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The Limits of Mathematics

Mises Daily: Thursday, November 29, 2001 by

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The college football national championship is decided--in large part--by computer programming, not on the field. While the format of major college football's method of deciding the national champion has been debated for eons (polls or playoffs?), the current method of choosing a champion suffers from the same fate as modern economic methodology, which is the failed but still ongoing attempt to explain human action through mathematical formulas.

Anyone who has taken intermediate or graduate economics or has read any of the best-known economics academic journals knows that mathematics dominates the profession and has been used extensively for many years. This methodology is employed by placing economic "variables" into a formal mathematical "model" that one either "tests" statistically or solves using calculus. The ultimate resolution is an "equilibrium solution," and it is especially good when one can arrive at an "efficient" end point. 

(I recall being at a presentation of an academic paper when the economist making the presentation declared, "Economists are happiest when price equals marginal cost."  Thus, we see the tried-and-true formula for ensuring happy economists. I do not know if economists are "sad" if price does not equal marginal cost.)

Austrian economists have long known that what much of the economics profession calls "doing economics" is an exercise in silliness. What is worse, many economists actually believe that unless a mathematically perfect "equilibrium solution" is not reached in real life, then a horrible failure is occurring that can only be rectified by tapping into the powers of the state. If this contention were true, then all economic exchanges would end in failure, since it is impossible to quantify human action. Thus, the only way we could be sure that an "equilibrium solution" was being reached would be for the state to oversee the entire process, something the ancients once called socialism.

This idea, of course, is preposterous. First, and most important, human action is not mathematically quantifiable. Humans do not act according to mathematical formulas, and it seems silly to use a complicated equation to describe something like an individual choosing to buy either a Coke or a hamburger. Second, such an idea assumes that those who work for government are omniscient--except when they are making exchanges as private citizens. (At that point, the government employees need other government employees to tell them what to do.)

All this brings me to the Bowl Championship Series formula, which is made up of the Associated Press Poll (voted by sportswriters), the Coaches Poll (voted by the NCAA Division I-A football coaches), the win-loss records of teams, the "strength of schedule" that each team plays, and a gaggle of "computer polls."  Individuals who feed data about each team into preset formulas in their computers create these polls, which are very influential in determining which teams will be the top two that will play for the national championship in early January.

As one who follows college football, I often find the results of computer polls quite bizarre. For example, one poll last October had North Carolina ranked in the top ten--despite the fact that UNC had lost its first three games. Teams will be ranked high one week, beat their opponents handily, and then find themselves in a free-fall when the new polls come out.

That this sort of nonsense would decide national collegiate football championships leaves one dumbfounded. However, after reading journals written by the "best minds" in the economics profession, it does not surprise me that college presidents and athletic directors have permitted themselves to be hoodwinked.

As in economics, the BCS formula assumes that we can quantify the actions of athletes, giving a cardinal value to the "quality" of their performances. For example, if the University of Miami Hurricanes, a perennial BCS contender, beat their opponent by 35 points, they receive more quality marks than they would for a 30-point win, since the computer polls heavily emphasize margin of victory.

Such an emphasis on margin of victory fails to deal with the realities of collegiate athletes. In an early November poll, the University of Tennessee was ranked fourth in the BCS poll. However, the team fell three places when it defeated its cross-state rival, the University of Memphis, by 21 points--a no-no, since Memphis had only a 4-4 record at the time. What the computer polls failed to absorb was that Tennessee led 42-7 and had reserves in the game when Memphis struck for three meaningless touchdowns in the fourth quarter that had no outcome in determining who would win.

(Being a Tennessee graduate, I suppose that I should be happy now that the BCS formula has--for the time being--penciled in the Volunteers as the nation's number two team, which means that if Tennessee beats Lousiana State University on December 8, it will play Miami for the national championship.  That the BCS computer polls have favored my favorite team does not change the fact that this is an absurd system.) 

Furthermore, the computer polls fail to measure the fact that at the Division I level, most teams have good athletes. The best teams have the best athletes, which means they can perform at high levels consistently. "Inferior" athletes, while still blessed with an abundance of talent, are able to achieve at high levels on occasion, but cannot be consistent over several weeks. That is why one occasionally sees "upsets" when an "underdog" defeats a heavily favored rival. In other words, emotions also play a large part in determining outcomes of games--something computers cannot measure.

One especially sees this phenomenon when "traditional" rivals play each other. On many occasions, the favorite will not only lose to a rival, but be routed, as was the case in the Auburn-Alabama game, in which the favored Auburn University Tigers fell 31-7 to a University of Alabama team trying simply to salvage a lackluster season. (On that same day, an "underdog" University of Southern California team routed its favored rival, UCLA, while a few hundred miles up the coast, heavily favored Stanford barely squeaked by its winless rival, Cal-Berkeley.)  Mathematical formulas upon which computer polls depend cannot predict something like this, nor can they even explain such a phenomenon. 

Computer polls are not the only system of choice used to determine who will play for the national championship. As mentioned earlier, sportswriters and coaches also rank teams. Their methodology is much closer to a legitimate reflection of human action, as in both cases, the participants engage in ordinal rankings rather than cardinal measurement, as is done with computer polls. Another way to say it is that the voters have no way of knowing in any standard measurement how much better the University of Miami's football team is than, say, the University of Florida. All they can do is to list Miami ahead of Florida and assume that the Hurricanes would beat the Gators under most circumstances.

Athletics, like economics, is an endeavor of human action. While we can see scores and statistics, there is no true way to quantify how good or bad a team may be. Indeed, if the computer polls with their mathematical formulas were so accurate and useful, then one would hardly see the need for a championship game after all. Just let the mathematicians pick the winner and save coaches, players and fans the trouble of having to play the game. Perhaps they can trust the whole thing to the group of elite mathematical economists.


William Anderson, an adjunct scholar of the Mises Institute, teaches economics at Frostburg State University.  Send him MAIL.  See his Articles Archive.