Oct. 25 (Bloomberg) -- One of the many delights of reading Tyler Cowen’s new book, “Average is Over,” is the instinctive effort to extend his twinned theses. The provocative little volume has generated a lot of controversy -- even President Barack Obama was asked about it on National Public Radio -- and, like many controversial works, it has been widely misread.

This isn’t a review, although I found the book mesmerizing; rather, it’s an effort to generalize from an analysis that Cowen aims at the probable future of labor and wealth. He argues principally two theses: The first is the familiar claim that rapid technological change is increasing the returns to cognitive capacity, resulting in a growing concentration of wealth, and a rapid shrinkage of jobs that can be done more efficiently by machines. The second (and the more provocative) is that the future belongs to those who are trained to work alongside the intelligent machines that will come to dominate every corner of the culture.

Cowen’s book discusses a number of cultural institutions and traditions, but he largely omits one that I dearly love, and to which his analysis may have special relevance. Aside from a warning early on that an intelligent machine might soon be capable of reporting on at least minor-league baseball, and a lengthy discussion of chess -- more on that in a moment -- he hardly touches upon professional sports.

Sports Technology

Right now, we use technology to popularize sports (we can watch games on our mobile devices) and sometimes to improve officiating (consider instant replay in football and the Hawk-Eye and related systems to assist line calls in tennis).

But this isn’t quite the same as integrating intelligent machines into the game. Helping the referee with line calls isn’t like Freestyle Chess, Cowen’s favorite example, where man and machine in effect put their brains together. No doubt the algorithms that would be needed to replace the players on the field are unlikely to develop in the near future: As Cowen points out, robots are often at their clumsiest performing nonrepetitive physical tasks. (Or maybe not.)

To be sure, there is some reason to think that success in sports is increasingly correlated with significant cognitive ability -- that is, smarter players may be the more successful. Might this explain much of the income concentration in sports, as Cowen thinks it explains the same phenomenon in other labor markets?

In professional football, for example, the top quintile on each team accounts for 60 percent or more of the entire amount paid in salaries -- a degree of income inequality that is actually higher than in the population at large. Salary concentration in Major League Baseball is even higher. In every professional sport, the proportion of income earned by those at the top of the distribution is rising. (This holds despite growing evidence that a highly unequal salary distribution within, for example, a major league baseball team is correlated with poor on-field performance.)

One can hardly attribute the growing income concentration in professional sports to the rise of intelligent machines. Nevertheless, intelligent machines may have an important role in the future of sports, replacing or augmenting not the players but the management -- both executives who decide which players to sign, and coaches who tell the players what to do on the field. Indeed, for the other half of Cowen’s thesis -- the superiority of the human-computer cognitive combination over either working alone -- sports should provide a fertile testing ground.

‘Moneyball’

We’ve already traveled a good way down that road. Statisticians and econometricians, compiling databases comprising tens of thousands of individual moments in sporting events, have made mincemeat of hoary sports truths of all sorts, from how to structure a starting lineup in baseball to when to kick a field goal in football. They have upended traditional methods for evaluating prospective players.

What’s odd is how little of this voluminous learning makes it onto the field. Notwithstanding the occasional celebration of someone who takes advanced metrics seriously -- think “Moneyball” -- the sports culture still tends to value the well-honed instincts of the grizzled coach or manager.

I am well aware that some teams use metrics in an abstract sense -- for example, in baseball, by limiting a pitcher to 100 or 120 pitches and then taking him out. In professional basketball, a growing number of teams use complex mapping technology to study their opponents’ games and create game plans. But this is different from involving intelligent machines in minute-by-minute coaching decisions on the field.

Those instincts are valuable, no question, and there are reasons that successful coaches are highly paid. Cowen, I suspect, would tell us not to dump the coaches, but to pair them with intelligent machines. As in his Freestyle Chess examples, over the great run of choices that arise during a game, the twinned intelligences, human and digital, will make the same decisions. The fun starts when they disagree. And this, Cowen says, is when the ability to understand the machines matters. One doesn’t slavishly follow them, but one doesn’t dismiss them, either. Rather, one learns to take their opinions into consideration -- very serious consideration.

Imagine an NFL team, trailing late in a game, that has to decide whether to kick a field goal that will narrow the gap a bit, or try for a touchdown to pull ahead. If the touchdown try fails, though, the opponent will almost certainly run out the clock. In this situation, unless time left is very short -- say, less than three minutes -- football coaches overwhelmingly choose to kick. The machine will frequently disagree: The chances of victory will turn out to be better if the team tries for the touchdown.

Gigantic Database

The machine has made up its mind based on statistical analysis of its gigantic database of what has happened in other games. (The algorithms are freely available online.) Nevertheless, its decision is necessarily abstract. The coach may know more about the capabilities of his team. He may have a stronger sense of who’s tired and who’s playing well. He may believe he has a read on the opponent’s tendencies. All of these individualized factors should go into the decision whether to trust the machine. But if he can’t come up with a good, articulable reason to reject the digital advice, the coach, like Cowen’s hypothetical Freestyle Chess player, should probably defer to the data.

Here’s hoping that in the near future, some enterprising owner of a losing sports team, wondering how to get the fans back into the stadium, will decide to give Freestyle Coaching a try. We can imagine the curious spectators pouring in, and the television reporters lining up to see how long it takes for the experiment to fall on its face.

Only the experiment won’t fail; that’s when the real excitement will start.

And OK, sure, we wouldn’t want the team that wins the Super Bowl to douse its digital coach with Gatorade. But sooner or later, some team that decides to pair its resident coaching genius with the artificially intelligent assistant is going to calculate its way to a championship, and the fans will go wild as the celebrating players hoist the laptop onto their shoulders and march happily off the field.

(Stephen L. Carter is a Bloomberg View columnist and a professor of law at Yale University. He is the author of “The Violence of Peace: America’s Wars in the Age of Obama” and the novel “The Impeachment of Abraham Lincoln.” Follow him on Twitter at @StepCarter.)

To contact the writer of this article: Stephen L. Carter at stephen.carter@yale.edu.

To contact the editor responsible for this article: Mary Duenwald at mduenwald@bloomberg.net.