The Vicious Law Of Averages

From an analytics perspective, a basketball game is a collection of thousands of intricately unique data points. At this moment in time we are able to measure and catalog a tremendous number of those data points, but many, many more still lie outside our reach. This enormous quantity of information simply can’t be held together in a useful way, with each point existing as a separate entity. Information is gleaned by looking for connections and patterns in those points. Often the simplest of statistical tools, like averages, are enough to smooth and group those separate points together. Like pulling back from a Magic Eye Poster, averaging data helps us make sense of the overwhelming stream of individual plays we watch unfold in front of us, creating an image, recognizable and comforting.

As a Pacers’ fan confidence can be an unfamiliar companion. The team has had plenty of success in the twenty years I’ve been watching them, but rarely can I remember cruising through a big game with any certainty of a positive outcome. The defining Pacers experience is still Reggie Miller’s late game heroics, but uncertainty is precisely what made them so enthralling. You always hoped the magic would be there, but you couldn’t ever quite count on it. However, as things began to unravel in the third quarter of Game 6 against the Knicks I found myself with an unexpected surge of calm because I saw a pattern developing in those disparate data points we call possessions.

In the third quarter the Knicks outscored the Pacers by eight, pulling dead even to begin the final quarter. New York had ridden a wave of absurdly accurate three-point shooting, making 6-of-7 in the quarter, but the real driving force was Carmelo Anthony. Through the first three quarters Anthony had scored 35 points, without a single turnover, on 13-of-22 from the field and 8-of-8 from the line. If you don’t have a calculator handy that’s an average of 1.35 points per possession, an obscenely efficient mark and well above his season average of 1.02. That efficiency had manifested with a collection of mid-range pull-ups and fadeaways from the post. Every shot was contested, but it didn’t matter – Anthony had the look. He was locked in, ready to put the Knicks on his back and drag them to an epic win.

But he was also playing way above his head, scoring at a rate of efficiency far above his season average.

The Law of Averages is a common statistical expression, but often misinterpreted. When you flip a coin you have an equal chance of landing on heads as you do of landing on tails. Stretched out over a large enough span of time the actual results of your flipping will eventually settle around the 50/50 mark. This is the Law of Averages. However, people often forget about the element of sample size. Six heads in a row doesn’t mean you’re due for tails. If you’ve landed on heads six times in a row, the probability of getting a tails on your next flip hasn’t increased. It’s still 50/50. Streaks of improbability will inevitably happen, but given a suitably large sample size the results will end up exactly where you expect them.

Going back to Game 6, just because Anthony made five shots in a row didn’t change the likelihood of him making or missing any his upcoming shots. The first three quarters were undoubtedly a streak of improbability but if the Pacers’ defense could maintain the same pressure and keep the odds stacked against him, eventually Anthony’s improbability would melt away. The only question was whether or not it would happen before the end of the game.

As the fourth quarter began in Game 6, the Law of Averages burst from the wings, wrestling Anthony to the ground. Over the next twelve minutes Anthony went 2-of-7 with three turnovers and not a single free throw. The graph below shows his rolling efficiency for the game, charted by each of the 34 possessions he used. Each mark on the line shows his overall points per possession up to that point. I’m sure you can spot the beginning of the fourth quarter.


In the end as his the game rolled along Anthony found himself right back where we’d expect him to be, at his season long-average. As his shots kept dropping, I saw this average lurking and creeping in the shadows, getting ready to work its magic.

Anthony’s average efficiency was at a very high level this season, but for a variety of reasons in this game they needed sustained offensive efficiency of an improbable level. Ironically, a lot of the Knicks’ offense this season was built around capturing and harnessing these bursts of improbability from him, J.R. Smith and Raymond Felton. Averages are not created by the consistent reproduction of a single act, they are an amalgamation of highs and lows. When the Knicks were able to pile highs upon highs, they were nearly unbeatable this season. But asking improbability to arrive when you need it most is a dangerous game. Michael Jordan seemed to have this ability. LeBron James has shown it at times. But as much talent as his offensive game encapsulates, Anthony has shown himself to be as subject to the law of averages as any other mortal man.

In some ways, the foundational element of this Pacers’ defense is not Roy Hibbert or Paul George, but the Law of Averages. Everything revolves around the belief that if they force you to take tough shots, you’ll miss enough for them to beat you. Sometimes tough shots go in, but the Pacers are counting on the fact that each game is a long enough sample size for the Law of Averages to catch up with their opponents. As Anthony was knocking down turn-arounds and fall-aways over their outstretched arms, the Pacers’ were putting their faith in the long-game, plugging away and hoping that their would be enough possessions for average to make an appearance.

Ian Levy

Ian Levy (@HickoryHigh) is a Senior NBA Editor for FanSided and the Editor-in-Chief of the Hardwood Paroxysm Basketball Network.