· Indians, A’s: These are the two AL teams who, coming into the season, probably had the widest range of possible outcomes. That’s not a bad way to start a season. Hope can thrive in that setting, and it’s not unreasonable, poisonous hope. It’s too bad, then, that Oakland’s hope has been pulverized, and that Cleveland’s seems soon to be wiped out, as well. Not only have the teams had, to different degrees, bad starts, but they’re now looking up at the shockingly successful Tigers, Royals and Astros. It’s like they both left their keys in the ignition when they got out of the car. The Indians locked themselves out; the A’s had their car stolen.

Now, let’s briefly talk about the central assumption on which faith in these fluctuations rests. The assumption: that what each team has done up to now shouldn’t totally upturn the expected range of outcomes for them going forward, and therefore, that we can still project their future performance based on some stable blend of their past performance and our previous projection for them.

I’m not sure that’s true. I know that makes me a believer in the gambler’s fallacy, but it has to be said: teams go through streaks and slumps throughout a baseball season. It doesn’t feel right to assume that those are randomly distributed, or random at all, nor that they won’t balance out to some degree over the long season. It also seems to me that the ever-shrinking number of games in front of a team should widen the spectrum of possibilities in terms of what they might do over that span, not shrink it. It’s easier to outplay one’s true talent level by 50 percent over 120 games than to do so over 160, so the chances of wild shifts in future performance actually increase as more games are played. Using 10,000 simulations of the season to derive these odds helps us account for that, but I’m not sure it’s fully captured.

Still, study this graphic carefully. Note how few teams have seen a drastic change in their expectations since the season began. For the most part, at this point in the season, your favorite team still is what we thought they were. What feel like huge peaks and valleys are probably relatively minor turbulence. Eventually, there will be a real change, but if you don’t learn to tell those apart from the cosmetic changes, you won’t fully appreciate the arc of baseball’s dramatic campaign.

Thank you for reading

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Pluthero
5/22
Very interesting, thank you. I do have a question regarding the Astros, you mention that they looked like a good defensive club coming into the season, but the depth charts have them as next to last in FRAA and have all year (or worse). I'm not sure how much effect this has on their projected record, but do you see this updating with the revelation that they are actually a very good defensive club?
cjrhgarmon
5/22
I'm also curious about the comparison of the Astros and Royals. Both started out the year with almost the same low expectations from Pecota, both currently have almost the same record, both play in divisions with another solidly "green" team (Angels and Tigers, respectively), yet the Astros playoff odds are higher than the Royals (even today's odds report has the Astros over 4 points higher than the Royals). Why the difference? Does it reflect a remaining schedule for the Astros that is easier or something else?
matrueblood
5/22
Four percent is not a 'real' difference in playoff odds. That's what the scaling and the discussion here is all about. Sure, they have slightly different specific numbers, but they're fundamentally in the same position. That small sliver of separation comes from the Royals having less clearance from the Tigers, and from the fact that more of the other teams in the AL Central are contenders at this point.
iorg34
5/22
Good stuff!
rnolty
5/22
Could you give us more detail on how the simulation is calculated? The glossary says it starts out with pre-season Pecota, and the season's results "are incorporated" as the season progresses.

It doesn't make intuitive sense to me that the Yankees odds could have almost doubled (from 15% to 27%) between the 2nd and 3rd weeks, even if they won 7 out of 7. And in general it just looks more volatile than I would have guessed.
matrueblood
5/22
Remember that nothing happens to a single team in a vacuum. The Yanks saw their percentage soar that particular week because they played well, but also because their chief rivals for playoff slots didn't. That's the explanation.

And as I write there at the end of the piece, it's a little more volatile than I would guess, too, at least in places. That stems mostly from PECOTA believing a team will play more or less to its expectation going forward, not accounting for any sort of compensation or reversion after a hot or cold streak.

I wish I could give more details on the simulation itself. I can't. Rob McQuown might be able to help you there. I know that we blend in differences between PECOTA and in-season performance slowly, so even at this point, the odds mostly reflect an expectation of playing to the preseason projection.
rnolty
5/25
McQuown pointed me at this link:


http://www.baseballprospectus.com/article.php?articleid=24332
kcshankd
5/22
This article seem blind to the most likely source of error - the projections being systematically off. Royals homer alert - but lottery ticket, really? PECOTA was the outlier in such a gloomy forecast, I suspect b/c it undervalues defense. The offensive explosion has been great, but PECOTA thought the pitching would be 100 runs worse in 2015. Isn't happening.
markpadden
5/28
So Volquez and Young are going to continue to post sub-3.00 ERAs?