The Super Bowl has come and gone, but there was something rather unique about Super Bowl LV. We bring you the second installment of our Sports Math blog series, where we take a mathematical look into this historic game. Enjoy!

In case you missed it, the Super Bowl was last weekend. While history was made on the field - and on a completely unrelated note, I think “Tommy B and the 10 Superb Owls” would make a great children’s book, but I digress - something never before seen had already happened as soon as Tampa Bay qualified for the Super Bowl. This is the 55th Super Bowl, but it is the first time that a team has gotten to play in the Super Bowl in their home stadium. The Super Bowl is awarded to different host cities and stadiums years in advance, and never before has the team whose stadium has hosted actually been one of the teams in the Super Bowl.

When I first heard this, my immediate question was “What are the chances?” How likely is it that a team would get to play in their home stadium during the Super Bowl in any given year, and how likely is it that it wouldn’t happen for 54 years?

To do the math here, we will first make a few assumptions to simplify the calculations. This is something that mathematicians will often do, and once we look at the results, we’ll come back and challenge our assumptions to see how they might have affected what we've found.

• Assumption #1: Super Bowl hosts and participants are selected at random every year. Or another way of looking at this is that every team and stadium has an equal chance to hosting and/or participating in the Super Bowl. From a mathematical standpoint, we can refer to these as Independent Events
• Assumption #2: We’ll assume there have been 32 teams in the league for the whole Super Bowl era. This just means we can treat every year exactly the same.

Part 1: Odds in any given year

So let's get started with the first question. In any given year, how likely is it that the host stadium’s team will make the Super Bowl? First, we’ll choose a team whose stadium gets to host the Super Bowl. Let’s call that Team T. Now, what are the chances that Team T makes the Super Bowl? Well, there are 32 teams in the NFL, and 2 of them make the Super Bowl every year, so the probability of Team T (or any other team) making the Super Bowl is 2/32, or 1/16, which is 6.25%.

So, in any given year, the odds of the host team making the Super Bowl are 1 in 16, or 6.25%

Part 2: Odds of no host in the first 54 years

Using our answer from part 1, we can say that while there is 1/16 chance of making the Super Bowl, there is a 15/16 (or 93.75%) probability of NOT making the Super Bowl in any given year. Based on assumption number 1 above, the probability of no host team playing in the Super Bowl for 54 years is (15/16)^54 = 0.03065…
This means that based on our assumptions, there was about a 97% chance that a host team would have played in the Super Bowl before this year! That’s not a guarantee, but it is certainly a bit surprising that we haven’t had a host in the Super Bowl before now.

So let’s take a look at our assumptions, to see how they may have impacted our calculations.

Part 3: Revisiting Assumptions

Assumption #1: There are a couple of issues with this assumption, one of which make it slightly less likely that the host team would have ever played in the Super Bowl.

• First of all, there have been 7 Super Bowls held in stadiums that weren’t the home team for any NFL team, so in those years, there was no chance of a team playing in their home stadiums. The Los Angeles Rams actually played in the Super Bowl in Los Angeles in 1980, but the game was played at the Rose Bowl, while the Rams played their home games at the Los Angeles Memorial Coliseum. The San Francisco 49ers had a similar experience in 1984. This means that there have only been 47 opportunities where a host team could have played in the Super Bowl, not 54.
• Secondly, not every city has the opportunity to host the Super Bowl. In fact, over 50% of Super Bowls have been held in Miami, New Orleans or Los Angeles. Additionally, the NFL prefers to hold the Super Bowl in warmer (or climate controlled) environments, so cities with outdoor stadiums like Buffalo really have no chance of hosting. This would impact the probability if another part of the assumption was wrong, and if consistently colder cities tended to have better teams (but that’s a topic for another post).

Assumption #2: This is definitely false, but it makes it more surprising that a host has never played in the Super Bowl.

• The NFL has grown significantly over the past 55 years, with only 24 teams competing for the Super Bowl in the first year, and growing slowly to the current size of 32 teams in 2002. This would impact our calculation of the odds of any given team making the Super Bowl in a year. Fewer teams = greater probability.

Conclusion

So to answer the questions that was on everyone’s (no one’s?) mind, it is somewhat surprising, though not outlandishly so, that a team had never played in the Super Bowl in their home stadium. But we can now say after Tampa Bay’s victory, based on evidence, if you make the Super Bowl in your home stadium, you have a 100% chance of winning! Right?