A Definition of Luck in Sports

This post is a little different than my others. I think it would serve my luck research well if I take some time to explain what I define as luck.

Luck is just my shorthand for a random process, and I admit using the word luck may be misleading. A random process is merely one in which the outcome cannot be controlled, and that each possible outcome has an equal chance of occurring. The accumulation of effects of several random processes results in a normal distribution, like balls bouncing down a Pachinko board.

Flipping a coin is not luck in a strict technical sense. It is dependent on its original position, the rate of spin imparted, the height of the toss, etc. But the outcome cannot be controlled, and each possible outcome is equally likely. Hence, it is indistinguishable from a true random process--what could just as well be called luck. In football, as in any sport, there are many processes similar to a coin flip.

One example would be a punt that first lands on the 5 yard line. Does it die on the 2 yard line or will it bounce into the endzone for a touchback? Once the punt hits the ground it is no longer under the influence of the punter in any way. Over time the randomness will average out and good punters will tend to prevent more touchbacks. But where this one punt lands today, in this one game, right now, is partly random.

Randomness can play a very strong role in the outcome of any single game. Consider a baseball game between a team and its perfect equal in every measure. In this evenly matched game, each team hits 9 singles. Team A happens to get its singles within 3 innings, then goes hitless for 6. Each inning of 3 singles produces 1 run. Team B's 9 singles happen to be spread across 9 innings, resulting in zero runs. Team A wins 3-0, although each team performed equally well.

The total number of singles produced by a team is controlled by the interaction of skills between batters, pitchers, and defense--certainly not luck. But, when the singles occur and how they are bunched cannot be controlled, and their distribution is equally likely throughout the game. Batters have zero ability to chose when their hits occur. If they did, everyone's average with "runners in scoring position" would be much higher. Therefore, when the hits occur is indeed random, and consequently, a sizable part of the outcome of a any single game is random.

It's why the Devil Rays sometimes beat the Yankees. They weren't the better team that day. They just benefited more from a random dispersion of events more than their opponents did.

Baseball managers have understood this effect for generations. This is partly why a team's lineup is usually constructed with its best batters bunched together in order. It maximizes the probability that hits will come in bunches. This technique skews the random distribution positively, but does not reduce the randomness of the process itself.

Football is very different from baseball, but the bunching effect exists on the grid-iron too. Scoring drives are not just dependent on achieving several first downs, but on achieving consecutive first downs. The total number of first downs earned is determined by the relative strength of each team, but how dispersed they are is random. So part of the game outcome is due to the teams' comparative strength, and part is due to a random process.

Randomness is an essential part of the physical universe. Perhaps instead of luck I should use the word chance or randomness. Luck implies superstition, to which I certainly do not subscribe. I do not believe one side or the other enters a contest with some Goddess of Luck smiling its side. Instead of saying "the Giants had luck on their side today," I should say "the cumulative outcome of uncontrolled random processes favored the Giants in this game."

But if you don't buy into randomness--what I call luck--you're in good company. Einstein denied it too. His feelings were summed in his quote "God does not play dice with the universe." Randomness offended his sense of a rational universe, just as many sports fans are offended by the role luck plays in sports. Unfortunately, his refusal to accept it brought his research to a dead end. Subsequent research led to quantum physics, which confirms randomness as a fundamental property of reality.

Lastly, if you don't believe in randomness you must not be reading this. One of the greatest human technological advances in history requires randomness to exist and be quantifiable--the microprocessor.

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5 Responses to “A Definition of Luck in Sports”

  1. jhc448 says:

    haha awsome

  2. Durwood Brundage says:

    you have not answered my question. I want to know what the o/u data tells me in predicting a NFL football winner :ie, Pittsburg open 5 1/2 today 6 o/u 35 Tennesee. what does the o/u number tell me?

  3. Anonymous says:

    As a layperson, I've never been fully comfortable with how the term "randomness" is used in these contexts. There seem to be two distinct situations in which it is used--two "referents" of the term. One is where there is pure physical randomness (a concept I cannot get my head around). The other is where there is such complexity that we aren't able to predict an outcome, though theoretically we could. The distinction is not relevant from a practical or pragmatic perspective, or is it? With respect to predicting football game outcomes, I probably put more stats than most people into the "random" bin and chaulk them up as "noise" for predictive purposes. And step way, way back to a macro-level, not-fully-quantitative "analysis". I'm psyched to have come across your site so I can see what sounds like an alternative approach with predictive power.

  4. Joe says:

    @Anon - I'm not seeing what you don't get about randomness in the context of the game. Essentially, it boils down to "shit happens". The ball bounces into the endzone for a touchback, or it stops on the 1. The tipped pass that lands in your hands or the opponent's. The call that could've gone the other way (officiating judgement calls are beyond your control). The dropped pass (similar to the above example that hitters cannot control WHEN they hit, just how often they do so). The botched snap or hand off. These things happen. That's the nature of luck, or randomness. You hope you get the bounces, cause if you don't... well, we've all seen teams dominate every facet of the game and still lose.

  5. Anonymous says:

    @Joe - I think the post you were replying to was in reference to the fact that these are not truly random events. With enough computer power and precise measurement, these "random" events such as whether the football will bounce for a touchback or stop dead on the 1-yard line would theoretically be perfectly predictable. It's just that our ability to predict with such precision falls so astonishingly short, that for all intents and purposes, the process is equivalent to being truly random.

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