### Probabilities of Playoff Droughts and Some Bold Playoff Predictions

Arizona, Buffalo, Detroit, Houston, and Miami are the only 5 teams in the league not to have a postseason appearance in the 5 postseasons since the 2002 realignment. Cleveland, San Francisco, and Oakland have not appeared in the last 4 postseasons. "Probability is like gravity. You cannot fight gravity." (A chocolate chip cookie to the person that gets that reference.) Eventually, the unlikely scenarios will happen, and fortunes will reverse. It's the cyclical nature of the league. So what are the odds of a team going on a 5-year postseason drought?

To simplify the calculations, I'm making two assumptions. First, each team has an equal probability of reaching the postseason. Second, the results of each year are independent of each other. Obviously there's a wide array of influences that affect the actual probabilities, but let's keep things simple. As it turns out, the simplest solution is pretty accurate. So the probability of a team having a playoff drought for X seasons is simply .625^{X}. The following table lists the probabilities and the expected number of teams experience such a drought at any given point in time.

Playoff drought of ≥X years | Probability | Expected number of teams | Actual number of teams | Year (latest possible) of last playoff berth |

1 | 62.5% | 20 | 20 | 2005 |

2 | 39.063% | 12.5 | 13 | 2004 |

3 | 24.414% | 7.8125 | 9 | 2003 |

4 | 15.259% | 4.8828 | 8 | 2002 |

5 | 9.5367% | 3.0518 | 5 | 2001 |

6* | 6.1527% | 1.9073 | 3 | 2000 |

7* | 3.9695% | 1.2305 | 3 | 1999 |

8* | 2.561% | 0.7939 | 1 | 1998 |

** Probabilities adjusted to account for there being 31 teams in the league 1999-2001. P(Missing playoffs 1999-2001) = 20/31 = 64.516%. Actual number of teams does not include Houston.*

For the most part, the number of actual teams with such playoff droughts match up with the expected number. The only aberration is the number of teams with droughts of at least 4 years. That list of teams is: Arizona, Buffalo, Detroit, Miami, Cleveland, Houston, San Francisco, and Oakland. The probability of having a drought of 6 seasons is 5.9605%, so only 2 (1.9073 to be exact) teams are expected to not have made the playoffs in the 2002-7 timeframe. In other words, expect two or three teams in the ARI, BUF, HOU, MIA, DET set to make the playoffs. Guess what two of the teams are expected to improve in 2007 based on actual vs. expected wins in 2006? Miami and Detroit.

**That's right. I'm calling it right now: Miami and Detroit are making the playoffs. And will fail immediately thereafter.**Trent Green will have a lot to do with Miami's success. And with a tough schedule, I don't expect them to go more than 9-7. Jon Kitna put up some very good yards per attempt numbers in 2006 but was hampered by really poor pass protection. The defense was very bad, too, but teams with good passing offenses tend to make the playoffs. Detroit could wind up 8-8 with an average passing offense made good to very good with better pass protection and the addition of Calvin Johnson. Plus, the NFC North is not a particularly strong division. At the same time, the article about rising and falling teams projects Detroit to finish last in the division (and Miami to finish first in the AFC East). Honestly, calling Miami and Detroit goes against every instinct I have as a football aficionado, but there it is. Both teams, after runs of bad luck, should gets runs of good luck. Regression to the mean. No risk, no reward. If I'm wrong, I will post a picture of myself with JACKASS written across it.

So I'm predicting neither Arizona nor Buffalo will break their skids. Both teams have not done anything to get appreciably better, but what are the odds of their playoff droughts continuing into 2008? Buffalo's last playoff game was the Music City Miracle in the 1999 season. 2 seasons of 31 teams and 6 seasons of 32 teams. (20/31)

^{2}*(20/32)

^{6}= 2.4809%. The chances of a team not making the playoffs from 2000-7 is 2.4809%. The expected number of teams with such a drought out of 31 teams is 0.76909. Based on my predictions for ARI and BUF, the actual number will be 2. The difference of 1.231 teams between expected and actual is not abnormal, looking at the table. Meanwhile, for the Cardinals, the probability of a team not making the playoffs from 1999-2007 is (20/31)

^{3}*(20/32)

^{6}= 1.6006%. Given 31 teams, the expected number of teams to experience such a drought would be 0.49619. So it's not ridiculous to think Arizona's not quite ready for primetime based on those odds.

Buffalo had a very good pass defense in 2006, which carries a high probability of a playoff berth (just not as high as with pass offense), but they lost their shut-down corner, Nate Clements, to San Francisco. Since the probable loss in pass defense won't be offset by the possible gain in rush offense with Marshawn Lynch, I don't see Buffalo improving, let alone enough to make the playoffs. Arizona will improve in Leinart's second year, but given how bad the other parts of the team are, I think it will be another year or two before Leinart will drag that team into the playoffs. Showing how much I think of them, I forgot to include Houston in my analysis in the first draft of this article. Houston actually came very close to being predicted as a faller to begin with (4.7810 expected wins, 6 actual, 1.2190 difference, with barrier being 1.233). They're just not very good in any area, and the division should be very competitive with Indy and the Jags.

In case you were wondering, the Bengals did a phenomenal job of fighting gravity from 1991-2004. The probability of a team experiencing a playoff drought in that time frame was 0.33711%.

To recap, the odds show that one or two of the Fantastic Four (ARI, BUF, DET, MIA) should make the playoffs this year. Given the last 6-8 years to color our perceptions, none of them seem likely to make the playoffs. But surprises happen every year, and streaks have endings. That doesn't mean you should expect great things from these teams. It just means things will swing their way for once. Both Detroit and Miami underperformed their expected wins based on my Value Over League Average stats (as well as Pythagorean Wins and DVOA Expected Wins), which also indicates they will be better in 2007. Improvements in passing offenses will lead to better records for Miami and Detroit, which might be just enough to push them into the playoffs.

*8-27-07: Took out paragraph about Green Bay and Chicago because it wasn't particularly relevant, and when I went back to check the projection, I found I had mixed up the order.*

## 2 comments:

I hope you're not saying those teams are due. That's called the "gamblers fallacy." Or am I misunderstanding your point?

If you're rolling a fair die, and you notice a 6 hasn't come up in many rolls, what's the probability you'll get a 6 on the next roll?

1/6. Not one bit higher or lower.

Rather, I think you've provided very strong evidence that some teams are "more than unlucky"--i.e. poorly run.

I think you're misunderstanding my point. If I were saying those teams were due because it's unlikely, then I'd be boosting Arizona in addition to Detroit. Poor management is always going to bump up those probabilities.

A number of factors went into my decision to pick Miami and Detroit. First, the number of teams that haven't made the playoffs in the last 4 years is unusually high. Maybe there's always one aberrantly large set. I don't know as I haven't taken a look at it. Second, of those 8 teams, only Miami, Detroit, and Oakland are projected to improve on their win totals. Miami had 8 expected wins, so an improvement to 9-7 isn't out of the question. Detroit has the benefit of playing in a weak division, with Chicago expected to regress. Also, I see Detroit having a stronger passing game than Minnesota or Chicago, and teams with very strong passing games usually make the playoffs.

So it's not as simple as "they're due." Those were the 2 of the 8 teams that I felt like I could make a reasonable argument for making the playoffs.

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