Chargers-Broncos odds and all your Broncos playoff odds for Week 17

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.

The Broncos beat the Chargers 17-3 only three weeks ago in San Diego, so this big spread with the Broncos at home (and the Chargers further reeling from injury) makes sense.

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
=  .113.

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
= .703

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)
= .039

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)
= .145

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)
= .145

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.