Thus: possessing the ball between your goal line and your 10-yard line is actually a deficit, worth a probable 1� points to the defensive team. The theoretical value for you increases, of course, as you move closer to the opponent's goal line, so that at your 45 your point value is a probable 1�, and it goes up to 2[2/5] at his 45. By his 25 your position is worth 3� points, it is 4� at the 15 and more than six inside the 10. (Carter assumed the automatic point-after, and thus rated a touchdown at a full seven points.)
The computer shows, therefore, that it is better strategy to turn over the ball to the opponent inside his 10-yard line, where its expected value to him is negative, than to risk a play that could well backfire and allow him lo take over on the 20. In other words, do not try a forward pass into the end zone on fourth down (or a long field goal) unless you are utterly confident of the play succeeding.
Carter's computerized logic thus at once contradicts the reigning philosophy of the kicking game in nearly all its facets, especially the current practice of punting the ball high and straight down the field, so that the coverage can run under it. It is Carter's researched premise that it would be wiser for a team to bring back the nearly defunct coffin-corner kick or, better yet, utilize a little-known—and rarely, if ever, used—rule and let the placement kicker boot it out of bounds inside the five.
"There shouldn't be anything degrading about a punter trying to keep the other team deep in its own territory," Carter explains, "but no one ever seems to practice it. They think it's a 'college' idea or something. But there is a rumor going around the league that they're going to start subtracting 20 yards from a punter's distance when the ball goes into the end zone. If that happens, then you can be sure that they'll start kicking for the sideline."
The Carter computer studies also found that the expected point values (according to field position) remain unchanged, totally independent of whether a drive is long or short, or however it began. For example, if a team racks up seven first downs before reaching the opposition 20-yard line, the probability that it will score a touchdown is no greater or worse than the team that reaches the same spot on a return, one long offensive play or through a turnover. In each case, the touchdown probability is the same. Thus, that hallowed word "momentum," without which no football coach could ever explain victory or defeat, has almost nothing to do with the outcome of a game.
The same can be said for turnovers. Carter discovered that a team's morale suffered not a whit after being scored upon and, amazingly, that a team is actually more likely to score immediately after giving up some points. The computer also indicated that a fumble was more likely to occur on the first or second play in a series but that an interception was more probable after a quarterback had thrown several times.
"Another aspect," Carter said, "is that as you move down the field by passing, your expected gain per pass diminishes because you're running out of field. In running the football, the gains start off low, get higher around the 50, then tail off again. In my interpretation, I believe it's because teams tend to be very conservative at their end of the field, and it's easier for the defense to prohibit them from big gains. But when an offense moves out to the 50, they're more wide open. Even in a running-game offense, you should be just as wide open and versatile at your end of the field as you are in the middle of the field. There really shouldn't be any legitimate reason why you should run conservatively on the 10-yard line."
Carter, however, is not likely to bend Paul Brown's ear with his statistical revelation in order to help in Cincinnati's struggle in the AFC Central Division. For one thing, his study is an illustration of quantitative analysis and therefore makes no allowance for specific individual talents. "If you wanted to use this." he said, "you'd have to tie in your personnel, and then you'd have to adjust it to your desires as a coach. You'd have to interpret it with respect to your own philosophy. A computer will never make coaching decisions. The idea is ridiculous. You're dealing with probability, and you can't assign a number to all probable events. You can't give a number to how players are going to react to their pregame meal. You can't program desire. That's why a coach has to adjust this stuff to his own team."
It is ironic that Carter, having mined his mathematical nuances from the computer, should now be riding the bench while Brown plays Ken Anderson, the Bengals' 23-year-old second-year unknown, who also happens to be a math major. Moreover, one wonders just what Carter would do with his newly discovered football findings if he were playing, since Brown has always called the plays for his quarterbacks.
In fact, Carter has no complaints on that score. "The coaches call the plays and that merely requires me to apply my mental faculties in other ways," he says. "I can't fault the system here. I've heard of other teams where they send the plays in from the bench, and it's a grab-bag approach. Our system is more scientific, and I appreciate that—enough so that I'll forgo any argument about calling my own plays."