Tell Me There’s A Chance: World Series Odds Need To Be Fixed

Being a sports fan is hard. On average, a major league team’s chance to win the World Series in a given year is 3.3 percent. I promise the math works out. Some teams, particularly larger-market teams, may have a greater chance, but for fans of any team you are more likely to end the season sad than happy. However, in April there is hope for every team. This is an old baseball cliché, but it is also generally true!

If you look at FanGraphs’ playoff odds, every team has a chance to make it at least to the wild-card game. Even the Phillies! So the cliché is grounded in a bit of reality, as clichés usually are. On the other hand, two teams are listed as having 0.0 percent chance of winning the World Series. Those darn Phillies and the Atlanta Braves.

Let’s talk about those Braves and their chances at fortune. For purposes of this exercise, we are going to assume that the playoff odds are correct up until the playoffs actually occur. Maybe you think the Braves 3.2 percent chance of making the playoffs is pessimistic. After starting 3-0, it has jumped from 3.1 percent, so that’s something! Maybe you think that is too low (or too high), but that doesn’t matter, this exercise could be done using many bad teams. The Braves have a 3.2 percent chance of making the playoffs but a 0.0 percent chance of winning the World Series. This is very unlikely to be true.

I don’t have the statistical skills to delve into the projection models, but I believe there is a fundamental flaw that essentially double dips on poorly projected teams. The playoff odds beyond simply making the playoffs are calculated assuming each team is as good or as bad as projected. The problem with this method is that it doesn’t comport with reality. If the Braves (or the Phillies, Diamondbacks, Rockies, Brewers, Twins or Rangers) make the playoffs, it will be at least partially due to them being a much better team than the projections thought they were. Of course, the projections know that this is possible, hence the slim odds instead of no odds of making the playoffs.

For purposes of this chart, I’m going to make generous assumptions on the decimal points that we cannot see. These assumptions work against my conclusion and I believe my conclusion still holds. For percentages that are listed as 0.0, I’m going to assume 0.05. * For 0.1, I’m going to assume 0.15. And so on. These odds all come from FanGraphs projections as of Friday, April 10, 2015.

Below is a list of teams with less than a 10-percent chance of making the playoffs. Assuming they make the playoffs, based on these conservative assumptions, the odds of these teams winning the World Series are:

Team                         1 in…

Phillies                      24

Rangers                     16

Twins                         16

Diamondbacks         19

Braves                     64

White Sox                  18

Reds                            30

Brewers                      36

Rockies                       39

The three teams in the AL actually don’t look that bad. I’d say they are perhaps a little too pessimistic, but not drastically so. In the NL, the Braves are the worst example, but the Reds, Brewers, and Rockies are all clearly unrealistic considering what we know about the playoffs (that it is something, perhaps a big something, of a crapshoot). My guess is that this could be fixed by regressing the odds of each team heavily towards a typical playoff team to account for the fact that poorly projected teams that make the playoffs are likely way towards the top end of their possible outcomes. If the Braves make the playoffs, it will be largely because they are good, and probably also because they got a decent amount of luck. I’m not saying they’d be 8-1 (as a division winner) or 16-1 (as a wild card team), which is what their odds would be based on coin flips. But there is no way the Imaginary Good Braves would go into the playoffs as 64-1 longshots to win the World Series. You don’t need a calculator or anything other than common sense to know this. And remember, I used very conservative assumptions. It is likely that if I had access to more significant digits, some of these numbers would look much worse.

 

*The Phillies listed odds of making the NLCS are 0.0 percent. Based on this, I halved the odds for winning the NLCS and then halved them again for winning the World Series. Thus, I conservatively estimated that the FanGraphs odds for the Phillies winning the World Series are 0.0125 percent. Thanks again, Phillies, for making things harder.





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smiley54663
9 years ago

I see the point you’re making, but I don’t think it’s something that should be implemented. Fangraphs lists these projected standings based on projected team TALENT. Based on talent alone, there will likely be 1+ teams whose win total vary by 8+ wins based on randomness / sequencing of hits. That means an 75 win talent could still win 86 games and be projected as a team with 75 win talent. The fact that they win an arbitrary amount of games that gets them into the playoffs (didn’t a sub .500 team win the NL west a few years back?) should not change the assumption of the projections’ numbers.

From my understanding, the team wins/playoff odds are based solely on the talent projections given. Then games are simulated and results are provided. In the end, that’s what baseball games come down to; true talent + random variation. If you have no qualms with the projections, you can’t have any qualms with the results.

Aaron
9 years ago

Imaginary good Braves thought exercise:
Let’s make them a no-vig +160 (8/5, ~38%) to win a road wild card game against the theoretical Pirates.
Then we’ll make them a +200 (2/1, 33.3%) underdog against the top-seeded theoretical Dodgers.
They then become +160 again against the theoretical Cardinals.
Finally, they enter the World Series as only a +150 (3/2, 40%) underdog to the theoretical Mariners.

Let’s run those odds in sequence:
1*2.6*3*2.6*2.5=50.7, or 49.7/1.

And those odds weren’t even exorbitant. I’ve seen much higher series prices in my day. 50 or 60 to 1 for a weak wild card team is not only possible, but even in some rare cases a possible understatement.

evo34
9 years ago
Reply to  Aaron

Well laid out example. The author needs a little help with the math of futures odds, apparently.

evo34
8 years ago
Reply to  TKDC

His example was most certainly not the “worst case scenario” — and that was the point. Making them a respectable WC team with no dominant team blocking their way, they would would still be 50-1 fair to win.

jacaissie
9 years ago

I like this–it’s very much like what Nate Silver and others do for the NCAA tournament: the double digit seeds have a better chance of making the sweet 16 or elite 8 than you’d think, because if they win, it means that they are probably better than the model had assumed.

AC_Butcha_AC
9 years ago

The projections and odds only reflect the reality NOW. Your point is somewhat incorrect since by the time the Braves actually made the playoffs they could very realistically be “more talented” than the projections think NOW. But they should be catching up the more indication there is for a greater talent level.

So if the Braves really made the postseason because they are vastly more talented than the projections think now… by the time they actually arrive there the projections and odds should have catched up to their performance and give them a greater chance to win it all ultimately.

If the reason the Braves made the playoffs is (in the projections/saberists POV) luck or random variation without indication for a greater talent level then this projection right now shouldn’t be too far off.

Also keep in mind that the odds are based on (10,000 IIRC) simulations. So there is a slim chance, that they may even have a 4% chance right now.

Sean Dolinarmember
9 years ago

I wanted to echo most of the comments on this article. Probability is one of my favorite topics in baseball/sabermetrics. Questioning projection models is really important, because projections should improve upon random guesses or intelligent guesses.

To summarize, our Playoff Odds simulate the season 10,000 times based on the Depth Chart projections at the current point in time. (AC was correct). So to address the WS odds, what you are looking at is the results of a 10,000-fold simulation of the entire season and playoffs. What you are suggesting is to forgo the regular season simulation, set the condition that the Phillies are in the Post Season, then simulate the playoffs from there, which would drastically change the odds. There’s more from Neil on how the Playoff Odds work: http://www.fangraphs.com/library/interpreting-playoff-odds-and-projected-standings/

Finally, what you are touching on is a concept in statistics called conditional probability. It’s pretty interesting and leads you to Bayes’ Theorem.

evo34
9 years ago

“But there is no way the Imaginary Good Braves would go into the playoffs as 64-1 longshots to win the World Series. ”

Apparently, you’ve never actually bothered glancing at sportsbook odds for bad teams that luck into the playoffs. They are often more than 50 to 1, esp. if there is a dominant team that year. Also, you don’t quite understand that FG considers making the wild card play-in game “making the playoffs.” [Sidebar to all baseball writers: making a 1-game playoff to get *into* the playoffs should not count as “making the playoffs.”] With that in mind, it’s entirely reasonable to think the Braves could be 64-to-1 (or even worse) to win it all if they make it to the play-in game.

evo34
9 years ago
Reply to  TKDC

I’m lying to myself, eh? What did I say that is inaccurate?

1) No, you clearly haven’t looked at Vegas odds after the regular season historically. You wrote, ““But there is no way the Imaginary Good Braves would go into the playoffs as 64-1 longshots to win the World Series,” and that’s dead wrong. [The fact that the Braves are 75-1 right now at one sportsbook has precisely nothing to do with how wild card teams are usually priced after the season]. A more interesting question is, what are the odds none of the 10 playoff teams this season are 64-1 or greater longshots after the reg. season ends?

2) By the way, who is offering you 64-1 that the Braves will win WS *if* they make the playoffs? That would require two things: a) Someone trusting FG odds table 100% 3 games into the season even though it only uses one sig fig., b) someone willing to accept a longshot bet with zero theoretical hold. If you find someone who qualifies for both, please let me know.

Dusty Baked
9 years ago

10000 seasons isn’t remotely enough to narrow down numbers for remote outcomes even before you figure in changes in talent level. So they made the playoffs 320 times in those 10000 seasons, almost all as a WC and mostly as WC2. So let’s say they’re on average 45% to win WC game (or not have to play it) and 40% to win each series. So they’d win 2.88% of playoffs (~34-1) for a total of 9.2, and FG has them winning either 4 or 5 or fewer in their simulations. The odds of winning 5 or fewer out of 320 2.88% trials is about 10% and 4 or fewer is about 5%. So they easily could have just run bad in the simulations. And with a handful of “awful” teams to examine, the odds of one of them running bad isn’t very remote at all.

You do have a point that their inferred talent will likely be higher if they do make the playoffs, but the numbers you’re comparing against aren’t nearly as precise as the decimal points represent. Even if 320/10000 was their exact (constant talent) expectation of making the playoffs, in 10000 simulations, they have a 5% chance of making the playoffs in 290 or fewer and a 5% chance of making the playoffs in 349 or more. Binomials are a bitch.

The Kudzu Kid
9 years ago

A = event the Braves win the World Series
B = event the Braves make the playoffs

P(A) = P(A|B)P(B) + P(A|B’)P(B’)
P(A) = P(A|B) * 0.032
P(A|B) ~ 1/64 (per article)
P(A) ~ 0.032 / 64 = 0.0005

I don’t see a problem with this math. The conclusion, though, is basically a 0 probability, which is what the site is reporting.