11/06/2012 02:43 pm ET Updated Jan 06, 2013

A Modest Proposal for Dealing With Corruption in College Sports


The 2012 college football season is well underway, and the usual dominant teams are crushing opponents in the march to one of the two coveted spots in the BCS Championship game. Meanwhile, we have among those contenders (and some pretenders), a contingent of teams that are ineligible for bowl games due to cheating sanctions (Ohio State, Penn State), teams coming off sanctions for cheating (USC), and teams currently under investigation (Oregon, Miami), and others(!).

Many, though not all, of the sanctions stem from hidden payments or benefits to student athletes. NCAA Football Bowl Series (what used to be Division I-A) and NCAA basketball players generate enormous revenues for their schools, but all they get are their scholarships. Given how expensive college can be, this isn't chump change, but it's not hard cash either. So you can at least see why players might succumb to agents who come around with shiny cars, apartments, and the like.

The most obvious suggestion is simply to pay the football and basketball players. The arguments against paying them are (1) it demeans the concept of the student-athlete by undervaluing education; and (2) it would allow rich programs to trample even more over poor programs.

The student-athlete concept seems silly to me. I mean, I was a teaching assistant part of the time during law school, and I got paid for that, because I was a student-employee. I don't think anyone would think that my law degree was devalued because I also worked as a teaching assistant for two semesters.

Ah, but I wasn't paid some exorbitant amount, because the supply of potential law and economics TAs far exceeded the number of spots. (I don't remember exactly but I think I got a $1000 fee reduction in my tuition, plus $12/hour.) Wouldn't schools like USC pay $5000/hour for their top recruits?

Here's my proposal for addressing those two points completely:

1. Schools can pay their student-athletes whatever they want, but they must report the wages transparently, with no under-the-table payments.

2. In order to normalize the impact of high wage vs. low wage teams, as well as to take into account the "student" side of student-athletes, all game scores will be adjusted by the Wage Differential Ratio and the SAT Score Differential Ratio.

The Wage Differential Ratio

We will consider the minimum wage paid to a student-athlete to be $10/hour, even if the player in question actually receives less than that.

During every game, there will be a time-weighted average salary for each team. The more minutes that a given player is in the game, the more his salary counts towards the team's average salary. We then take a ratio of the two teams' average salary, and adjust the game score accordingly.

For example, say that at half-time, rich USC has a time-weighted average salary of $150/hour, while poor UCLA has a time-weighted average salary of $25/hour. The ratio is 6:1, so we would multiply UCLA's score by 6 for the adjusted half-time score.

The wage differential ratio can change throughout the game, depending on the mix of players who've been playing. A team that finds itself losing according to the adjusted score could either try to score more points, or lower the wage differential by playing more cheaply-paid players.

In short, the wage differential ratio exists to even the playing field for those universities who cannot or chose not to pay exorbitant wages. It provides a market-mechanism for dealing with unbalanced salaries paid to student-athletes.

The SAT Score Differential Ratio

Similarly, during every game, there will be a time-weighted average SAT score for each team. The more minutes that a given player is in the game, the more his SAT score counts towards the team's average SAT score. As with the wage differential ratio, we take a ratio of the two teams' average SAT scores, and adjust the game score accordingly, except that this is an inverse multiplier, meaning that you want the higher SAT average.

The SAT score differential ratio exists to validate the role of academics in the student-athletics. Teams that chose to focus on recruiting athletically gifted but low-scoring players might find themselves handicapped against a slightly less-talented, but considerably higher SAT scoring team.

(Note that the SAT is not without limitations, but its flaws tend to afflict individuals, whereas we are dealing with entire teams here; any flaws should not be isolated to any particular university, but rather, should be systemic problems that tend to affect all more or less evenly. I debated whether to have the SAT score differential ratio combined with a GPA differential, but the problem is that schools might have different levels of grade inflation, or "Mickey Mouse" classes for athletes. The SAT suffers from neither of those problems.)

Game Theory and the Differential Ratios

The two differential ratios offer a whole new level of game theory in college sports. First, consider how recruiting plays out. Although schools may be tempted to pay as much as they can for the top high school players, the wage differential will start to get too severe at some point. In addition, the whole concept of "top" player takes on a new complexity. If the top player can barely scrape by with, say, a 1000 (out of 2400) on the SAT, whereas the next best player at the same position scored a 1500, who's really going to be considered the top player? No doubt the 1000 score player will still get recruited, but he might not be able to command the same salary as the 1500 score player.

Second, consider the in-game coaching decisions to be made. If your starting quarterback (1200 SAT, $125/hour) is having a dreadful game, do you stick with him in the hope that he'll pull himself together, or do you take him out and sub in the backup quarterback (1600 SAT, $30/hour) for an instant boost in the two differential ratios?

Clearly, coaching will require a whole new set of math-related skills!

Cheating and the Death Penalty

Since this proposal lets schools pay athletes whatever they want, there's no more excuse for under-the-table payments, gifts from boosters, etc. Any school that cheats by actually paying players more than it reports should get the NCAA death penalty (ban on football or basketball for 2 years), and any player who takes gifts from boosters, etc. should be banned from further NCAA participation.

Okay, if you're still reading, obviously I don't think this proposal would ever get take seriously. But it sure would make for fun math problems during football and basketball games.