Probability, the Playoffs, and the Indianapolis Colts

December 31, 2015 at 5:05 pm 1 comment

With one week left in the NFL season, Dan Graziano had this to say about the Indianpolis Colts’ chances of making the playoffs:

Indianapolis can still win a third straight AFC South title. Really, it can. All it needs is to win and then have the Texans, Bengals, Chargers, Jets, Saints, Chiefs, Patriots and Browns all lose. The league will throw in the partridge in a pear tree.

Colts HelmetIf the Colts win and the Houston Texans lose, both would be 8-8, and the first four tiebreakers for deciding which team makes the playoffs – record against one another, record against divisional opponents, record against common opponents, and record within the conference – would not be enough to decide who makes the cut.

It then comes down to strength of victory and strength of schedule. And for things to play out in the Colts’ favor, a lot of things have to go their way.

Fox Sports referred to this as long shot, comparing it to a recent win by a horse who was 200-to-1:

Sure, going 9 for 9 here looks dim, but long shots come in every once in a while.

Are the Colts’ odds as good as that horse’s? Seems not.

Using a simplistic model, assume that each of the nine necessary outcomes are equally likely. That alone would put the Colts’ odds at 511-to-1. (Since 29 = 512.)

But it’s not that simple. The following chart from 538.com gives the probability of each team winning their game this weekend:

NFL Week 17 - Game Probabilitiess

The good news is that the Colts have an 81% chance of winning their game against Tennessee. The bad news is that it seems unlikely that any of the Texans, Bengals, Chiefs, or Patriots will lose, let alone all four of them. So putting all those numbers together, the Colts’ chances of making the playoffs are:

0.81 × 0.20 × 0.22 × 0.84 × 0.54 × 0.69 × 0.15 × 0.18 × 0.77 = 0.0002 = 0.02%

or, more precisely, about 4,311-to-1. That’s more than a long shot; that’s an extended-to-an-unfathomable-distance shot.

The Colts are in the unenviable position of Lloyd Christmas in Dumb and Dumber, “So, you’re telling me there’s a chance…”

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The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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