## Super Bowl Probabilities

Carolina is still the slight favorite, mostly thanks to their easier task this weekend. On the AFC side, Pittsburgh has the edge. Arizona fans, don't hold your breath...but that's exactly what I would have told Giants fans last year.

% Probability

 Team Conf Champ SB Champ CAR 45 25 PIT 39 21 NYG 34 17 TEN 32 14 PHI 16 8 BAL 16 7 SD 13 5 ARI 5 2

One thing that hits me when I look at this table is that the "best" team probably won't win the Super Bowl. You might not agree the best team is Carolina. That's fine. I'm not sure if they are or not. It might be Pittsburgh or the Giants or any of the other remaining teams. But whoever they are, they're probably not going to be the champs.

This isn't a new revelation to me at all, but it's particularly clear now perhaps because there isn't a definitive favorite this season. The task of winning 3 or 4 playoff/Super Bowl games, even for a dominant team is so improbable that no one team would realistically have a greater than 50% chance. A team would need an average 80% chance of winning each of three games against playoff caliber opponents to just have a 50/50 shot at taking home the Lombardi Trophy. (0.803 = 0.51).

### 8 Responses to “Super Bowl Probabilities”

1. Anonymous says:

What is the "best" team if not the winner of the championship protocol?

Or: What does "best" mean? In my world, it usually means most suited for a purpose or highest (or lowest) score on a defined dimension.

I have always contended the winner of the Superbowl is by definition the "best."

2. Anonymous says:

I have always contended the winner of the Superbowl is by definition the "best."

I consider the winner of the Super Bowl to be the "Champion".

At Wimbledon the 12th seed can win, in MLB an 83-win team can take the World Series (the Cards 2006). They aren't the "best" but they are the champions.

It's no slight to them -- you play to win the championship.

When you are the best and lose (Cards with 105 wins get swept in four straight in 2004) it's pretty bitter.

3. Anonymous says:

You pose 2 vary different scenarios. In tennis, the purpose of a tennis season is not to win Wimbledon. Wimbledon is one of many tournaments which players can enter or not. Additionally, players can have different yet legitimate goals which might or might not include winning Wimbledon.

In MLB, as in NFL, the goal is to win the championship. One team will be successful per year, the others won't. So what is "best?" The most talent in their player roster? It takes more than talent. The definition of team extends beyond the starters, or even the players and includes the entire organization.

4. Anonymous says:

I think the definition of the best team is the team who was the best over the entire season including the postseason. Someone who would win it all if we played the same matchup 100 times. Not who would win it all in a one and done setting. Probably something like Mr. Burke's or FO's ranking after the playoffs are done and all of those games are included is about as good of a way of saying who the best team is but even then the season and playoffs may not have been long enough as luck can effect a significant amount of 19-20 games. I think Jim's claim of calling them "champion" is right. I dont think the NFL or MLB tries to claim that the best team is the champion, they just say champion. It is the media who tries to claim they were the best team.

5. Anonymous says:

JMM: I look at it this way...

A sports team's goal is "Win the Championship." If you win it you are The Champion and have achieved your goal.

What's the best method of achieveing this goal? Build the "best team". The best team is that which has the highest probability of beating all the other teams in any given contest.

Failing that, building the best team that you can maximizes your chances of achieving your goal, even if somebody else's chances are greater. (Alternative methods of achieving the goal, such as bribing the refs every week, seem less promising.)

Does the best team win every game or contest?

Of course not. The '27 Yankess lost near 30% of their games. Logic dictates that in the NFL there must be one "best team" each year, yet there's only been one team in NFL history that won all its games -- so clearly the "best team" loses games, and "better" teams lose to "inferior" teams with some regularity. This is due to contingency/chance/dumb luck, which also plays a role in game outcomes.

I mean, say the "best team" plays the 2nd-best, and in doing so meets the definition being the "best team" by having the hightest probability of all teams at beating the 2nd-best (this is a legit championship game) yet that probability is only 55%. Clearly luck is going play a big part in that game outcome.

In a "short series" chance plays a larger role in determining the outcome than in a longer series -- and no series is shorter than one game, such as an NFL playoff game or Super Bowl.

So how does one define the "best team" -- the one with the highest probability of winning -- specifically, and by degree of superiority over other teams? There are lots of different takes and methodologies on this at stat sites like this one, Football Outsiders, Wages of Wins, etc. (Not to mention offices in Vegas). The details of methodology are debatable in practice, but the basic principle is pretty clear and certain.

So ... the objective is to win the championship and become The Champion. The method of maximizing your chance of success at doing this is to build the best team possible. Does attaining your objective and becoming The Champion prove you also had the one best team that had the best chance of winning? No, not at all, because the team with the lesser chance sometimes wins.

Does that matter? No, because you attained your objective and are The Champion! Why be defensive about being the "best" too? That doesn't matter (until you start figuring your odds of repeating).

6. Anonymous says:

We all agree on the definition of "champion" and that becoming champion is the goal. However, I don't find solace in either buzz's or JG's explanations.

Buzz uses the best in the total season as the definition of "best." While I appreciate and don't object to his rational, using a word as part of the definition doesn't clarify much.

"...because the team with the lesser chance sometimes wins." Well, if there are different methodologies out there and they are debatable, how can we say any of them are "right" if reality ends up disagreeing with them?

Using last year as an example, a true model should have predicted the success of the Giants. The fact the regular season, and all manners of statical models didn't, can be attributed to the failing of them as models. The outcome was the outcome. The probability of the Giants winning last year's SB is now 100%. The failure is on the models used to predict the result, not the result.

7. Unknown says:

"Using last year as an example, a true model should have predicted the success of the Giants. The fact the regular season, and all manners of statical models didn't, can be attributed to the failing of them as models."

This can only be attributed to a failing of the model if the model creates absolute, boolean predictions. In other words, if the model said, "The New England Patriots WILL WIN the Super Bowl." then any outcome to the contrary could arguably be used to refute the model itself. But clearly Brian's model does not do that. His model, like most modern statistical analyses, merely tries to determine the probability that a given event (a team winning a game) will occur.

If a team has a 90% chance of winning a game, then almost anyone would admit that the team is better than its opponent. But even in this scenario, the far-inferior opponent still has a 1-in-10 chance of pulling off the upset. If the inferior team pulls off that upset, does that refute the model? No! It only shows the magnitude of the upset.

You cannot refute, nor can you validate, a statistical model with any single outcome. A single game is meaningless in the overall value of the model. A single playoff run is still too small a sampling to validate or invalidate a model. In fact, I believe very strongly that it takes at least several complete seasons of data to properly assess the value of any given model.

Let's take your logic for a test drive. I will give you a 6-sided die. On ONE of those faces there will be a "New York Giants" label. On the FIVE remaining faces there will be a "New England Patriots" label. Before you roll the die, I am going to crank out two different prediction models that will try to determine the outcome of your roll. The two models yield the following predictions:

Model #1's Prediction:
You WILL roll "New York Giants"

Model #2's Prediction:
There is an 83.3% (5-in-6) chance that you will roll "New England Patriots"
There is a 16.6% (1-in-6) chance that you will roll "New York Giants"

Before you roll the die, first notice that the second prediction model didn't really make a prediction at all. It didn't say, "You will roll 'New England Patriots'". It merely said that there is an 83.3% probability that you will do so. In colloquial terms, you could say that the New England Patriots are the "best" bet. In casual conversation, you might say that model #2 has "predicted" a roll for the New England Patriots. But in reality, model #2 offers no concrete prediction and it does not define the "best" team, merely the one with the highest probability of winning.

So you roll the die and, seemingly against the odds, you roll a "New York Giants". Does that mean that Model #1 is brilliant? Does that mean that Model #2 has failed? The fact is that neither can be concluded from the results of a single trial.

Finally, let's imagine that you roll the die 1,000 times (with the same predictions from both models) and it comes up "New York Giants" exactly 450 times (45%). What does that say about our two models? It invalidates them both!

Both models would be invalidated because the first model gives an implied probability of 100% by saying that you WILL roll "New York Giants" every time. With the clarity of a valid data set it can now be shown that the Giants obviously did not have a 100% chance of turning up on the die. Model #2 would also be highly suspect, because even though it was more likely to "predict" the correct die roll than Model #1, it clearly underestimated some factor that caused "New York Giants" to be rolled far more than was expected (perhaps the die was weighted).

8. Anonymous says:

Thank you for that explanation. Before we get too far down this tangent, let me restate my initial thought. The "best team" is by definition the winner of the championship game. Often people make a statement like, "the best team didn't win the championship." Without a generally accepted definition of "best" or at least an accepted set of criteria, that statement is meaningless.

I don't believe the outcome of one trial correct validates or doesn't validate a model. A model can be valid and give a wrong prediction for a single event, it can be invalid and give a correct prediction. As I mentioned above, my point was about the definition of "best" team, not the validity of models.