Super Bowl Repeat Frequency

July 3, 2009 7:00 AM

What's the correct analysis of the frequency of repeat Super Bowl winners?

Help provide me some facts/perspectives to prove my point to my friend (or prove me wrong, I guess...). This is a statistical question, really:

I'm a Steelers fan, my friend isn't. In discussing the upcoming NFL season (a little early, I know), I state that the Steelers have got to be one of the favorites heading into the season. He responds with "well, you pretty much know they're not gonna win because repeating as Super Bowl champs is so rare".

I counter with my opinion that it may not happen all the time, but it's not that rare.

Teams have repeated a Super Bowl champs 7 times: Green Bay in the '60s, Pittsburgh 2x in the '70s, San Fran in the '80s, Dallas & Denver in the '90s, and New England in the '00s.

There have been 43 Super Bowls, but we both agree on using a denominator of 42, since the Super Bowl 43 winner (Pittsburgh!) has not yet had the chance to repeat.

My friend's perspective is that since repeats have only happened those 7 times, thus 7 out of 42 (1 in 6), that repeats are rare.

My perspective is that out of those 42 Super Bowls, 14 wins were part of team's back-to-back win performance, so you have to count both wins, not just the 2nd, to analyze the frequency of this event. Thus, 14 out 42 (1 in 3) Super Bowl wins are part of teams' back-to-back Super Bowl winning events. And therefore, it's not that rare.

Who's looking at this from the correct perspective?

posted by glenngulia to sports, hobbies, & recreation (22 comments total)

wow, I just realized I missed Miami in the '70s...

thus, my friend's number would be 8/42=19% & mine would be 16/42=38%
posted by glenngulia at 7:07 AM on July 3

Assuming your statistics are right, it seems to me that both perspectives are accurate. Me, though, I'd say the right number of incidents to consider would be 42--Super Bowls II through XLIII. In XLIII, the Giants could've repeated. But nobody could've repeated in Super Bowl I.

This reminds me of that riddle about a duck walking behind two ducks, a duck walking in front of two ducks and a duck walking between two ducks. How many ducks? Three.

You're both right. Whether 19% or 38% is rare is a matter of opinion.
posted by box at 7:15 AM on July 3

The frequency of an event is the number of times that event occurs in the set.

It sounds like your event is repeat Super Bowl wins, not merely winning a Superbowl. If you are saying that there have been 14 repeat Super Bowl wins, then 14/42 = 33.33%.
posted by dfriedman at 7:17 AM on July 3

The number you are looking for is the conditional probability: what is the probability that a team will repeat, given that it has just won. This is the situation you are in now, and it gives about his number. You can close the gap with yours by throwing a couple more out (not penalizing for not three-peating), but your friend is more correct.
posted by gensubuser at 7:22 AM on July 3

I'm definitely no mathematician, but it seems to me that 7/42 isn't very rare at all.

In Super Bowl I, there were 16 teams in the league. Last year, there were 32 teams, and only five of those have never been to a SB (though as a former Clevelander, I should point out that they won a few championships in the pre-SB days).

So, all things being equal, the chances of a team repeating an SB win would be between 1/16 and 1/32. 7/42 is a much better chance than that.
posted by box at 7:28 AM on July 3

I think box is looking at part of this correctly. You do have to look at 42 Super Bowls for his reason and not yours. Winning the first Super Bowl in the pair doesn't do anything except keep the previous winner from repeating.

Let's take a look at gensubuser's idea though and throw out the Super Bowl after a repeat. That leaves us with 8 repeats out of 34 Super Bowls (23.5%).

There are various other factors, such as the probability that a team repeats even getting into the playoffs or having a winning season (something my Falcon's haven't figured out how to do yet). Just looking at the 8/34 probability of a repeat champ assumes that the previous year's winner will reach the Super Bowl again.
posted by theichibun at 7:37 AM on July 3

Your friend is more correct.

Your basic question is "how likely is it that, given a chance to repeat as super bowl winner, a team is able to do so?"

First we have to identify the number of opportunities for repeat winners - that is, the number of years in which the super bowl winner could have been the same as the previous year's winner. There have been 43 Super Bowls. In 42 of those, there was an opportunity for the winner to repeat: we exclude Super Bowl 1 because, by definition, the winner could not have been a repeat winner. We do not exclude Super Bowl 43, because that year the winner could have repeated from the previous year.

Now we identify the number of successful repeats. On 8 occasions, the super bowl winner has been the same as the winner of the previous year's super bowl.

So, given 42 opportunities, teams successfully repeated 8 times. 8/42 = 19%.

Here is why we do not count all the wins, as you argue: Consider the Patriots' repeat in 2004 and 2005. 2005 counts as a successful repeat, because only New England was in a position to repeat, and it did. 2004 does not count as a successful repeat, because only Tampa Bay was in a position to repeat, and it failed to do so.
posted by googly at 7:43 AM on July 3

Your friend is wrong. Steelers are a favorite.

Even if you go by your wrote "repeat" statistics, which are not really applicable in today's salary cap NFL, being a favorite to win the Super Bowl still doesn't put your odds more than 15%. It's simply that difficult to do, mostly because an NFL playoff game can be lost on a whim (fumble, interception, field goal, tuck rule, leaping overhead catch, interception return from the endzone etc...).

Compare the Vegas odds to the repeat odds. Might shine some insight...

But going beyond statistics, the ability for a team to repeat in the NFL requires a sustainable core nucleus (e.g. Patriots with Brady, Seymour, LB Core and Bellicheck), some good off season additions, missing the injury bug and some serious luck throughout the season.

Steelers have all the ingredients they can control. Can they avoid injury and play to their capability? It's yet to be seen.
posted by stratastar at 7:47 AM on July 3

The two of you are answering different questions.

You are answering the question "What percentage of Super Bowls are part of back-to-back Super Bowl wins".

He is answering the question "What is the chance that the current Super Bowl winner will win the next Super Bowl".

The latter, not the former, is the question that the two of you are asking. So, your friend is correct (at least, in the mathematics; in his characterization of 1 in 6 as "rare", he's way off).
posted by Flunkie at 7:48 AM on July 3

Or, think of it this way:

Flip a bunch of coins. Let's say you flip a hundred of them. Now consider flipping a hundred and first time: What's the chance that you'll get the same heads-or-tails as you got on the hundredth flip?

I assume that you will agree that the chance is 50% (with a fair coin).

But that's not the number you would get via your method of calculation. If you go back over those 100 flips and count every flip that was the same heads-or-tails as the flip before it or the flip after it, you would likely get a number near 75, not near 50.
posted by Flunkie at 7:56 AM on July 3

One more post, and then I'm outta here.

Thus, 14 out 42 (1 in 3) Super Bowl wins are part of teams' back-to-back Super Bowl winning events.

You may be able to see the flaw in your reasoning by considering the fact that Pittsburgh has already, preemptively, lost half of their opportunity to have Super Bowl XLIII be part of a repeat, because of the fact that were not the Super Bowl XLII champions.
posted by Flunkie at 8:12 AM on July 3

Flunkie-

On your 1st comment: I agree that my friend I are asking 2 different questions. I'm trying determine what's the better question to be asking here.

On your last comment, (and based on many comments I'm wrong from a statistical perspective here) I'm throwing out the SB43, not SB1. If the Steelers win SB44, then their back-to-back can count toward the then recalc'd total.

I guess my perspective is that of a team owner/coach/player who sets a goal to win back-to-back SBs (maybe b/c that's what's remembered in history more than a 1-and-done deal). If I'm this hypothetical guy, I look to the #s and see that of all SB winners w/ a chance to repeat (SBs 1-42), 8 of them did. Therefore, 16/42 SB wins were part of a back-to-back event, which makes it seem not that rare.

Is there not some sort of statistical explanation (and I'm grasping at straws here) that validates my 16/42 (38%) figure as the best description of the point I'm trying to make?

Or is the answer that I'm wrong and this is simply a conditional probablity problem, meaning you must use SBs 2-43, which results in 8/42=19% (or maybe best case of the gensubuser/theichibun modified version of throwing out 8 to get 8/34=24%)?
posted by glenngulia at 8:49 AM on July 3

Like you say, you're grasping at straws here.

Do you really think that there's an almost-forty-percent chance of back-to-back Super Bowl wins?
posted by box at 9:03 AM on July 3

I guess my perspective is that of a team owner/coach/player who sets a goal to win back-to-back SBs (maybe b/c that's what's remembered in history more than a 1-and-done deal). If I'm this hypothetical guy, I look to the #s and see that of all SB winners w/ a chance to repeat (SBs 1-42), 8 of them did.

Exactly. What you are asking about here is the action of repeating, not the total number of wins. The coach is focused not on the first win, but the second one.

Therefore, 16/42 SB wins were part of a back-to-back event, which makes it seem not that rare.

No, this is where your logic is flawed. The rare event is not both wins, but rather the second win alone. Think of it this way: Pittsburgh won Super Bowl XLIII. You do not consider that win "rare," because they are simply the super bowl winner. If they win Super Bowl XLIV, that win is the rare event. But it does not magically make the XLIII win "rare." The rarity is winning the second SB, not the first.

Is there not some sort of statistical explanation (and I'm grasping at straws here) that validates my 16/42 (38%) figure as the best description of the point I'm trying to make?

As Flunkie said above, the only question that this is the correct answer to is "What percentage of Super Bowls are part of back-to-back Super Bowl wins?" There is nothing wrong with this question, but it doesn't really seem to be the one that you and your friend are addressing.
posted by googly at 9:11 AM on July 3

Box-

Well think of it this way...

Looking at the SBs 1-42, 26 of them have been won by a team that didn't win the previous or subsequent year, while 16 have been won by a team that did win either the previous or subsequent year.
posted by glenngulia at 9:20 AM on July 3

Looking at the SBs 1-42, 26 of them have been won by a team that didn't win the previous or subsequent year, while 16 have been won by a team that did win either the previous or subsequent year.

So what? That has nothing to do with the question.

The question you and your friend were originally trying to answer was the chance of the Steelers repeating.

The question that you have morphed that into is not the same as that. That's why it has a different answer.

The real question: What's the chance of a Super Bowl winner winning the next Super Bowl?

The question you have morphed it into: What's the chance of a Super Bowl winner either winning the next Super Bowl or having already won the previous Super Bowl?

Your friend answered the question that both of you asked. You're answering a question that no one has asked. I'm really not sure what else to say.
posted by Flunkie at 10:07 AM on July 3

Thanks, all!
posted by glenngulia at 10:17 AM on July 3

So assuming its OK to round 8/42 to 1/5 and 16/42 to 2/5, could we all agree that the following statement is accurate?

2 out of 5 past SB champions have come as part of a back-to-back SB-winning accomplishment. Thus, if the history of the previous 42 SB winners is any indication, the SB 43 champion Pittsburgh Steelers have a 1 in 5 chance to repeat as SB winners.
posted by glenngulia at 11:05 AM on July 3

Imagine that you want to draw a heart from a full deck of cards. You have a 1 in 4 chance. What is the chance that you, after putting the card back, draw another heart? It's 1/4 x 1/4= 1/16.

Your strongest argument is that by winning the second Superbowl, teams wildly over-perform against random chance.
posted by klangklangston at 12:50 PM on July 3

Of course, sometimes you draw the card with the ranked poker hands on it. That year, the Super Bowl champs were the Montreal Expos.
posted by box at 12:56 PM on July 3

The NFL network just did a show on myths in football, one of which they covered was the repeat winners question. They basically said that it's really difficult to win it, so it's just rare that a team will win it twice at all, regardless of whether it's consecutive wins, and that winning it twice in a row is no more harder the second time.

As Flunkie said - flip a coin twice and the chance of it repeating the same result is still 50/50.


That said, I would think the chances change now with the salary cap and things. If you win a superbowl, chances are a lot of the players who took you there are going to go up in price, stopping you from keeping them all. Winning the followup would thus be about effectively coaching rookies and drafted players to continue a style that you found success with. Then again, by that logic, should the Detroit Lions have gone a season without a single win, after what should have been quite a good draft year for them prior to it? It becomes very complicated with all the variables.

I've been considering these thoughts since seeing that segment the other day. Perhaps though, I'm just overthinking. I don't know!
posted by opsin at 2:24 PM on July 3

Poisson Distribution?
posted by ZenMasterThis at 4:05 PM on July 3