The Denver Broncos are heavy favorites in Week 17 as they play for the AFC West Championship, perhaps the biggest favorites they've been all season. The Broncos opened as seven-point favorites against the San Diego Chargers, but that line quickly moved in Denver's direction, who are now nine-to-ten-point favorites, according to the latest NFL odds.
We all know that the Broncos can still land at the No. 1 through No. 6 seeds (except 4); using BettingTalk.com's point-spread based probabilities, I decided to calculate the odds for Denver landing at each spot. I could have used a different analytic as a starting point, but chose this for simplicity and the strength of the historic sample size. (I have a Bachelors of Science in Math and Computer Science; I rarely get to use the former in my every day life. Indulge me!)
The spreads that matter
- San Diego Chargers (+9) at Denver Broncos - DEN has 80.7% chance of winning
- Oakland Raiders (+7) at Kansas City Chiefs - KC has 75.2% chance of winning
- New England Patriots (-10.5) at Miami Dolphins - NE has 86.0% chance of winning
- Baltimore Ravens (+9) at Cincinnati Bengals - CIN has 80.7% chance of winning
Note: I'm ignoring the probability of ties in all of these calculations as negligible.
Odds for the Broncos to win the No. 1 seed
The Broncos can only get the No. 1 seed with a win AND a Patriots loss. See that "AND"? That's multiplicative, as far as stats go. Referencing the spreads-based odds above, that is
Odds of a Broncos win * Odds of a Patriots loss
= (.807) * (1.0 - .86)
= .807 * .14
The Broncos have an 11.3% chance of winning the No. 1 seed.
(Although, if you look at the Dolphins locker room right now, it's probably less than that).
Odds for the Broncos to win the No. 2 seed
It's lucky the No. 1 seed calculation was relatively easy, as an intro to this type of statistical calculation; here, the math gets a little trickier. The Broncos can get the No. 2 seed in a number of situations, but ignoring ties and making sure we are keeping our distinct sub-scenarios mutually exclusive, it basically boils down to two:
The Broncos win AND the Patriots win OR
The Broncos AND Chiefs AND Bengals each lose
Let's plug in the numbers; "OR" is additive, and as we know, "AND" is multiplicative. That calculates to
(Odd of Broncos win * Odds of Patriots win) + (Odds of Broncos loss * Odds of Chiefs loss * Odds of Bengals loss)
= (.807 * .86) + (.193 * .248 * .193)
= .694 + .009
The Broncos have a 70.3% chance of winning the No. 2 seed.
Since we ensured our sub-scenarios were mutually exclusive, it's now easy to combine (add) these two, showing that the Broncos have an 81.6% chance of a playoff bye.
Odds for the Broncos to win the No. 3 seed
Ensuring mutual exclusivity is the hardest part to these statistical situations. We have to make sure our sub-scenarios don't overlap. Therefore, the Broncos land at No. 3 if and only if:
The Broncos lose AND the Chiefs lose AND the Bengals win
= (.193 * .248 * .807)
The Broncos have a 3.9% chance of ending up the No. 3 seed.
Adding these three scenarios up, the Broncos have an 85.5% chance of winning the AFC West.
Odds for the Broncos to get a Wild Card
This would mean the Broncos lose the AFC West. This scenario also only happens if
The Chiefs win AND the Broncos lose
= (.752 * .193)
The Broncos have a 14.5% chance of ending up a Wild Card.
Let's do a math check; there's another way to calculate this Wild Card probability. We know the Broncos have a 100% chance of making the playoffs. We also know they cannot land at Seed #4. Therefore, the odds for a Wild Card are simply 1.00 - (the sum of all the distinct seed probabilities we previously calculated).
The odds of the Broncos making the playoffs MINUS the odds the Broncos get the No. 1 OR No. 2 OR No. 3 seed
= 1.00 - (.113 + .703 + .039)
= 1.00 - (.855)
The math checks out, and my math professor will be proud (I will literally share this on my Calculus teacher's Facebook wall in a bit).
Put another way, the Chiefs have a 14.5% chance of winning the AFC West.
All the Broncos need to do is take care of business vs. the Chargers at home, as nine-point favorites, to make that impossible.