by Laerte de Araujo Lima, guest blogger
The NBA's 2015-16 season will be one for the history books. Not only was it the last season of Kobe Bryan, who scored 60 points in his final game, but the Golden State Warriors set a new wins record, beating the previous record set by 1995-96 Chicago Bulls.
Has any other point guard in NBA history matched Stephen Curry’s performance during their initial seven seasons?
As a fan of both basketball and Six Sigma, I set out to answer this question methodically, following these steps:
ESPN recently published their list of the 10 best NBA point guards, which puts Magic Johnson first and Curry fourth. ESPN considers both objective factors (NBA titles, MVP nominations, etc.) and subjective parameters (player vision, charisma, team engagement, etc.) to compare players. In keeping with Six Sigma, I want my analysis to be based on figure and facts; however, ESPN's list makes a good starting point. Here are their rankings:
This is the easiest part of the job. The NBA web site is a rich source of data, so we are going to use it to check the regular-season performances of each player in ESPN's list. This makes the data average well balanced among all players, because we are going to use the same number of matches per player per season.
In my opinion, the following CTQ factors (based on NBA standards criteria) best characterize point guard performance and how they add value to the team's main target—winning a game:
| CTQ |
CTQ Definition |
Rationale |
| PTS |
Average points per game |
Impact of the player on the overall score makes a positive contribution to winning the game. |
| FG% |
Percentage of successful field goals |
Player efficiency in shooting makes a positive contribution to winning the game. |
| 3P% |
Percentage of successful 3-point field goals |
Player efficiency in the 3-point line shoot makes a positive contribution to winning the game. |
| FT% |
Percentage of successful free-throw field goals |
Player efficiency in the free throw makes a positive contribution to winning the game. |
| AST |
Average assistance per game |
Assisting teammates makes a positive contribution to winning the game. |
| STL |
Average steal per game |
New ball possession and counterattacks make a positive contribution to winning the game. |
| MIN |
Average minutes player per game |
Player's strategic importance to the team. |
| GS |
Games per season where player is part of the initial 5. |
Initial starts indicate importance in terms of strategy, as well as fewer injuries. |
With the players, critical factors, and the source of data defined, let's dig into the analysis.
When I opened Minitab Statistical Software to begin looking at each player's average for each CTQ factor, I faced the first challenge in the analysis. Some players did not have the same CTQ measurements in the NBA database. They had played in the NBA’s early years, and the statistics for all CTQ factors weren't available (for example, the 3-point shot didn't exist at the time some players were active). Consequently, I decided to exclude those players from the analysis to avoid discrepancy in the data. That leaves us with this short list:
To compare these players, I used the statistical tool called Analysis of Variance (ANOVA). ANOVA tests the hypothesis that the means of two or more populations are equal. An ANOVA evaluates the importance of one or more factors by comparing the response variable means at the different factor levels. The null hypothesis states that all means are equal, while the alternative hypothesis states that at least one is different.
For this analysis, I used the Assistant in Minitab to perform One-Way ANOVA analysis. To access this tool, select Assistant > Hypothesis Tests... and choose One-Way ANOVA.
By performing one-way ANOVA for each of the factors, I can position the players based on the average values of their CTQ variables during each of their first seven seasons. After compiling all results, I deployed a Decision Matrix (another Six Sigma tool) to assess all the players, based on the ANOVA results. The ultimate goal is to determine if Curry’s average performance is superior, inferior, or equal to that of the other players.
Let's take a look at the results of the ANOVA results for the individual CTQ factors.
The Assistant's output is designed to be very easy to understand. The blue bar at the top left answers the bottom-line question, "Do the means differ?" The p-value (0,001) is less than the threshold (< 0.05), telling us that there is a statistically significant difference in means. The intervals displayed on the Means Comparison Chart indicate that Curry and Nash both had huge variation in their average points-per-game in the first 7 years. Statistically speaking, the only player with a average PPG performance that was significantly different from Curry’s is Kidd; all the others had similar performance in their first 7 seasons.
As in the previous analysis, the p-value (0,001) is less than the threshold (< 0.05), telling us that there is a difference in means. However, the interpretation of analysis is clearer. In terms of statistical significance, Curry’s performance is better than Kidd's (again), but not better than Magic's, and it is similar to that of the all other players.
Again, we see that Nash has tremendous variation in his field-goal percentage, and Kidd exhibits the worst average FG% among these players.
To my surprise, based on this comparison chart Magic has the worst performance—and the most variation— among the players for this factor. On the other hand, Curry has an extremely high average performance, with small variation, and this is what we see in the Warriors games.
If we take a closer look at the three highest performers in this category, Nash, Stockton, and Curry, we see that Nash and Curry’s performances are slightly different. Interestingly, the variation in Stockton's data prevents us from being able to conclude that statistically significant difference exists between his average and those of Curry or Nash.
As happens in many Six Sigma projects, the results of this factor contradict conventional wisdom: how could Magic Johnson have the lowest average for this factor? I decided to dig a little bit deeper into Magic’s data using the Assistant's Diagnostic Report, which offers a better view of the data's distribution. we can see an outlier in Magic's data. According to this analysis, he actually had a season with 0% of 3-point field goals!
I could not believe this, so I double-checked the data at the source. To my surprise, it was correct:
In the free throw analysis, Curry's performance is similar to that of Nash and Paul, all of whom performed better than the other players. Once again, Kidd (whom I have nothing against!) has the worst performance.
For this factor, both Nash and Curry are at the end of the queue with similar performance. For this factor, it's also clear that while Stockton has both the highest average and small variation in his performance, he's still comparable with Isiah and Magic.
Again, the p-value (0,001) is less than the threshold (< 0.05), telling us that there is a statistically significant difference in means. It is clear clear that Nash is not a big “stealer” when compared with the other players. It's interesting to see that Curry’s mean performance is better than Nash's and worse than Paul's, but is not statistically significantly different from the mean performance of the remaining players.
For the first time, the ANOVA results have a p-value (0.075) greater than the threshold (< 0.05), telling us that there is no statistically significant difference in means. It is clear that Nash's performance has huge variation, indicating that his contribution was very irregular in the first 7 season (perhaps due to injuries, adaptation, etc.). The amount of variation in Curry's performance follows Nash's.
For this final CTQ, we can see that the p-value (0.006) is less than the threshold (< 0.05), indicating that the means are different. In this case, Stockton and Kidd's means differ. Curry’s presence in the initial 5 in the first 7 season is not statistically significantly different from that of any other other palyers.
Let's take a look at the Diagnostic Report. We can see that Stockton's performance in this CTQ is incredible—he started all seasons' games in the initial 5, showing his importance to the team
Based on the analyses of these criteria, we now have a final have the final outlook based purely on the data. We can use Minitab's conditional formatting to highlight the differences between players for the different factors (> means "better than", < means "worse than", and = means similar).
From the analysis, we can conclude that
Based on this analysis, perhaps we need a few more seasons' worth of data to compare these players overall performance and reach a more certain conclusion.
About the Guest Blogger:
Laerte de Araujo Lima is a Supplier Development Manager for Airbus (France). He has previously worked as product quality engineer for Ford (Brazil), a Project Manager in MGI Coutier (Spain), and Quality Manager in IKF-Imerys (Spain). He earned a bachelor's degree in mechanical engineering from the University of Campina Grande (Brazil) and a master's degree in energy and sustainability from the Vigo University (Spain). He has 10 years of experience in applying Lean Six Sigma to product and process development/improvement. To get in touch with Laerte, please follow him on Twitter @laertelima or on LinkedIn.
Photo of Stephen Curry by Keith Allison, used under Creative Commons 2.0.