01 January 2010

Victory Weighted NFL playoff scenarios (2/2)

First things first: Officially, there are seven contenders for the two AFC wild-card spots. Victory Weighting, however, eliminates Jacksonville. With a Strength of only 27, the Jaguars cannot hope to reach the minimum Strength (33) required to clinch a wild-card spot.

Two other factors make figuring out the Victory Weighting scenarios even easier.
  • Pittsburgh plays at Miami. Since any result for one team implies one (and only one) corresponding result for the other, we can act as though there are only five contenders.
  • Four other teams have already secured the division championship, so no one can be eliminated "upward" as a division champion.
Officially, the Jets and Baltimore control their playoff destinies. Under Victory Weighting, though, it's the Jets and Steelers who are in control. With only 31 Strength, the Ravens actually face a grim outlook. Here are all the AFC wild-card contenders, with their Victory Weighted chances to advance:

New York Jets (Strength 33, 8-7)
Probability of qualifying: 67.2%
Final game: vs. Cincinnati, 2020 EST
Advance with: a win, or losses by Houston, Baltimore and Denver
  • Because they play the last game of the day, the Jets and Bengals may be deciding other teams' fates.

Pittsburgh (Strength 33, 8-7)
Probability of qualifying: 65.4%
Final game: at Miami, 1300 EST
Advances with: a regulation win at Miami
Eliminated by: a regulation loss
  • Victory Weighting gives the Steelers lots of advantages. Unfortunately, they lose all tiebreakers, so an overtime win may not be enough. Combined with a Jets win and a Houston regulation win, an overtime win would actually eliminate the Steelers.

Houston (Strength 32, 8-7)
Probability of qualifying: 13.5%
Final game: vs. New England, 1300 EST
Advances with: a win over New England and a Pittsburgh loss or tie
Eliminated by: a regulation loss, or a Jets win and a Steelers regulation win
  • The Texans can also advance if Pittsburgh needs overtime to beat Miami. In that case, a regulation win leaves them tied with the Steelers, and Houston then wins the tiebreaker. Unfortunately, they have to beat the Patriots to have a chance.

Baltimore (Strength 31, 8-7)
Probability of qualifying: 2.90%
Final game: at Oakland, 1615 EST
Eliminated by: a loss, a tie, or wins by the Jets and Steelers
  • If Houston manages a regulation win, then a win by either the Jets or Steelers would eliminate Baltimore. The Ravens' chances are poor because so many of their qualifying scenarios involve ties, only 16 of which have occurred in the last 35 years.

Denver (Strength 31, 8-7)
Probability of qualifying: 2.07%
Final game: vs. Kansas City, 1615 EST
Eliminated by: a loss, a tie, or wins by the Jets and Steelers
  • Apart from the fact that they lose the head-to-head tiebreaker to Baltimore, the Broncos' situation is almost exactly the same as the Ravens'.

Miami (Strength 29, 7-8)
Probability of qualifying: 2.00%
Final game: vs. Pittsburgh, 1300 EST
Eliminated by: any result other than a regulation win
  • Even if the Dolphins win in regulation, Baltimore, Denver and Houston must all lose, and the Jets must lose in regulation. Any other combination sends the Dolphins home.
To make the percentages below a little easier to understand, note how specific tiebreakers play out.
  1. The Steelers lose all tiebreakers.
  2. The Jets win any tiebreaker with the Steelers with a better Strength within the AFC.
  3. The Jets owns the head-to-head tiebreaker with Houston.
  4. Houston wins any tiebreaker with the Steelers. The Texans would have either a better overall won-loss record or, more likely, a better Strength against the teams that both they and the Steelers have played.
  5. Baltimore wins any tie with the Jets or Steelers with a better overall won-loss record.
  6. Baltimore wins ties with Houston with either a better overall record or a better AFC strength.
  7. Baltimore owns the head-to-head tiebreaker with Denver.
  8. Denver wins tiebreakers with the Jets and Steelers for the same reasons Baltimore does. See points 5 and 6.
  9. Miami owns the head-to-head tiebreaker with the Jets. Because these two teams are AFC East rivals, the Jets cannot advance until Miami does.
  10. Miami wins any tiebreaker with Houston with a better AFC Strength.
  11. With a win, Miami would own the head-to-head tiebreaker with the Steelers.

How Victory Weighting could screw the Steelers

Pittsburgh won at Denver, so they would win a head-to-head tiebreaker with the Broncos. The Steelers also own the divisional head-to-head tiebreaker with Baltimore. Although each team beat the other once, the Ravens' win required overtime, so the Steelers have the better two-game Strength (5-3).

But Pittsburgh's lead over both teams is 2 Strength points, or, essentially, half a game. If the Steelers end up with the same Strength as either the Broncos or Ravens, they are guaranteed to lose, because they would have an inferior won-loss record. The head-to-head tiebreakers can never come into play.

Calculating the percentages

(¡Cuidado! Medium-low-level math appears below.)

While there are six contenders, two of them play each other, reducing the number of scenarios from 7,776 (6^5) to 3,125 (5^5), which further reduce to 475 distinct scenarios. Each possibility has a tiny probablility of actually occurring. The chance that any team earns a wild card is just the sum of the tiny probablilities from the distinct scenarios in which it qualifies.

The easier way to compute the probablities is to assume that each contender has the same chance to win in regulation, win in overtime, tie, lose in overtime and lose in regulation. In that case, the tiny probablity for each distinct scenario is just the number of times out of 3,125 that it occurs, divided by 3,125. All the number crunching leads to the following unweighted chance that each team advances to the playoffs.
New York Jets
These numbers don't quite reflect reality, because since the NFL adopted overtime in 1974, less than 5% of all regular season games have required an overtime. The 16 ties represent only 0.19% of all games played since then. It would be more accurate to assume, based on past results, that regulation wins and losses each occur 47.34% of the time; overtime wins and losses, 2.57%; and ties, 0.19%. The percentages in the main table result from recalculating the tiny probabilities using these weights.

Not surprisingly, the odds for the Texans, Ravens and Broncos suffer, since they depend so strongly on overtime results and ties.  The other three teams' qualifying scenarios don't involve as many ties, so their chances improve.  That goes especially for the Dolphins, for whom ties are absolutely deadly.

One last thing

The calculations ignore the odds of any contender actually winning or losing its game this week. For examples, Baltimore and Denver have weak opponents, so their chances may be better than the 2-3% cited in the main table. Similarly, since they host New England, the Texans' 13.5% chance may be an overestimate. The Victory Weighting scheme would make no attempt to account for the odds for individual games, whose calculations reside in the province of, well, professional odds makers.

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