Comparing Probability Models: MLB Playoff Probabilities Update

As the season comes to a conclusion, we will continue to produce probabilities for each MLB making the playoffs. With 10-12 games remaining for each team, the need for urgency arises and teams outside the playoff picture need to start posting near perfect records (Rockies of 2007); or teams inside the playoff picture need to have epic meltdowns (Red Sox of 2011).

Either way, there is one constant fact that should always hold true: there will be three division winners and two wild card teams in the playoffs. However, sites such as ESPN don’t agree. Take for instance their updated Hunt For October page. Their page gives probabilities for each MLB team of making the playoffs. They indeed skimp on giving estimated probabilities of winning a division or winning a wild card, but they do give probabilities of making the playoffs. Let’s consider one curious case from their site.

ESPN's Hunt for October for the NL West. There is a chance no team wins the NL West?

ESPN’s Hunt for October for the NL West. There is a chance no team wins the NL West?

In the National League West division, ESPN predicts that Los Angeles has 99.4% chance of making the playoffs. Similarly, the San Francisco Giants are predicted to have a 0.1% chance. Combined with the three eliminated teams of Arizona, San Diego, and Colorado, this means that at best there is a 99.5% chance that any of these five teams win the division. So where does the other 0.5% go? We simply cannot assume rounding errors, as this would still give a 0.3% offset that is unaccounted for at best.

To investigate, if we add all the National League probabilities together, we should expect 500%, as there are 5 teams that make the playoffs. Instead, we have 499.3%. Meaning that ESPN is claiming there is a chance that less than five teams can make the playoffs. Interesting. At least it’s not as bad as Yahoo’s Jeff Passan not understanding odds, but this is a simple fact to check.

Updated Probabilities:

For our system, after another two games have played out for most teams, here’s the resulting probabilities.

Playoff probabilities for every MLB team as of the morning of 23 September.

Playoff probabilities for every MLB team as of the morning of 23 September.

Recall that we run a Markov simulation of 10,000,000 simulations to obtain each probability. Therefore this is an estimated probability and teams that are not guaranteed a spot may really have a 99.99999% chance but simulated to 100%. Similarly, teams with really a 0.0004% chance may have simulated to 0%.

Here, we see the following playoff picture:

National League: Pittsburgh vs. Chicago, Los Angeles vs. New York; St. Louis #1

American League: New York vs. Houston, Texas vs. Toronto; Kansas City #1

The National League looks pretty much locked up, with very little room for shuffling match-ups. The American League is relatively wide open as the Angels and Twins are finding themselves 2-2.5 games out with 11-12 games to play. Cleveland, Baltimore, and Seattle are log-jammed in that “requiring a hot streak” region as they are 4.5-5.5 games out. Unless drastic actions have occurred, the American League has realistically come down to  a three team race for the final wild card spot that Houston currently owns.

How the Minnesota Twins Get In:

Minnesota has 12 games remaining: 6 versus Cleveland, 3 versus Detroit and 3 versus Kansas City. Houston has 10 games remaining: 1 versus Los Angeles tonight, 3 versus Texas, 3 versus Seattle, and 3 versus Arizona. Los Angeles has 11 games remaining: 1 versus Houston, 3 versus Seattle, 3 versus Oakland, and 4 versus Texas. The silver lining for Minnesota is that both of their main competitors are vying for an American League West title versus Texas, and both are 2.0 – 4.5 games out. Unless Houston splits with Texas and the Angels sweep the Rangers, there’s little hope for the Angels to win the division. Despite this, if Texas splits the Houston series, Texas will need to battle Los Angeles hard to win the division. Both situations puts Minnesota in a bonus.

Minnesota needs to focus on the final six games against Cleveland. As Cleveland is still mathematically in the race, only 4.5 games out, if the Indians drop the first two games of these six remaining games their probability of making the playoffs drops to well below 1%. This will make the Indians an easier target to go 3-1 in the final four games.

In order to make the playoffs, the Twins need to cover three wins that separate them from the Astros. While the Astros have Texas, Seattle, and Arizona, Houston is expected to win 5 of their remaining 10 games. This means the Twins need to post an 8-4 (or better) record to finish the season. It will be improbable if they cannot finish off the Indians and take the series 5-1.

How Los Angeles Gets In:

The Angels have an even more difficult task than the Twins for making the playoffs. For starters, the Astros are expected to win 5 games over the last 10. With the Angels down 3 wins and with only 11 games remaining, the Angels need to post an 8-3 record to remain competitive. However, the Angels have a much tougher road than the Twins: Seattle, Oakland, Texas. For the Angels to make the playoffs, they have to win or split every series. This gives at worst a 7-4 finish; most likely not recovering the 2.5 game deficit to the Astros (one game out). This indicates that the Angels need to sweep the Athletics and attempt to win the Rangers series. If there is a team to do, the Angels can… they are 10-5 against the Rangers this year.

Other Teams?

Sorry other AL teams. While you are considered in the race, there will need to be miracles to play out. For instance the Cleveland Indians must cover six wins against Houston and three wins against Minnesota and Los Angeles each. Cleveland at least controls their fate against the Twins with six remaining games. However, the Indians have three games against the Royals and three games against Boston. If we suppose the Indians sweep Boston, they still require an 8-2 record against Minnesota (6 games) and Kansas City (3 games). If Minnesota and Cleveland split their remaining series 3-3, both teams are out.

Let’s see how this season plays out. We will update the probabilities in another couple days. Hopefully the games get a little closer, unlike the National League.

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