Tie-breaking Procedures

[TomTerrific]

I was idly pondering the tie-breaking procedures should some combination of the Pats, Cincy, and Denver finish the regular season tied. To review, here are the two and three-team procedures

Two Clubs

1. Head-to-head, if applicable.
2. Best won-lost-tied percentage in games played within the conference.
3. Best won-lost-tied percentage in common games, minimum of four.
4. Strength of victory.
5. Strength of schedule.
6. Best combined ranking among conference teams in points scored and points allowed.
7. Best combined ranking among all teams in points scored and points allowed.
8. Best net points in conference games.
9. Best net points in all games.
10. Best net touchdowns in all games.
11. Coin toss.

Three or More Clubs

(Note: If two clubs remain tied after third or other clubs are eliminated, tie breaker reverts to step 1 of applicable two-club format.)

1. Apply division tie breaker to eliminate all but the highest ranked club in each division prior to proceeding to step 2. The original seeding within a division upon application of the division tie breaker remains the same for all subsequent applications of the procedure that are necessary to identify the two Wild-Card participants.
2. Head-to-head sweep. (Applicable only if one club has defeated each of the others or if one club has lost to each of the others.)
3. Best won-lost-tied percentage in games played within the conference.
4. Best won-lost-tied percentage in common games, minimum of four.
5. Strength of victory.
6. Strength of schedule.
7. Best combined ranking among conference teams in points scored and points allowed.
8. Best combined ranking among all teams in points scored and points allowed.
9. Best net points in conference games.
10. Best net points in all games.
11. Best net touchdowns in all games.
12. Coin toss

Things could get really complex, but one straightforward case to analyze is both the Pats and the Bengals going undefeated for the season. In that case, there's a two club tie-breaker, and tie-breakers 1, 2, and 3 don't apply, which brings us to Strength of Victory (SoV). I believe SoV is that combined records of all the opponents you've beaten. To clarify, double-counting is allowed, so if you beat KC twice then you get to add in KC's record twice when computing SoV.

Currently, both CIN and NE are 8-0, and the combined records of the teams they've beaten are 26-41 and 28-38, respectively. This is why current playoff standings charts show the Pats as the #1 seed.

If both teams go undefeated, what is the probability for each of them that they will win the Strength of Victory tiebreaker? To start with, I used 538's ELO-derived probabilities for winning each game going forward. CIN's expected SoV at this point is 117.5-138.5, while NE's is 119.7-136.3. We have to adjust this slightly since we are contingent on both teams going undefeated, so we have to subtract from SoV the fractional victories the ELO prediction was providing to CIN and NE's opponents when they played those teams. Doing this brings us to a contingent expected SoV for CIN of 115.1-140.9 (44.96%) and NE of 117.8-138.1 (46.02%), or an expected margin of 2.7 wins in SoV for NE over CIN.

Given those expected values, what are the chances, then, that NE actually finishes with a higher SoV? We treat the above values as the mean, and use the standard binomial variance formula for n flips of a weighted coin. For p I used the expected success rate for CIN and NE's opponents. Doing all this, it turns out that the probability that CIN's SoV exceeds NE's if they both go undefeated is about 41%.

BTW, it's a good thing Denver lost, which means it's unlikely (though still not impossible) we get a 3-way tie that has to use SoV as the tiebreaker, because Denver's expected SoV is currently around 48.83%, meaning it would have been extremely likely that they finished with the best SoV

 

[Stitch01]

Pats and Bengals have common games with the Bills, Steelers, Texans, and Broncos so record in those games will be used before strength of victory. Wont come into play in the unlikely case both teams are 16-0, obviously, but shows that Broncos game is going to be uber important for tiebreakers. Pats beat Denver, Denver beats the Bengals, and its really likely the Pats are the 1 seed.

 

[tims4wins]

Pats and Bengals have common games with the Bills, Steelers, Texans, and Broncos so record in those games will be used before strength of victory. Wont come into play in the unlikely case both teams are 16-0, obviously, but shows that Broncos game is going to be uber important for tiebreakers. Pats beat Denver, Denver beats the Bengals, and its really likely the Pats are the 1 seed.

Yeah I have a sneaky feeling that we may end up rooting for Denver to win that game against Cincy - feel like they are going to tack on another loss or two. This is especially true if the Pats win in Denver. If the Pats lose in Denver, then who knows.

 

[Stitch01]

Yeah if the Pats win in Denver than Denver has to play three games better than the Pats in their other games to pass the Pats. Very likely would want them to beat the Bengals.