Anchoring in College Football Rankings: How some schools get Au-burned

TLDR:  "Past research has shown that colleges with a successful football team experience an influx of donations, student applications, enrollment, and student quality." 

However, subjective rankings of football teams can be biased through anchoring. "Evidence for anchoring can potentially be illustrated through the initial assignment a preseason ranking: these preseason rankings can have a major impact on a team's final ranking."

"Initial results suggest that a team's rank before the game explains an incredible 83% of team's ranks after the game."

As a new-comer to the USA, I have quickly found that college is synonymous with football. Every Saturday in Autumn, tradition would have it that groups of former students gather round in their college sweaters to watch their alma mater kick off against a rival school. Among the friendly banter comes a point of high contention: the ranking of each of school's football team.

Before the College Football Bowl Subdivision (FBS) season even begins, a group of independent sports writers known as the Associate Press (AP) release their preseason rankings of the top 25 schools. At the conclusion of the each week of games, these top 25 rankings are updated (note that  rankings after the 25th school are generally considered to be too noisy to be a great indicator of relative strength).

To uphold their reputation as an independent and objective news organization, we may expect that the AP could potentially have any team occupy the highest rank after each week. However, if we have learned anything from behavioural economics (not to mention specifically from my previous posts) we know that humans tend to anchor on reference points. If this were true, we would expect to see that each team's past ranking strongly affects their current ranking.

To test this theory, I collected the AP rankings and game results for 2016 FBS season from Sports-Reference.com. I then classified the top 25 rankings into one of four categories: 1 to 5, 6 to 10, and 11 to 25. All other teams were classified as Not Ranked. 

I then ran an ordered logistic regression which I used to predict how each team will be ranked following their game. In order to predict each team's new rank, I used only three pieces of information: their own rank before the game, their competitor's rank before the game, and the score differential between the two teams.

For the abstract mathematically inclined, the model is of the following form:

Rank Category_i,t = f(Rank Category_i,t-1, Rank Category_j,t-1, Score Differential)

Surprisingly, my initial results suggest that a team's rank before the game explains an incredible 83% of team's ranks after the game!

In attempt to help visualize the results, I have created an interactive graph for you to play with. By altering these three variables - own rank, opponent rank, and score differential - the graph below will display the predicted AP ranking for the next week. All you need to do is fill in the green cells by choosing the ranking category for each team and a non-zero integer for the score differential! Then the predicted new rank will appear below!

As this is my first attempt at an interactive graph, I would love to hear feedback on it, especially if you are having any sort of difficulties with it.

Note that the rankings are actually based on valuable information. In other words, the AP does not randomly assign rankings but instead chooses to give a team a top rank if they are among the top teams in the nation. However, evidence for anchoring can potentially be illustrated through the initial assignment a preseason ranking: these preseason rankings can have a major impact on a team's final ranking. To demonstrate this, I reassigned the preseason ranking of every team and simulated the season to predict their final ranking. Using this methodology way we can test questions such as:

• Would perennial top 5 Alabama still be in the top 5 if their preseason ranking was outside of the top 25? 
• If an otherwise not ranked team instead had a top 5 preseason ranking, would they be able to stay in the top 5?

In short: yes, and yes.

For a longer explanation, I began by reassigning all preseason rankings as Not Ranked for all teams (but their opponents keep their true ranks) and simulated the season. In this world, as summarized in the table below, the model predicts only 4 teams could break into the top 25. Here we see that Alabama proves to be a true top 5 team and is heavily favoured by the model regardless of their preseason ranking.

In the second but-for world, I reassigned all of the teams as top 5. Unsurprisingly, many more teams are able to stay in the top 5 than were able to get into the top 25 as seen above. According to the model, even Auburn had an acceptable season and could have stayed in the top 5.

To contextualize this, at the end of the season the top four FBS teams get to play for the College Football Playoff National Championship (although these teams are ranked by a different set of people but they too may be influenced by the same anchoring effect). In 2016, these three games which make up the championship drew a total of nearly 65M viewers. Past research has shown that colleges with a successful football team experience an influx of donations, student applications, enrollment, and student quality.

In the end, as long as there is some anchoring in the FBS ranking system, the best FBS teams will not necessarily always get the opportunity to be the best team in the country. Unfortunately, these real life biases could hurt a school in the long term through missed private donations and missed high quality students.

Until then, may hopefully the best team win gets ranked higher.