Entropy and the 2012 Baltimore Ravens
Introduction
Entropy is one of those those topics that I never really understood for years despite working on a Ph.D. that requires understanding of this concept. I understand the Physics definition of entropy (George Carlin was a fan) but the information systems field has its own definition of entropy. From Wikipedia:
In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent in the variable's possible outcomes.
This definition has always bothered me because when it says that entropy is the “average level of information” then it implies an equivalence between information and entropy, and intuitively I’ve always felt that the more information you have the LESS entropy you have. The “surprise” and “uncertainty” falls more in line with my understanding of entropy. Information reduces uncertainty and the more information you have the less like you are to be surprised. So I think my best interpretation of this definition is:
Entropy represents all POTENTIAL information about a subject. In a high entropy environment, there is more uncertainty (or many possibilities) and in a low entropy environment, there is more certainty and only one possibility.
In the following sections, I will summarize the Ravens 2012 Championship season and discuss some of the chronological inflection points of the Ravens season and discuss how Entropy changed in the NFL season from the start of the 2012 season to the end of that year’s Super Bowl.
The 2012 Super Bowl Champion Baltimore Ravens
The Baltimore Ravens won Super Bowl 47 for the 2012 season (even though the Super Bowl game itself was in 2013) but after week 15 of the regular season most people weren’t even sure if the Ravens would make the playoffs. With only two weeks to go the Ravens had lost three games in a row including a decisive loss against the Denver Broncos. I remember Joe Flacco throwing a horrible pick six in that Week 15 game. I probably just wanted the season to mercifully end at that point.
There were several points in that season that I would consider inflection points late in that season. The most notable ones happened during their playoff game against the Broncos.
Joe Flacco throws the Mile High Miracle, tying the game with less than a minute to go. The Ravens are losing 28-35, and Joe Flacco throws a bomb to Jacoby Jones for a touchdown. It required one of the defenders to make a critical mistake to even happen. This is the most famous moment in the game and the one we will focus on.
There are other critical inflection points in the Ravens season and it is amazing how a few key (mostly) isolated events could change the eventual outcome (Ravens winning Super Bowl). For example, if Jacoby Jones drops the the pass, do the Ravens win that Broncos game? Do they win the Super Bowl? How much do the probabilities change based on these handful of events? I watched the following video about the Jacoby Jones catch. It’s speculation but it shows how important that one event was to the the Ravens.
Entropy Through the Season
At almost every point in the season, and especially during the playoffs, most people did not not expect the Ravens to win the Super Bowl. In fact, I remember thinking at the time that if someone had bet on the Ravens winning Super Bowl 47 after Week 15 they would have gotten a substantial payout. While they were favored in their first playoff game against the Colts, they were heavily unfavored in their matchups against the Broncos and Patriots and slightly unfavored in the Super Bowl against the 49ers.
We can make guesses about who’s going to win the Super Bowl at any point in any given season. In fact, at the beginning of the 2012 season the Patriots were favored to win. As the season progressed and teams won and lost games, these probabilities changed. At some point teams would have been eliminated from playoff contention. As the number of teams eligible for the playoffs decreased, we gained information (in the form of knowing which teams were NOT making the playoffs and therefore NOT winning the Super Bowl) and lowered entropy.
When the NFL season ended, there were 12 teams in the playoffs. That means there were 20 teams NOT in the playoffs and could never win the Super Bowl. So when someone asked who was going to win the Super Bowl, it was “not those teams” with 100% certainty.
After the wild card round, there were 8 teams left. That means that 24 teams were NOT winning the Super Bowl.
After the divisional round, there were 4 teams left (Ravens, Patriots, 49ers, Falcons). That means that 28 teams were NOT winning the Super Bowl.
After the conference championship games, there were 2 teams left (Ravens and 49ers). That’s 30 teams NOT winning the Super Bowl.
And after the Super Bowl, there was one Super Bowl champion, the Ravens. We reached 100% certainty and zero entropy.
The bullets above only talk about the results of the games, but as mentioned in the previous section there are individual events WITHIN the games that also change the probabilities of any team winning the super bowl. They now show the probabilities of a team winning a game changing every second based on the immediate events that happened so far in that game. For example, this article shows the following graph showing the chance of the Ravens winning Super Bowl 47 every minute:
Information and Entropy
If we look at a timeline of the 2012 NFL Season, at the start any of the 32 teams could have won the Super Bowl, but at the end of the season there was only one winner. Any given Sunday, any NFL team can beat another, but over time we can say, with certainty, that some teams will not win the Super Bowl. We also learn which teams are the most likely (have a higher probability) of winning the Super Bowl. In other words:
At the beginning of the season we had maximum entropy, the least information, and any of the 32 teams could potentially have won the Super Bowl.
At the end of the season we had zero entropy because we know who won the Super Bowl and we had the most information about the 2012 NFL season.
This is why I like the idea that entropy represents potential information. Most of the time, the more information we have (when I say information I mean useful information, not misinformation or non-information) the less uncertainty we have and the less