“Scaled Sabermetrics” – New Statistical Methods in Basketball

Storyline: What happens when a fan applies a new set of statistics to basketball? A coach listens. A team performs. Written by Nicholas Coombs, Billings, MT. Connect with Nick on Facebook.

As I was settling into my final undergraduate year, the NCAA Division III Men’s Basketball coach at Castleton State College approached me to say: “I hear you know a thing or two about statistics. I need your help.” As the opportunistic student of research I heard the man out. His team had won the North Atlantic Conference (NAC) Championship the year prior, something that hadn’t been done at CSC in over a decade, and four of his five best players graduated in the off season. Needless to say, he was a bit concerned.

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“Perhaps you can do something with this. I’ve read a lot about how people use statistics in sports all the time.”

Just to provide a bit of context, I began to study statistics in school because I quickly understood its need and appreciation it has in just about any field. Data are everywhere. The ability to accurately and efficiently transfer technical information to those who may benefit from it is an incredibly marketable skill. That’s why I instinctively jumped into an independent study for this coach.

But first came the design. How would I help him? What exactly does he need? These are the kinds of questions I spent a lot of time considering beforehand.

Let’s first consider this: many sports, particularly baseball and basketball, track statistics and structure player value around numbers that do not directly link to a team’s probability in winning. Just as Billy Beane did back in ’02, he wasn’t primarily focused on RBIs or Home Runs (not to say they don’t serve importance). Instead, he considered On Base Percentage (OBP), which associates highly with runs being scored. Runs scored is really the only statistic that matters when a team aims to win a game. I implemented a similar design here.

It’s interesting to note that this coach, unlike any other coaching scheme I’ve ever seen in basketball, substituted like the court was an ice rink. Every 45 seconds to 1 minute he would swap out all five players and get fresh legs resembling a line change in hockey. This is what brought on the notion to consider a plus/minus (+/-) ratio–a common statistic used in hockey. It represents a player’s impact relative to their presence in the game. It’s measured by taking the difference between the team’s points scored and the opponent’s points scored while that player is in play.

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Calculating this statistic in basketball, however, requires some control with the contrasting way the game is played, particularly with how points may be acquired in multiple ways. There’s no foul shooting in hockey but, in basketball, a player who draws a foul while taking a shot is permitted to go to the free throw line to earn uncontested points for his or her team. These are points that accumulate to the total points scored throughout the game just like in-game points and cannot be disregarded.

So I implemented the plus/minus ratio to track players as they came in and out of the game in dozens of five-man permutations. In addition, I would individually ‘reward’ or ‘punish’ players for their involvement with the points generated from free throws. Totaling these ratios together provided an ‘overall plus/minus ratio.’

By the middle of the season, the men’s basketball team had played well over a dozen games and close to thirty by the end of the regular season. I created a chart with each game represented by a point on the x-axis ordered by the point differential at the end of the game. To aim in detecting positive linear associations, I created a graph, the first point of which represented the team’s greatest defeat (-40) with the last point representing the team’s greatest victory (+36).

Each player that had an appropriate level of involvement in each game (as qualified by a set of parameters defined by the coaching staff) then had an individual +/- ratio to pair to the team’s. What this did in terms of research was to show the discrepancies between players with their contributions to winning. When the team performed poorly, how did they do? When the game was close, how did they do? When were they dominating?

Placing this into a straight line regression allowed me to generate an equation that confirmed: 1) which player(s) have a more positive contribution overall; and 2) which player(s) performed at a much more consistent rate regardless of the outcome of the game.

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All of that was fun, but here’s where research links to application. Considering the upcoming matchups and anticipated outcomes I advised the coach from the middle of the season on to play specific players more or less in conjunction with how valuable I have defined their presence on the court. When the team was projected to lose, I would advise a higher frequency of players that have been shown to establish consistency. Against sporadic scoring and foul intensive defenses, I would advise a higher frequency of players that have cashed in at their increased value from the line.
The cool thing was that he actually took my advice. In order to acquire these statistics, I would go to the games with a clipboard in hand and collect my data. I witnessed results of my research in action.

I had a bigger goal set for the team. I’d be supporting them in a different way, a greater way.

Even though the Castleton State College Men’s Basketball team was projected to perform significantly worse in the 2012-2013 season, they advanced once again to the finals of the North Atlantic Conference Championship and lost by a very slim margin (6 points). And this was all done without considering any of the widely-used statistics we all associate with the game of basketball.

Since the end of this project I have earned a Master’s degree in Statistics and served currently as a research statistician for a hospital in Montana. I continue to find other opportunities to share my knowledge with different kinds of people, all with different goals in mind. Whether it’s maximizing profits or minimizing risk, determining news appropriateness, deciding the most effective way to design a catalog–or even how to win a basketball game–it all comes down to the design. And it all comes down to the statistics.