I am not a math guy at all. For the most part if it involves more than a cursory understanding of numbers and basic math, I’m out. However, there is one exception: basketball stats. While discussing the Spurs even scoring distribution, I suggested to my dad that there should be some sort of stat that would measure how evenly or unevenly distributed a team’s scoring is, one that goes a bit further than just measuring assists and how many scores were assisted. My dad is a math guy and he told me that such a statistic is very easy to calculate and already exists, known as "standard deviation."
This stat basically explains the average deviation of individual players’ scores from the team scoring average. On a team with big superstar focus like Miami, there would be a high standard deviation with many of the points going to LeBron James, Dwayne Wade, and Chris Bosh. On the other hand, teams who distribute their scoring more evenly like San Antonio have a much lower standard deviation.
The first game where we ran these stats was the November 23rd game against the Cavaliers where we noticed a particularly even scoring distribution. Every Spur scored at least 6 and the scoring leader, Danny Green, had 17. The Cavaliers averaged 7.38 points per player with a standard deviation of 5.55 points while the Spurs averaged 9.69 points per player with a standard deviation of only 3.25 points.
Another example is the Dec. 13th game against Minnesota. Kevin Love scored 42 for Minnesota in a great individual effort. This would give the Wolves a very high standard deviation vs. the more even distribution of the Spurs. The Wolves averaged 11 points per player with a standard deviation of 12.71 while the more balanced Spurs averaged a similar 10.64 points per player but with a standard deviation of 9.16. The lower the standard deviation, the more evenly distributed the scoring is. The higher the standard deviation, the less evenly distributed the scoring.
This stat could go for any category as well, rebounds, assists, steals, and blocks and could give a solid statistical analysis of how well rounded a team is in any particular category. As team ball becomes more and more the norm in the NBA, standard deviation stats can go a long way in showing which teams distribute their scoring the best.
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Note: Original calculations were slightly off as a result of using a similar formula for a slightly different process and have been corrected.