This is the time of the year for joy and family and gifts--all that good stuff. But more importantly, it’s also the time for teams to jockey for playoff seeds. I get the sense that the conventional wisdom is that yes, seeds are somewhat important, but the notion that ‘just get in the playoffs and anything can happen’ is the dominant view. But as we'll see, seeding is critically important.

We’ve seen many wildcard teams make it to, and even win, the Super Bowl. There are four wildcard berths each year, and when we see a wildcard team make it to the Super Bowl, it’s noted, highlighted, and becomes part of the team narrative. No one remarks when the #3 seed makes it to the big game, despite it being less likely than *either *of a conference’s two wildcard seeds to make it.

Although it’s certainly true that ‘anything can happen’, that’s really only true from the perspective of a neutral observer. If you’re looking at the chance that any one of the four wildcard teams make it to the Super Bowl, you’ve got a pretty solid chance of seeing that happen. But if you look at it from the perspective of one particular wildcard team, your chances of going to the Super Bowl are relatively slim. It’s all a matter of perspective.

Football commentators certainly understand that seeds are important—a team would always prefer a higher seed. But I sense that they don’t fully appreciate how critical seeds are in the current NFL format. I hear talk about having home field advantage and having a week off to get healthy, but commentators seem to overlook the most important part of a playoff bye: It’s an automatic win in the first round. Maybe it’s overlooked because it’s so obvious, but those other considerations pale in comparison to the value of a free win. Right away, a bye practically doubles a team’s chance of making it to the Super Bowl. *Doubles*. A different way of thinking of the playoff format is that the top two seeds are the only two that actually ‘make the playoffs’, and the other four seeds must first win a play-in game.

To isolate just how critical seeding is, I calculated the chances each seed would make it to the Super Bowl due to seeding alone, ignoring differences in team strength.

I gave home teams a 60% chance of winning each game. Although the league-wide average is 57%, that number includes many mismatch games. When teams are close in ability, home field becomes more decisive. (Think of it this way: If the Packers played the Maryland Terrapins, the outcome wouldn’t depend at all on where the game was played.)

The probability for the #1 seed is straightforward. It’s just 0.6*0.6 because they need to win 2 home games. The #2 team needs to win 1 home game and has a 60% chance of being on the road in the conference championship (if the #1 seed wins its first game) and a 40% of being at home (if the #1 seed loses.) The total probability for the #2 seed would therefore be 0.6 * [(0.6*0.4)+(0.4*0.6)], which comes to 0.288. The probabilities for the other seeds become more complex but can be calculated the same way.

Here is how the probabilities work out for each seed. Also listed are the actual proportions of Super Bowl appearances since 2002 when the current format began. Keep in mind that the 'actual' numbers reflect the effect of both seeding and team strength, and that there are only 18 observations since '02, so they will be statistically noisy. Also note that the chances will not sum to 100% due to rounding. (Thanks go to my research intern for compiling the actual numbers.)

Seed | SB Prob | Actual |

1 | 36% | 44% |

2 | 29% | 22% |

3 | 11% | 11% |

4 | 10% | 6% |

5 | 7% | 6% |

6 | 6% | 11% |

You can see that the #1 seed has about

*six times*the chance of a wildcard team to make it to the Super Bowl. The #2 seed has nearly

*five times*the chance. These are enormous differences, and they’re due to seeding effects alone.

Right now the 49ers and Saints are jockeying for the #2 seed in the NFC. The loser of that battle will fall from a 29% shot to an 11% shot at making the Super Bowl.

In the AFC, the biggest battle is between the Ravens and Steelers for what is most likely going to be the #2 seed, assuming the Patriots win out. The loser of the AFC North battle will sink to the #5 seed, cutting their chance of making the Super Bowl by over a

*factor of four*, from 29% to 7%. In other words, the division champion quadruples its chance of making it to Indianapolis in February.

When it comes to making it to the Super Bowl, seeding alone is critically important, far more so than even team strength.

I can understand why Seed #1 would result in a actual % vs. expected, because the #1 seed is awesome, and thus probably wins > 60% of its games against lowest remaining seed.

I also understand why seed #4 is under it's expectation, this is more likely to be the worst division winner...who probably doesn't belong in the playoffs. (I'm looking at you NFC West)

Whats up with Seed #6? I would expect seed #5 to be the one who "overperforms".

I'm gonna second Anon's statement: what the hell is going on with Seed 5 and 6?

Anon - I wondered that about #6 as well.

When you consider that any successful run from #6 starts with beating #3 and #1 it seems even odder. Answers on a postcard.

It would be interesting to see the average win % and average WPA for each of the seeds.

@anon - sample size.

Anons, the data is from 2002-2010 so there have only been 9 opportunities for each conference to make the Super Bowl. Pit in '05-'06 and GB last year are the only 6 seeds to make it to the SB while NYG in '07-'08 was the only 5 seed. Not that big of a deal, right?

It appears that there are only 19 data points in this set. So that means 2 appearances vs. 1 appearance. Noise.

Before small sample size was pointed out, my thoughts regarding the 6th seed was it could be a team peaking at the right time. Maybe it was brought down early in the season by bad luck/injuries, and now its getting a stretch of good luck/healthy players.

Also, to really drive home the importance of the bye, just give every team a 50/50 chance. .5*.5=.25 for the top 2 seeds. .5*.5*.5=.125 for the rest. All but the most ardent Tebow fans should be able to understand that.

Dan S is correct.

Over the long run, we should expect the 5th seed to over-perform and the 4th seed to under-perform their expected SB appearance rates. 4th seeds are the weakest division winners (like SEA last year or whoever wins the AFC W this year), while 5th seeds are often really good teams just behind a slightly better team--think BAL and PIT or NYJ and NE.

I'm going to edit the post to underscore the small sample effect.

Regarding the #6 seed sometimes outperforming the #5 seed...

There was a study, I think at Pro Football Reference's blog, that showed that tiebreakers tend to favor the team with the worse actual skill level.

1990-2001 (three divisions instead of 4), the only teams that made it to a Super Bowl were the 1, 2, and 4 seeds.

"I also understand why seed #4 is under it's expectation, this is more likely to be the worst division winner...who probably doesn't belong in the playoffs. (I'm looking at you NFC West)"

The 6% for the #4 seed that made the SB is Cardinals. NFC West gets #4 more often than any other division. But you are talking about a small samples size and 1 sample difference.

Also in 9 years NFC West sent 2 teams to Super Bowl. That is about the expected value (2.25). Given then there is usually no WC team from NFC West you can say that NFC West outperforms other divisions in how much success they get after getting in playoffs.

i think this year when either steelers/ravens play broncos's and tim tebow the effect would be lot less significant. but then again that is a subjective judgement on my part

Thanks Brian for doing this. I was actually thinking about doing the exact same thing, so you just saved me a lot of work. I too think too little is made of the fact that getting a bye means you 100% cannot lose in the first round.

I really don't like the discontinuity between #2 and #3, but I don't know how to resolve it withou radical changes to the playoffs.

Steve, is that because you think both AFC North teams would have a large road presence?

For the Steelers, it's noteworthy that their starting FS cannot play in altitude due to a medical condition.

"No one remarks when the #3 seed makes it to the big game, despite it being less likely than either of a conference’s two wildcard seeds to make it." Why is it the case that #3 is less likely than #5 or #6?

"Right now the 49ers and Saints are jockeying for the #2 seed in the NFC. The loser of that battle will fall from a 29% shot to an 11% shot at making the Super Bowl."

If the 49ers and Saints had equal probability of obtaining the 2nd seed, wouldn't the fall be from 20% to 11%? 29x + 11(1-x) is only 29 when x is 1, indicating the seed is already locked up...which of course nullifies the entire argument.

Semantics, yes, but otherwise the importance of the battle is overstated.

Hi Michael,

I think it is because I think the steelers and ravens are above average teams and the broncos are a below average team. i think the steelers or ravens should kill the broncos but then again it is just my opinion. so what that would mean if i am correct in my assumption is that the free game does not matter in this instance as either team should kill the broncos and essentially get a free win.

@Michael: there is no such thing as a "free win" in the NFL. Perhaps the Steelers and Ravens have a better than 40% chance of beating the Broncos in Denver (as this simplistic model assumes) but 40% is probably closer than your ridiculous suggestion that we use a 100% Bronco loss model in place of the model used in the article.

And the historical predictions are an almost perfect match to actual outcomes observed: ONE extra sixth seed made it, ONE extra first seed, and one too few second and fourth seeds.

Pitt and Balt should be fighting tooth and nail for that second seed while NE will do all possible to keep the #1.

@ anon: you wrote:

"If the 49ers and Saints had equal probability of obtaining the 2nd seed, wouldn't the fall be from 20% to 11%? 29x + 11(1-x) is only 29 when x is 1, indicating the seed is already locked up...which of course nullifies the entire argument."

No, you miss the entire argument. The model does not care which team is BETTER, only which team gets which seeding which results in which teams get byes and which teams get to play at home.

So the fight for seeding IS the issue (in this simplistic model) NOT which team is actually better!

@ anon:

"If the 49ers and Saints had equal probability of obtaining the 2nd seed, wouldn't the fall be from 20% to 11%? 29x + 11(1-x) is only 29 when x is 1, indicating the seed is already locked up...which of course nullifies the entire argument."

I didn't even ask, where the hell did you get your formula of 29x + 11(1-x) anyway? Pulled that out of some warm dark place with no justification. Back to 7th grade math for you.

@ Dan "It appears that there are only 19 data points in this set. So that means 2 appearances vs. 1 appearance. Noise. "

9 years. 2 conferences. 18 data points.

Unless Tebow is the 19th?

@ SkyJo ""No one remarks when the #3 seed makes it to the big game, despite it being less likely than either of a conference’s two wildcard seeds to make it." Why is it the case that #3 is less likely than #5 or #6? "

#3 is less likely than #5 and #6 COMBINED, not individually. Review the table.

@Michael your wrote: "For the Steelers, it's noteworthy that their starting FS cannot play in altitude due to a medical condition. "

total BS.

What is the medical condition, and how is it he played in Denver on Nov 9, 2009, Jan 22, 2005, Oct 21, 2007, and perhaps in preseason, college, or high school games of which I am unaware (although quite doubtful for college or high school of course).

Your brand of BS seems to come in particularly large bags.

Clark ended his 2007 season early after having his spleen and gall bladder removed, after a game in the thin air of Denver's Invesco Field at Mile High caused health problems with Clark's blood due to sickle cell trait (because of this, whenever his team plays in Denver, Clark does not play). Clark lost 30 pounds after the removal, but has returned to the Steelers in 2008.

From Wikipedia. I personally remember Clark sitting out Pitt's last game at Denver

Is there any data on the idea of teams "peaking at the right time?" You hear about this a lot, and just this weekend my father and I were talking about whether or not the Packers had peaked too soon, and my thoughts were A) is my Dad saying that just because the Packers happened to lose in week 15 instead of, say, week 5, and B) I suspect that the whole "peaking at the right time" phenomenon is about as real as in-game momentum. I'm curious if there's been any actual analysis don on that.

Could someone write this into a probability formula?

Love this analysis. I'd agree with both notions that the "problem with 4 and 5" is probably that they are weak teams who have won in a weak division and that the success of 6 teams is a "peaking" team (because of injury, player development, coaching strategy, who knows). However, I'd translate that into team strength which means that seeding isn't more important than strength, as the article concludes. Thanks for delicious food for thought, Kip

Noticed a small error. I decided to verify these probabilities and for seed #3 got 11.7%. So in your table, that entry should round up to 12% and the overall total would be 100%.

The probability for seed 3 with your assumptions is exactly 0.4*probability for seed 2. They both play a home game first (P=0.6), they both have the same probability of winning the conference championship (P = 2*0.6*0.4 as shown above). The difference is the 3 seed plays an extra road game (P=0.4)

P 3seed = 0.4*0.288 = 0.1152

Thanks, Brian, I enjoyed this.

I look forward to updates, anticipating your addition of such as W/L records, say, to control for the hypothetically smaller difference in strength of #4 & #5 seed teams.