The 2020-21 NBA season has concluded, and it’s time to look towards the upcoming offseason. The first major event in the offseason is always the NBA Draft, where college and international players are selected by teams looking to improve their roster. Most of the attention is focused towards the top few selections, where the worst teams from the previous seasons acquire the best new players. However, the draft is equally important for contending teams that have picks in the latter part of the rounds, since it allows them to potentially add a player who can immediately improve the team.

One of the most sought after players every draft are “3 and D” players. These players excel at both shooting from the perimeter and defending. Both rebuilding and contending teams search for these two-way players because they will boost their performance on both offense and defense, serving as the perfect complementary players. Some of the best 3 and D players in the NBA today include star players like Kawhi Leonard, Paul George, and Jayson Tatum, in addition to lesser known players like Terance Mann, Mikal Bridges, and OG Anunoby. In this article, I will attempt to forecast the best shooters and defenders in the 2021 draft class, then assess which players are the most likely to blossom as two-way players during their time in the NBA.

## Predicting Perimeter Shooting

One of the most valuable abilities in the NBA today is three point shooting. Teams are taking more three point attempts than ever, with the average number of three point attempts per game having increased since 2011. With increased reliability on perimeter shots, teams must put maximum effort into acquiring players that can shoot well, especially in the draft. Using college and international stats, we can estimate the NBA three-point percentage for the players in this draft class.

### Model Specification

In order to forecast the perimeter shooting ability of future NBA players, I conducted a multiple linear regression. The sample for the model was players drafted between 2011 and 2019 who had at least 500 minutes and 20 three point attempts in college/international play. The dependent variable in this model was NBA three point percentage. Even though NBA three point percentage is not a perfect estimator for perimeter shooting ability because it cannot take into account factors like shot difficulty, it is the best easily accessible statistic for shooting talent.

Some initial variables that I added to the independent variables included the natural log of draft pick^{1}, draft age, college three point percentage, college free throw percentage, college three point attempt rate^{2}, college free throw rate^{3}, wingspan, and body mass index (BMI). These variables were all included for specific reasons: free throw percentage and three point percentage are likely to be great predictors for future shooting ability, the free throw rate and three point attempt rate can help to distinguish those who shoot a lot from those who do not, and the physical attributes (Wingspan and BMI) account for the difference in shooting between bigs and guards.

After running this initial regression, there were several insignificant variables. These included three point attempt rate, the log of draft pick, the draft age, and wingspan. In order to test for joint significance, I ran a Wald Test where the null hypothesis was that the coefficients for draft age, three point attempt rate, log of draft pick, and wingspan were all zero. The p-value of this test was 0.203, indicating that the null hypothesis could not be rejected. After omitting these variables and testing for additional variables, the following independent variables were used:

- Free Throw Percentage (FTP)
- Three Point Percentage (TPP)
- Free Throw Rate (FTR)
- Body Mass Index (BMI)
- squared Body Mass Index (BMI_2)

The next step was to test for heteroskedasticity. It was possible that the variance of the residuals were correlated with an independent variable, so I ran a Breush-Pagan test for heteroskedasticity. The p-value of this test was 0.034, meaning that there was statistically significant heteroskedasticity in the model. The variance of the error terms correlated with college three point percentage the most. In this model, players with a lower three point percentage had a greater variance in predicted NBA three point percentage, while players with a greater percentage had a smaller variance.

As seen by the regression output above, college three point percentage was a significant predictor of the squared residual of the unweighted model. Therefore, I decided to use a weighted least squares regression as opposed to the ordinary least squares regression. In the weighted regression, the weights were the reciprocal of the predicted squared residual based on the regression above.

Before running the final model, I tested for one more potential bias: sample selection. In order to eliminate players that had a low sample of college play or NBA three point attempts, I filtered the data so that the players included in the regression passed the following requirements:

- At least 100 NBA 3-Point attempts
- At least 500 College/International minutes played
- At least 20 College/International 3-Point attempts

This eliminated numerous players that did not shoot many perimeter attempts in college or the NBA. Because players such as these were not included in the sample, their predictions from this model would be invalid. Therefore, I used a Heckman procedure to correct for the sample selection. I used college three point attempt rate and the log of draft pick as the independent variables in the probit regression, where the dependent variable was whether the player was in the sample or not. Then, I created an adjustment term, which equalled the pdf of the probit outcome divided by the cdf of the probit outcome^{4}. The adjustment term was added to the weighted least squares regression, and the final regression is shown below.

In the final regression model, we can see that all the terms are statistically significant except for the Adjustment term. Therefore, it is likely that there is some sample selection, but not a large amount. From the regression, we can also see the impact of each statistic on a draftee’s predicted NBA 3-Point percentage. The impact of college free throw percentage and three point percentage are very similar: a 1 point increase in either will result in about a 0.1 point increase in predicted 3-point percentage in the NBA. Free throw rate has the largest impact on NBA 3-point percentage, shown by a highly significant p-value. Players that have a higher free throw rate in college likely to be worse perimeter shooting in the NBA. Lastly, players with a larger weight to height ratio are more likely to be worse shooters than those with a smaller weight to height ratio. Unfortunately, though, NBA 3-point shooting is largely a random process as only a small amount of the variation in NBA perimeter shooting can be explained by college statistics.

### Model Predictions: 2011-2019

Now that we have a model for predicting 3-point percentage in the NBA, we can see how it performed on past players. The players in the sample with the largest predicted NBA 3-point percentage are shown below.

Damyean Dotson, Sviatoslav Mykhailiuk, and Denzel Valentine had the highest projections, but none of these players have met their expectations. In fact, the only players with a top 10 projection that have exceeded their expected NBA 3-point percentages are Gary Trent Jr and Mikal Bridges.

The lowest projected NBA 3-point percentages in the sample are shown above. Marcus Smart and Tony Wroten had the lowest projected 3-point percentages. We can see that the model does a good job in distinguishing good shooters from bad ones as the players with a low projected 3-point percentage often did have low percentages in the NBA. Only 3 of the 10 lowest projections had an NBA 3-point percentage above 30%.

Although players from the 2020 draft were not included in the sample, I applied the regression results to their college stats to generate their predicted NBA 3-point percentages. The highest predicted three-point percentages belonged to Justinian Jessup (38.8%), Aaron Nesmith (37.3%), Tyrese Haliburton (37.3%), Desmond Bane (37.0%), and Saddiq Bey (36.8%).

## Predicting Defensive Performance

The second part of 3 and D is defense. All great teams need to have a defense that can limit their opposing team’s scoring. Similar to three-point percentage, it is likely that some college/international statistics can provide insight into future NBA defensive performance.

### Model Specification

For the sample of the defensive linear regressions, I used players that had at least 100 games played in the NBA and 500 minutes played in college. Defense is a difficult ability to measure numerically as many defensive plays are not captured in the box scores. For example, forced field goal misses and forced turnovers would likely be better measures for defense than blocks or steals, respectively, but are not recorded and therefore cannot be used. Therefore, I turned to advanced statistics to measure defense. The dependent variable of the regression was NBA defensive box plus minus (DBPM), which is an advanced stat that can be interpreted as the average number of points per 100 possessions that a player adds to his team defensively compared to the average NBA player. There are other defensive advanced statistics (like individual defensive rating and defensive win shares) that could be used, but I chose defensive box plus minus because it was easily accessible, easy to interpret (positive values indicate good defenders while negative values indicate weaker defenders), and accounts for position (defensive win shares do not). Obviously, defensive box plus-minus does not perfectly capture an individual’s defensive ability, but it does provide a measurable and relatively accurate assessment^{5}.

One issue in creating a defensive model was differences in recording statistics between college and international players. For college players, several advanced statistics (like steal percentage, block percentage, individual defensive rating, and defensive box plus minus) were readily available for their collegiate years. However, players that played internationally prior to the draft did not have these statistics included in the places that I retrieved the data (Tankathon.com and College Basketball Reference). They did have simple statistics, like rebounds, steals, and blocks, though. Therefore, I ran two separate regression models: one included a sample of only college players, whereas the other included a sample of both college and international players. The model of only college players included advanced statistics, while the model using both college and international players could only incorporate simpler statistics.

First, I will explain the college only model. The independent variables in this model were the natural log of draft pick, wingspan (in inches), rebounds per 36 minutes (REB), steal percentage (STLP), the natural log of block percentage (BLKP), personal fouls per 36 minutes (PF), individual defensive rating (DRTG), and defensive box plus-minus in college (DBPM.col). The final results of the regression model are displayed below.

Each of the variables included in the regression were significant at a 0.10 significance level, with all but the log of block percentage and personal fouls significant at the 0.01 level. The model accounted for 54.08% of the variance in NBA defensive box plus-minus, indicating that it does a pretty good job of estimating good and bad defenders. I tested for both heteroskedasticity and sample selection, but neither test yielded significant results, so no adjustments were necessary.

There are some interesting results from examining the coefficients of the variables in the regression. The first is that the natural log of draft pick has a significant positive coefficient. Since draft picks with lower numeric values (like pick 1 or 2) are better than draft picks with higher numeric values (like pick 30 or 40), one would expect the coefficient to be negative. However, the positive coefficient indicates that players drafted later are often better defenders. One possible explanation is that offense takes higher priority for better draft picks, although this would have to be explored further to discover the real reason. Additionally, it seems that steals and rebounds are more predictive of future defensive performance than blocks are, shown by their respective p-values. Another surprising finding is that individual defensive rating has a positive coefficient. Since individual defensive rating is lower for better defenders, the expected sign on this variable would be negative. One explanation for the positive coefficient is the relationship between individual defensive rating and defensive box-plus minus: both are advanced statistics measuring defense and are moderately correlated (r = -0.778), but the p-values show that defensive box plus-minus does a better job of estimating NBA defensive performance.

The results of the regression for both college and international players (does not use advanced statistics) are shown above. The independent variables are slightly different, with steals per 36 minutes (STL) substituting for steal percentage and blocks per 36 minutes (BLK) subbing for the log of block percentage, while individual defensive rating and college defensive box-plus minus omitted entirely. The natural log of draft pick, wingspan, rebounds per 36 minutes, and personal fouls per 36 minutes all remain in the regression. This regression performs slightly worse as it accounts for 44.08% of the variance in NBA defensive box-plus minus. The sign of each variable is the same as the previous regression, showing that the results are still similar even when omitting advanced statistics.

The graphs shown above further analyze the results from the defensive regressions. The residuals of the college only regression were slightly right skewed, while the residuals from the second regression look to be more approximately Normal. Additionally, the standard deviation of the residuals is 0.69 in the college only model and 0.76 in the model including all players. Therefore, a 90% confidence interval in predictions for the college only model would be the expected value from the regression +- 1.13. In the model of all players the confidence interval be the prediction +- 1.25.

### Model Predictions: 2011-2019

For the final predictions by the model, I used a combination of the two regression models estimated earlier. For players that played in college prior to being drafted, I applied the college only model using advanced statistics, whereas I applied the all player model using no advanced stats for those who played internationally. The best predicted NBA defensive box plus-minuses are shown below.

The model did well at the top, predicting that Matisse Thybulle, Nerlens Noel, Robert Williams, and Jordan Bell would develop into great defensive players. It also fared well with its predictions for Mo Bamba, Kyle Anderson, Anthony Davis, and De’Anthony Melton. Unfortunately, it missed on players like Kurucs, Ray Spalding, Mitch McGary, and Chris McCullough. Still, 80% of the top 15 predictions were positive defenders in the NBA.

Shown above are the players who had the worst predicted NBA defensive box plus-minus. The model was good in picking the players that would struggle defensively as none of the players displayed above had a positive defensive box plus-minus.

Again, I also applied the models to the 2020 draft class. The best predicted defenders from the 2020 draft were Aleksej Pokusevski (yhat DBPM = 1.64), Paul Reed (1.51), Xavier Tillman (1.47), Tyler Bey (1.27), and Udoka Azuibuike (1.02).

## Combining Perimeter Shooting and Defense

After I constructed models to predict future three point shooting and defensive ability, I needed to find a way to combine the two to create a value that evaluates the 3 and D potential of a player. I wanted a metric that would value shooting and defending equally, but would also incorporate the fact that 3 and D players have to be good on both sides of the floor. Therefore, I created the 3 and D Score, which was the 100 times the geometric mean of the percentile of the predicted 3-point percentage and the percentile of the predicted defensive box-plus minus. The 3 and D Score can range from 0 to 100. The geometric mean is a better choice than the arithmetic mean because it places higher importance on being good at both shooting and defense. The best 3 and D players from the 2011-2019 sample are displayed below using the 3 and D Score.

When looking at the results above, it seems that the 3 and D Score is only moderately accurate. Matisse Thybulle has thrived defensively in the NBA, as predicted, but his perimeter shooting remains off as he shot just 30.1% from three in the 2021 season. However, Thybulle is still a young player and has the potential to increase his 3-point percentage to his predicted value of 35.8%. In fact, during his rookie year, Thybulle actually shot 35.7%. If he can find that efficiency again, he will become one of the premier 3 and D players in the NBA.

Most of the players who graded highly in the 3 and D Score have fared well in the NBA. Both Mikal Bridges and Reggie Bullock have been good perimeter shooters and defensive players. Donovan Mitchell, Cameron Johnson, and Michael Porter have each shot very well in the NBA, although their defense has not lived up to expectations. Both Matisse Thybulle and Chuma Okeke are great defenders, but need to work on their shooting. Denzel Valentine has been average in both areas through his career. The two major misses were Jordan Adams (although he actually did shoot well and defend well in the NBA) and Jacob Evans, both of whom did not last in the NBA. In addition to the 2011 to 2019 drafts, I also applied the models to the 2020 draft to see who the best two-way player were last year.

It is interesting to see the results from last year’s draft class, although it is too early to be able to judge their NBA performances as they have only played one year. Tyrese Haliburton looks to be one early success of the model, placing 3rd in the Rookie of the Year race with a 3-point percentage above 40% (although he does need to improve defensively to meet his predictions).

## 2021 Predictions

### Perimeter Shooting

Now that the specification for the 3-point shooting and defensive models have been completed and analyzed, we can look towards applying the models to this year’s draft class in order to get a look at who may be undervalued players. When applying the predictions to this year’s draft, I included only the top 60 players of ESPN’s NBA Draft Board as of July 16. Additionally, since draft pick was included in several models but the draft has not yet taken place, I used ESPN’s big board ranking as a substitute for the player’s draft pick. First, we can explore the best perimeter shooters in the 2021 NBA Draft.

The best projected three-point shooters in the 2021 draft are Trey Murphy III (38.8%), Corey Kispert (37.2%), Isaiah Todd (36.9%), Jalen Green (36.8%), and Chris Duarte (36.6%). Keep in mind that these predictions have a standard error of 5.8% when using a 90% confidence interval. Furthermore, these predictions may be underestimates because league-wide 3-point shooting efficiency has been increasing. Nevertheless, Trey Murphy III of Virginia looks to be the best option for teams looking for perimeter shooting. With an ESPN rank of 18, a 43% three-point percentage, and 95% free throw percentage, Murphy should be ranked higher than 18th, in my opinion. Other mid first round shooting options in addition to Trey Murphy include Corey Kispert, Chris Duarte, and Jared Butler. Jalen Green, the projected number 2 pick to the Rockets, is likely to be a good shooter in the NBA as he shot 36% from 3 and 84% on free throws with a low free throw rate in the G-league. Some potential second round players that project to be good shooters include Isaiah Todd, Isaiah Livers, Quentin Grimes, Tre Mann, and Kessler Edwards. On the other hand, players that may not develop into good shooters despite taking many college 3-point attempts include Daishen Nix, Luka Garza, Sharife Cooper, Kai Jones, and Keon Johnson.

### Defensive Ability

The best defensive players projected by my two defensive models are shown above. Herbert Jones is far, far above the rest of the class with a projected NBA DBPM of 1.34. The SEC Defensive Player of the Year had a very high DBPM in college and forced many turnovers by stealing the ball, which boosted his projection significantly. Next is Isaiah Jackson, who projects as a good rim protector in the NBA, blocking 4.5 shots per 36 minutes in college. His projection is higher than that of Evan Mobley, a projected top 3 draft pick. While all of the players displayed above are either forwards or centers, there were also some guards that had a good projected DBPM. The three best guards based on projected NBA DBPM were Chris Duarte (projected DBPM = 0.37), Juhann Begarin (0.32), and Miles McBride (0.24). On the other hand, the weakest defenders of this draft class seem to be Cameron Thomas (-1.74), Sharife Cooper (-1.64), Corey Kispert (-1.06), and Jalen Green (-0.89).

### 3 and D Score

Chris Duarte and Franz Wanger are the best 3 and D options of the 2021 NBA Draft. Both have a high projected 3-point percentage (Duarte = 36.6%; Wagner = 35.9%) and defensive box plus-minus (Duarte = 0.37; Wagner = 0.78). Both players are projected to go in the top 20 of the draft, and for good reason. Any team can use players that can both shoot and defend well. Duarte, age 24, can provide these skills immediately, and is therefore best suited for a contending team. Wagner, on the other hand, is only 19 years old and could improve his shooting and his defense even more to become a premier player in the NBA. I believe that Franz Wagner should be a top 10 pick.

Further down the list, there are more first round 3 and D options. These include Jared Butler, Miles McBride, and Jalen Johnson. Butler actually scores higher than Baylor teammate Davion Mitchell in the 3 and D Score, but is projected to go in the late 1st round. His services would be helpful to contending teams like the Lakers, Nets, and 76ers. The same goes for Miles McBride, who is projected to be picked in either the late 1st round or early 2nd round. Jalen Johnson, on the other hand, could be picked in the late lottery or in the back half of the first round due to his character concerns. However, if teams are not alarmed by his character (after leaving Duke midseason), he projects as a positive defender with 3-point shooting potential.

Most of the other players on this list are projected to be 2nd round picks. Even though they may not be picked early, teams should still give these players a chance as they have the potential to develop into good two-way players.

## Team Needs

When selecting players in the draft, a team has to take into account its needs. Since I have examined the 3-point shooting and defense in the draft, I looked at which teams need either skill the most. In order to do this, I ran two regressions. The first used net rating as the independent variable and 3-point percentage as the dependent variable. The second used net rating as the independent variable and defensive rating as the dependent variable. After running the regressions, I found the residuals, then divided by the standard deviation of the residuals to create a standardized residual score. The reasons that I took so many steps was that I wanted to judge team needs based on the relative skill of each team instead of using raw numbers. Bad teams are obviously going to need both shooting and defense, but by taking the residuals of the regressions, it looked at their needs based on their current level. Additionally, I standardized the residuals in order to make them more comparable.

Two graphs showing team needs are displayed below. The first uses four quadrants, where the placement of a team in a certain quadrant tells if they need shooting, defense, both, or neither^{6}. The second graph plots net rating on the horizontal axis and relative need on the vertical axis. Therefore, teams towards the right on the second graph are better than teams towards the left, and teams towards the top need more defense whereas needs towards the bottom need more shooting^{7}.

From these graphs, we can determine some good player-team fits in this draft. First, we can look at the teams that need defense, but already shoot well (bottom right quadrant in graph 1). These include the Kings, Trail Blazers, Nets, and Clippers. The Kings, who have the 9th overall pick, should set their sights on Franz Wagner, Jalen Johnson, and Alperen Sengun as each of these players have a high projected NBA defensive box plus-minus. The Clippers and Nets, who have picks 25 and 27, respectively, should target Isaiah Jackson, Day’Ron Sharpe, Chris Duarte, JT Thor, and Miles McBride. The Trail Blazers currently do not own a draft pick, but if they acquire a 2nd round pick, they should attempt to pick Herbert Jones, Aaron Henry, or Jericho Sims.

Next are the teams that need shooting but are fine defensively (top left quadrant in graph 1). These teams include the Lakers, 76ers, and Grizzlies. The Grizzlies, who recently traded for the 10th pick, should pick Corey Kispert, Trey Murphy III, Franz Wagner, or Davion Mitchell. The Lakers and 76ers both have picks in the late first round, so they should aim for Trey Murphy III, Chris Duarte, Jared Butler, Quentin Grimes, Tre Mann, and Nah’Shon Hyland.

After that, there are teams that need defense and shooting equally (bottom left quadrant in graph 1). The Pelicans and Mavericks are two teams that had worse defense and shooting than expected by their net rating. The Pelicans, who traded down to pick 17, should go for 3 and D players like Jared Butler, Jalen Johnson, and Trey Murphy III. The Mavericks do not have a draft pick, but should trade into the 2nd round to acquire Isaiah Livers, Kessler Edwards, or Joel Ayayi.

Lastly, there are the teams that fared well in both shooting and defense given their net rating (top right quadrant in graph 1). These teams include the Knicks and Warriors. Instead of targeting 3 and D players, both these teams may want to select players that have skillsets elsewhere, such as playmaking offensively. The Warriors, with picks 7 and 14, may want to select Scottie Barnes and Moses Moody, while the Knicks (picks 19 and 21) may want to get Sharife Cooper or Cameron Thomas. Each of these players do not project well as 3 and D players, but have offensive playmaking skills, shot creating skills, or defensive potential.

## Conclusion

By using college/international statistics, we can see which players are more likely to shoot well or defend well in the NBA. NBA 3-point percentage can be estimated by college free throw percentage, three point percentage, free throw attempt rate, and BMI, but is still largely a random process. Defensive ability can be predicted by advanced stats like college DBPM, steal percentage, and block percentage, in addition to simpler statistics like draft pick, wingspan, rebounds, and personal fouls. The best projected shooters in 2021 are Trey Murphy III and Corey Kispert, while the best projected defenders are Herbert Jones and Isaiah Jackson. One of the most valuable types of players in the NBA, though, are 3 and D players, meaning those who can both shoot and defend well. The best 3 and D players of the 2021 NBA Draft are Chris Duarte and Franz Wagner.

Footnotes:

- 1. I used the natural log of draft pick in order to account for the talent differentials across different sections of the draft. For example, the gap between the first and second pick is often far greater than the gap between the 31st and 32nd pick. A linear term for draft pick would not be able to incorporate these differentials, but the logarithmic term does.
- 2. Three Point Attempt Rate (TPAr) = Three Point Attempts / Field Goal Attempts.
- 3. Free Throw Rate (FTR) = Free Throw Attempts / Field Goal Attempts.
- 4. The Adjustment term = pdf(z) / cdf(z), where z = 0.571 + 3.52*TPAr – 0.463*ln(Draft Pick)
- 5. For reference, the top 10% of defenders in 2021 had a DBPM above 1.2, and the bottom 10% of defenders in 2021 had a DBPM below -1.5. The average is supposed to be zero, but the distribution is slightly left skewed.
- 6. The y-axis has “inverted” in parenthesis because before the transformation, the positive residuals of defensive rating meant that a team had bad defense. This is because better defensive teams have a lower defensive rating.
- 7. The y-axis of this graph is the sum of the standardized residuals instead of the difference because the defensive rating standardized residual had the opposite interpretation as the 3-point percentage standardized residual (positive residual for defense = bad defense, positive residual for shooting = good shooting). Therefore, when I multiplied the standardized residual for defensive rating by -1, then used the difference, the negatives canceled and became a positive.