After years of playing fantasy basketball, I realized that drafting strategies and the discussion surrounding them havent changed much. Whats been lacking is a mathematical discussion of these drafting strategies.
For example, the statement assists are rare is generally accepted as truth without assessing to what extent it is true. When statistics like only six players average over 2.0 blocks a game are used, they arent used very rigorously. Is 2.0 blocks a good benchmark?
Using R, I wanted to extend the statistical conversation regarding fantasy basketball and relate it to drafting strategies. With a little analysis, I crafted some new methods for drafting the optimal fantasy basketball team
8-Category and 9-Category Fantasy Basketball
In fantasy basketball, a league of managers choose NBA players to make up their fantasy team. The statistics accrued by these NBA players in real life are allocated to the fantasy teams of these managers.
In 9-category fantasy basketball, managers typically compete against other managers to accumulate the most points, rebounds, assists, steals, blocks, 3-pointers made, highest field goal and free throw percentage, and lowest number of turnovers. 8-category leagues usually do not have turnovers as a category.
But what factors should we look at when trying to draft the best team? Certainly the rankings provided by services like ESPN and Yahoo provide some guidance, but if youre looking to gain the most points across the board, a little technique called the Gini Coefficient can point you in the right direction.
Analyzing Fantasy Basketball with The Gini Coefficient and Correlation Sums
The Gini coefficient is used as a measure of distribution. A Gini coefficient of zero indicates completely even distribution, where everybody has the same amount. A score of one indicates maximum inequality, where one body has the entire amount. Using a Gini coefficient in fantasy basketball should reveal the competitive balance within each statistical category. Managers may decide to focus on or avoid categories that are notably top-heavy, where a few NBA players produce a significant portion of the statistic for the league. Its great to be at the top of a top-heavy category, but a team with a middling performance in this area may be better off focusing on other areas.
Using R, I calculated Gini coefficients for the various Fantasy Basketball metrics and produced this table:
Statistic Per Game | Gini Coefficient |
Points | 0.19 |
3 Pointers Made | 0.47 |
Blocks | 0.46 |
Assists | 0.38 |
Rebounds | 0.25 |
Steals | 0.24 |
Turnovers | 0.24 |
Since it may be hard to visualize what Gini coefficients represent, I've included two graphs. The y-axes represent the statistic being produced and the x-axes represent the players. The straight line represents what perfectly even distribution or a Gini coefficient of zero resembles. Maximum inequality or a Gini coefficient of one could be understood the maximum area between that line of equality and the line of data points, which is orange in this case.
In our graphs, the bottom 50% of scorers are responsible for almost 40% of all points, while the bottom 50% of 3-point shooters account for not 20% of all threes made--hence, the different Gini coefficients.
Now, because fantasy performance is based on real-life performances of players, weaknesses inherently arise. Generally, players that generate many assists also generate many turnovers and those who accumulate blocks do not usually make three-pointers. To quantify and extract the relationship between categories, I used R to generate the chart below.
Each intersection represents the correlation between the row and column. Red indicates negative correlation, while blue is positive. The darker the shade, the stronger the correlation.
Statistic Per Game | Correlation Sum | Gini Coefficient |
Points | 0.88 | 0.19 |
3 Pointers Made | -0.37 | 0.47 |
Blocks | -0.16 | 0.46 |
Assists | -0.11 | 0.38 |
Rebounds | -0.06 | 0.25 |
Steals | 0.20 | 0.24 |
Turnovers | -2.02 | 0.24 |
The sum of correlations for a given variable is the sum of correlations for that variable relative to other variables. The correlation sum is used to indicate the statistical potential benefit to other categories if one were to ignore a certain category.
With this data in hand, you can begin to create strategies on what categories to focus on, what what you should ignore. A manager that punts on a certain metric, like turnovers, can draft players without regard to their turnover statistics with the aim of strengthening the remaining scoring categories.
Punting on a certain metric also changes how players are ranked and evaluated since the default rankings take into account each category. Note that on ESPN and Yahoo!, punting a category does not the change the visible default rankings and so, must be done by the manager.
Turnovers
Lets start by examining turnovers. Simply put, turnovers are no fun. Turnovers are correlated with a negative performance in five categories, with only a fair positive performance in three. The sum of these correlations is the most negative, coming in -2.03 (second-most negative score belongs to 3PTM at -0.37). While intentionally increasing turnovers does not boost performance overall, carefully ignoring them generally offers a potential boost that ignoring other categories does not offer.
A middling Gini coefficient also indicates that each player more or less contributes their fair share of turnovers. Punting turnovers would then require a fair amount of re-evaluation of more than a few potential picks.
While this strategy is not the easiest to execute, it is by far not the hardest, while also offering the biggest boost. Interestingly, this strategy has been presentedas a competitive option by Zachary Samuels and Paul Raff at the 2010 Sloan Sports Conference ( http://www.sloansportsconference.com/?p=2800 ) .
Points
At the opposite end of the spectrum lies points--the most popular category with basketball fans. Points have the highest correlation sum at 0.88 and a Gini coefficient 0.19. A high correlation sum indicates that players that score more skew toward stronger fantasy performances overall, while a low Gini coefficient indicates that the scoring averages of players is relatively evenly distributed.
These two features back up the conventional wisdom that punting points is the most difficult strategy. A high correlation sum indicates that poor execution of this plan can lead to hampered performance in other categories.
On the other hand, since the scoring averages of players is relatively evenly distributed, ignoring these scoring averages drastically changes the evaluation of many players. This may allow you unhampered access to players of your choosing, since its unlikely that other managers are evaluating players in the same manner. Altogether, punting points offers the highest risk and reward.
Three Pointers Made
Punting 3PTM is the most natural drafting strategy due to its high Gini coefficient (0.47) and low correlation sum (-0.37). A relatively high concentration of three pointers in relatively few players means that if a manager were the miss out on the best long-range shooters, theres little hope of dominating this category. At the same time, domination of this category would be more assured than domination of other categories and would require fewer players than dominating points would.
Interestingly, 3PTM, assists, and steals are negatively and positively correlated with the same categories, yet the low correlation sum of 3PTM makes it the more obvious category to punt. Additionally, as indicated by a high Gini coefficient, relatively few players are contributing a significant portion to 3PTM, which means that punting 3PTM entails re-evaluating fewer players than punting points requires, so its simpler in that regard.
Steals & Assists
In terms of red and blue valence, points, 3PTM, assists, and steals all post similar palettes. However, the strength of the valence varies, as assists register a sum of -0.10 and steals with 0.20. Furthermore, they also differ in Gini coefficient with assists at 0.38 and steals at 0.24. If one is unable to acquire a dominant base of assists nor a base of steals, one might consider punting assists before punting steals, since punting assists offers the greater statistical boost and trying to catch up in assists is more of a wild goose chase compared to trying to catch up in steals.
Blocks
Similar to 3PTM, blocks are unequally distributed with a Gini coefficient of 0.46. However, its correlation sum is -0.16, indicating that while punting blocks may be as simple as punting 3PTM, its overall statistical boost will be less than half. Regardless, its important to remember that its correlation sum is still the second lowest amongst all categories.
Rebounds
Finally, we come to rebounds. Rebounds (0.25) are similarly distributed like turnovers (0.24) and steals (0.24) but unlike turnovers (-2.03), which are a clear punt, and steals (0.20), which are clear do not punt, rebounds lie somewhere in the middle (-0.07).
In this case, punting rebounds lies between punting steals and punting assists in terms of simplicity and offering the greatest overall statistical boost.
Conclusion
Overall, punting turnovers appears to offer the most benefit and is relatively simple to execute. Punting 3PTM and blocks are next in this category, followed by assists, rebounds, and steals. Punting points has been confirmed to offer the highest risk and reward.
Note, though, that its just as important to weigh these factors within the context of your own league while drafting. If the managers in your league appear to be punting 3PTM, it may be time for you to target 3PTM, hoping to exploit an unappreciated category.
Hopefully this article has provided a good statistical assessment of the fantasy landscape and drafting strategies. Ill be employing these strategies to unearth which players are surprisingly helpful and unhelpful. But lets just keep this little secret between you and me, OK?