Free substitution. Allow fresh players into the game. This will make for more aggressive and faster play, which should lead to more scoring. Free substitution will also allow better strategic use of players with special skills. Shorten the field. The ball will then spend more time within striking distance of the goal. Increase the size of the goal. The most direct way to increase scoring. Slope the field. Have the field slope toward the nets, both from the sides of the field and the center of the field. This will keep the ball closer to the goal area. Furthermore, this change will lead to a host of new scoring strategies. If a team can be distracted from the game -- by, say, a staged fight or a naked fan running across the field -- the ball will just roll into the goal. Use two balls. Having two balls in play will increase the number of shots, and spread out the defense. The balls can be color coded, with one ball being worth two points and the other ball one point. Add a goal tunnel. Have a corrugated metal tube that runs into the goal from beyond the goalie area. If someone can kick the ball into the tube, it is an automatic goal, since the goalie cannot defend it. New and entertaining strategies can be added with this feature. For example, players can be "tunneled" by being slammed against the sharp metal edges of the tube, thereby increasing the physical component, and with it, the entertainment value of the sport.

Now that the U.S. team has been eliminated, and with it the thrill of having an emotional attachment to the World Cup, I can go back to reflecting on why soccer is so boring. The basic reason is not so hard to come by: there is not enough scoring. Because there is not enough scoring, the bulk of the playing time passes with no concrete result, and the outcome is unnecessarily random. Even when a great team is matched up against a mediocre team, if you were to replay just a few critical seconds out of the hour and a half of action, the outcome might be different. Yawn at the wrong moment and miss the meat of the game.There is an analytical basis for determining the amount of scoring a sport should have, and soccer is well below the ideal.First, the greater the number of scores, the lower the chance for a lucky win by a team that is inferior. The number of scores required to move this random component to an acceptable level depends on the nature of the game. For example, if I were up against a professional basketball player in a game that involved each of us taking shots from the foul line, there is a reasonable chance I would win if the game consisted of only one shot each. If we each took ten shots, I would almost never win. On the other hand, if I were up against a world-class sprinter, one race – one score – would be enough. Absent a hamstring pull, he would win a hundred times out of a hundred.Countervailing the benefit of having the outcome determined by more scores is the negative effect of having too much scoring. Up to a point, the more scores, the more interest and engagement for the spectators. But there is a turning point. Create a game with too many scores and the individual scores become inconsequential.So in designing the ideal scoring for a sport, you want enough scores to reduce the chance of one team wining by dumb luck. The more randomness in any one score, the more scores you will want, so that a clearly superior team will win most all the time. But you don’t want to overdo it with the scoring. I think that soccer and hockey have too few scores, basketball and tennis have too many, while baseball and American football are somewhere near the sweet spot. This sweet spot can be determined empirically. A sport has enough scoring if a team that, in a large sample of games, tends to lose to most everyone rarely beats a team that tends to beat everyone.This is all preamble to a way to improve soccer: have more scoring. It will reduce the random component, and lead to more minute-by-minute excitement. Change the game so that a dominating team wins by 10 to 5 rather than 2 to 1.Here are a few changes I might propose in soccer to increase its entertainment value and reduce the randomness of the outcomes.