The Winning Formula: Balance

It may be the trendiest topic in the NBA: balance. Do you need it? Do you want it? What really is it? Every NBA GM, analyst or fan may have a different opinion. Should a team be built around one (or more) superstar(s) or should it be evenly assembled with complimentary parts? Not only has it become popular for superstar players to pair up (Heat) or teams go all-out to obtain a superstar (Rockets), it has become commonly accepted that this is the best way to build a successful team. However, when well-balanced teams such as this year’s Nuggets showed us inequality might be overrated, I began wondering which is the better way to build a team. The truth is, there really is no right answer; there have been successful teams built with both symmetric and skewed distributions. However, by analyzing certain performance statistics, Win Shares and salary data from the past 11 NBA seasons, I tried to determine which approach was more reliable.

Read more after the jump

Basic Statistics

I wanted to find a way to measure this balance, or imbalance, and analyze whether it was to a team's benefit, or detriment. A perfect way to do this was using the statistic of standard deviation. Standard deviation measures spread from the mean, so if a team has a higher standard deviation of points, they had more spread out scoring. If they have a lower standard deviation of points, they had more balanced scoring. However, this measure is greatly influenced by the actual amount of points scored. Teams with who score more points are naturally going to have a higher standard deviation of points. To control for this, I divided each players scoring total by the total number of team points, resulting in a percentage that estimates each player's share of the team’s points scored in a given season. I then took the standard deviation of those percentages, resulting in the Adjusted standard deviation of points (Adjusted SD). A team with a higher Adjusted SD of points had a majority of its points come from a few players, while a team with a lower Adjusted SD of points had a balanced scoring attack. The same obviously applies for assists, rebounds, 3-pointers, steals, blocks, and turnovers.

           

It turns out that the way these stats are distributed amongst the team has a significant impact on the season total of the stat, the team’s offensive rating (Points/100 possessions), and their overall winning percentage. Using single regressions, I found that having more spread out scoring contributions (a higher Adjusted SD of points) leads to more points overall, a higher offensive rating and more wins. The same applies to assists, rebounds, steals and blocks. In other words, uneven assists (or rebounds, etc) leads to more overall assists, a higher offensive rating, and more wins. The same logic even applies to turnovers, as having a wide spread of turnovers leads to more on court success, probably because you want your turnovers limited to your primary ball handler. Interestingly enough, unlike all the previous stats mentioned, having a wider spread of turnovers doesn’t predict having more overall turnovers.

This is the same thing Nima Shaahinfar found in his analysis, summarized here. His results differed from mine in that he found that rebounds should be evenly dispersed amongst a team, as it creates a more efficient offensive and defensive unit. Shaahinfar reasoned this means better offense and defense arecreated if everybody crashes the boards. He used lineup statistics, whereas I used season aggregate data. He accounted for the stats of players in relation to the lineup they played with, while I used season totals, combining all of a team’s lineups into one data set. My method may be less precise, but I still feel that looking at how a team’s points, rebounds, etc, were allocated across an entire season is a valuable exercise and the results still have significance.

Using my data in multiple regression models yielded some note-worthy results. The most interesting one is displayed below in regression model 1, predicting offensive rating. The model predicts that, while controlling for how well a team shoots overall (FG%) and how well it shoots the three (3P%), the spread of those 3-point shot attempts and overall shot attempts is significant. With a positive coefficient on Adjusted SD of Field Goal Attempts and a negative coefficient on Adjusted SD of 3-Point Attempts, the model tell us that teams benefit from an uneven distribution of overall shots, but an even distribution of 3-point attempts. This shows us two things. First, successful offensive teams have many guys taking threes. Second, taking the Adjusted SD of 3PA into account, the fact FGA should be unbalanced means that our 2-point shots should have an uneven distribution as well. These results coincide with Shaahinfar’s results displayed in his blog.

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  Note: the analysis here is kind of tricky. If you have a lower Adjusted SD of 3PA, or a more even distribution of people shooting threes, you probably have just more guys who can shoot threes. Every team has at least three players who can hit a three, but when your guys 5, 6, and 7 are shooting threes, they are shooting them for a reason; they’re probably good at them. So it makes sense that a team with a low Adjusted SD of 3PA has a higher Offensive Rating, they have a lot of guys who can hit threes. The practical advice: load up on effective players who can shoot threes.

All of these results must be taken with a grain of salt. For example, the Warriors this past season had the most spread out 3PA (highest Adjusted SD of 3PA) mostly due to the Splash Brothers. The numbers show that offensive efficiency increases when those measures are lower, but this wasn’t the case for the Warriors and no team is going to pass up on Reggie Miller 2.0 and Reggie Miller 2.5 to keep their spreads as even as possible. The point is, over the past eleven seasons, the trend is that better offensive teams have had a balanced 3-point attack, but clearly every team has their own formula.

An interesting way to look at this concept of balance and imbalance is shot attempts and points. I ran single regressions on both the Adjusted SD of Field Goals Attempted and points. The models predicted an increase in the adjusted spread of both shots taken and points scored is better for your team. Did this hold true this past season? Well, listed below are the top and bottom 10 teams in spreading out both shot attempts and points. As you can see, this is an indicator of success.

 

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Win Shares

Another interesting stat to look at is Win Shares, basketball’s version of Wins Above Replacement(WAR). Win Shares relies heavily on Offensive and Defensive ratings. Developed by Dean Oliver, Offensive and Defensive ratings mostly use basic box score statisticssuch as PTS, FTA, REB, 3PM, AST, STL, BLK, and TOV as the inputs. By encompassing how effective a player was on the offensive and defensive end, a Win Share essentially represents the number of wins contributed by a given player. The sum of all the Win Shares on a team results in a number very close to their actual win total. So, by dividing each Win Share by the total number of Win Shares, the resulting percentages represent the proportion of a single win that can be credited to a given player. Looking at the standard deviation of these percentages (Adjusted SD of Win Shares) shows the distribution of a team’s overall contributions. How spread out or balanced does a team want its players’ individual impacts to be? Interestingly enough, it is better to be as balanced as possible. When put into a regression model while controlling for previous winning percentage, the Adjusted SD of Win Shares had a negative coefficient, meaning more spread out Win Shares is damaging for a team. In regression 2 below, I added in the Adjusted SD of specific stats that are part of the Win Share formula and modeled the non-independence amongst teams by including a random intercept. The results are similar.

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-->I also performed a similar regression, but added in the totals of all the individual stats as well (total points, assists, etc) and the adjusted SD of these stats all remained significant. This tell us that both the quantity and distribution of these stats are important.

Wait how does this make sense? You want more spread-out scoring, passing, rebounding and defending statistics, yet a balanced distribution of Win Shares, a statistic that is essentially a direct measure of a players scoring, passing, rebounding and defending? Yes, this is true and it stresses an important point. Players must have roles. Successful teams have players playing to their strengths in certain areas. They have players who score, other players who rebound, others who assist; all ideally contributing to a balanced distribution of Win Shares.

The takeaway here is that the public perception of players is skewed towards individual stats over team impact. I claimed earlier that an uneven dispersion of points, or having a player dominate the scoring, predicted more overall scoring. However, the correct way the phrase it is that having a player whose role is to score leads to a more effective offense. The same goes for having a player whose role it is to pass and get more assists, etc.

Other Measures

Want one more way to look at balance on a team? How about the allocation of minutes and funds? The results from a multiple regression predicting winning percentage from the standard deviation of minutes and Adjusted SD of Salary (because some teams differ a lot in their overall salary) are below.

 

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When regressing against winning percentage while controlling for previous year’s success, the spread of a team’s payroll has a positive relationship. Essentially, more successful teams have an unbalanced distribution of their salaries. The same results were found for minutes played; a more uneven allocation of minutes predicts more success. The reasoning behind regression 3’s results are much more obvious. If a team is evenly distributing its minutes and not having just a few players play the majority of the time, it probably doesn’t have any great players. And if a team’s salary is very balanced, it probably doesn’t have a great player on the team who is worth a big contract.

Applying this same logic to the previously mentioned measures of spread like points and rebounds, it makes sense why bad teams tend to have more balanced scoring. They have nobody who can score in bunches and differentiate himself from the rest of the pack. That’s why teams pay a premium for production, why one-dimensional scorers like Carmelo Anthony get max-deals, and even why irrational scorers like Michael Beasley, JR Smith, and Jamal Crawford have a place in this league (Thank God). But what we learned earlier with the application of Win Shares into the equation is that if you have a scorer, leave him to scoring. Surround him with other guys who can defend, rebound, pass and hit threes. Everybody else should ideally contribute an even share of these other statistics.

Conclusion

I started this post talking about balance. Do NBA teams really want balance? Well the answer is yes, in some respects, and no, in others. It depends on your team. An optimal roster should have unbalanced salaries, but this doesn’t mean all players shouldn’t contribute. Successful teams have had a more even distribution of Win Shares, meaning they receive significant contributions from everyone. You want players with specific roles, and players who know those roles. Does that mean you don’t want a player like LeBron James, who can lead his team in rebounds, points and assists and any given night? Of course not, he’s the best player in the league. No team isn’t going to sign LeBron because he will skew their allocation of Win Shares. Certain players tend to ruin all the analytics done in the NBA. They usually have LeBron or Durant in their name. Thanks a lot guys.

Contact Joey Shampain at joseph.shampain@gmail.com with any questions

Also check out part one!