Raptors Cage

The Scoring Balance Coefficient: Basketball’s Newest Advanced Stat

Similar to countless other youth sports fans out there, my dream is to one day have a career in basketball. Basketball, and the Raptors have been one of the few constants throughout my life. Through every up, and through every down, I knew I could look forward to that 7:00 PM tipoff, and for a couple hours every day that the Raptors played, everything unrelated to the game would vanish. 82 days each year, for as long as I can remember, the Raptors have been my rock.  Sitting in front of the television and cheering for my dinos is my sanctuary. I’ve played basketball for as long as I’ve known I could walk, and the game has taught me that a lot of life’s values can be learned within those 94-feet of hardwood.

I’ve spent some personal time studying the CBA (Collective Bargaining Agreement), and building NBA rosters through the MyLeague game mode simulation on NBA 2K. Give me any team to use, regardless of how doomed their franchise may look, and I promise you that within a couple seasons I could win you some virtual hardware.

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As soon as my basketball playing days were over, I found the opportunity to write at Raptors Cage. It was a perfect opportunity for me, since I was focused on improving my literature skills, and applying them in a basketball context could help me develop my knowledge of the game while also getting some reps in putting my fingers to the keyboard. I love it, and no matter where life takes me, I want to do this until the day I die.

Today, I have something new to share though: the NBA’s newest advanced statistic, that I like to call the Scoring Balance Coefficient (SBC for short) – a stat that I’ve derived using existing statistical formulas. We often hear fans and commentators casually speak about how offensively balanced a basketball team is, without having a measure for that, until now. It’s not flawless, but the SBC is a logical and formulaic attempt to explain how offensively balanced a team is.

Due to time constraints (exam season is approaching, so forgive me), I have only found the SBC for each team’s starters, in addition to one more specific Kyle Lowry-related application that I’ll dive deeper into later on in this article. If you’re a stat junkie like I am, or you’re simply wary of where this teenage blogger derived a new NBA statistic from, feel free to read through the appendix at the bottom where I attempt to explain the math behind the SBC.

Enough about me, here’s some basketball talk:

It was a busy week around the NBA: Carmelo Anthony made his debut as a Portland Trailblazer, and last night, our Toronto Raptors tied the NBA record for consecutive home wins against divisional opponents, at 32 straight games dating back to last season. After Joel Embiid’s first scoreless game of his career on Monday, against none other than Marc Gasol who is officially living rent-free in the heads of all Sixers fans, the Raptors have improved to 12-4 on the season, and hold onto the 4th seed in the Eastern Conference. Just in case you haven’t heard it enough times already, this was without Serge Ibaka and Kyle Lowry, who are both expected to return sometime during the next week-or-so. It’s like we’re David, everyone else is Goliath, and we’re beating them without our sling.

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Monday night’s win also made it the 8th time this year that Kyle Lowry was not in the starting lineup, which matches up to his 8 appearances in the starting lineup – optimal for a statistical comparison. Ever wondered if the starters’ offense is more balanced with Lowry or without him? The identical 6-2 records in each 8 game split wouldn’t give you much to hang on to, but the SBC will.

What I wanted to find out was whether the starters’ scoring was more balanced with a backcourt of Kyle Lowry and Fred VanVleet, or if the starters’ scoring was more balanced with a backcourt of VanVleet and Norman Powell. To my surprise, it was the latter.

The starters with a backcourt of Powell and VanVleet posted an SBC of 446.0, while the starters with a backcourt of Lowry and VanVleet had that of 495.1, signifying that the offensive scoring load was almost exactly 10% more balanced swapping out Lowry for Powell.

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Is this a good thing, or a bad thing, one might ask? I was curious too, so I took the SBC’s of the starting lineups for all 30 NBA teams, compared them to the winning percentages of each respective team to make a graph, and found a correlation between the two variables.

As can be seen from the chart, using the Scoring Balance Coefficient as the independent variable, and the Winning Percentage as the dependent variable, we can see that there is a slight positive correlation.

In English non-mathematical terms, having a less balanced offensive style leads to winning more games. This would mean that despite Lowry in the lineup leading to a less balanced offense, it is beneficial for the team. Who knew that having a 5x All-Star on the court would help win some more games?

If you are interested in finding out where each team ranks in terms of SBC, feel free to take a look at the chart below.

Ladies and gentlemen, welcome to the newest NBA advanced stat: the SBC, to let you know how balanced, or unbalanced an NBA team’s offensive scoring load is among their players.

Appendix:

Hello, stats junkies, and welcome to my more detailed explanation of how I’ve come up with this stat. As I mentioned earlier, the SBC was derived by first finding the average among each starter’s scoring figures, then finding the squared difference between each players points in each game and the average, and then taking the sum of all of those values. This number then has to be adjusted for the variance from game to game, which is found by taking the scoring average overall throughout all the games, then finding the squared difference between the mean of each individual game and the overall mean, and summing these values up.

Finally, the sum of these two numbers gives you the overall SBC, and dividing that by the number of games played gives you the true SBC.

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