### By: Claire Jiang and Wilson Yu

The NBA Draft is a highly anticipated annual event where teams get the chance to recruit top talent in hopes of building a dynasty and making championship runs. For organizations that have not performed so well, this is their chance to level out the playing field by establishing a young core for future success or by targeting a specific player that fulfills their missing piece. Teams cross their fingers to win the lottery and may even be incentivized to “tank” in order to secure a top pick for the upcoming season.

With all the buzz on draft night every year, we want to evaluate just how important these picks are by assessing the historical successes of players at each draft pick. Will a team’s luck in the lottery make or break the team’s foreseeable future? How many 2nd round picks are reasonable to trade for a higher pick? To help resolve these questions, we will look at the average value of each pick and analyze the frequencies at which they appear in all-star games and later rounds of the playoffs.

Before we dive into this topic, we want to address the role of chance. Chance can play a significant role in the trajectory of a player’s career, especially when projected from the day they are drafted into the league. Players may suffer career-changing injuries or be drafted into a team that inhibits their performance. They may also be fortunate and have external factors contributing to their improved success aside from just talent and work ethic. We recognize the fickle nature of a player’s success relative to the pick they were drafted at on the night their NBA career started. However, with a sufficient amount of data, we hope to minimize these factors and uncover material results through our analysis.

## Value of Draft Picks

We first want to determine the value each draft pick brings to their team, which we will define as how much a player contributes to their team’s wins. Adopting this definition, it is appropriate to use the metric of Win Shares because it is a statistic designed to quantify the number of wins a player is individually responsible for. For example, if a team had 60 wins in a season, then the team has approximately 60 Win Shares. These win shares are divided up among the team members based on how much each player contributed to the wins. We finalized on the metric, Win Shares Per 48 Minutes (WS/48), because it adjusts for the number of minutes a player has played, placing newer players and veteran players alike on the same playing field.

To give a little more context for WS/48, let’s briefly discuss how it is calculated. Win Share is the sum of Offensive Win Share (OWS) and Defensive Win Share (DWS). For OWS, we first calculate the Marginal Offense for the player which can be understood as how many points the player outscores/underscores the average player, adjusting for number of possessions. Next, we have the Marginal Points Per Win, which is roughly how many points it takes for a team to win on average, accounting for the team’s pace. OWS is then calculated as (Marginal Offense)/(Marginal Points Per Win), which intuitively makes out to be how many team wins a player is responsible for based on how many points they scored. The calculation for DWS follows very similar principles. The Marginal Defense for the player can be interpreted by how many points the player prevents the average player from scoring per possession, scaled by how many minutes they played relative to their team and scaled by how many defensive possessions their team had. Using the same Marginal Points Per Win from before, DWS is calculated by (Marginal Defense)/(Marginal Points Per Win), which is essentially how many wins a player is responsible for based on how many points their defensive play stopped. It is critical to note that a player’s Win Share is cumulative throughout their career, so veteran players are likely to have much higher Win Shares just as a result of playing more seasons. WS/48 is used to remedy this. It calculated by (Win Shares)/(Total Career Minutes)*48, which tells us, on average, how many Win Shares a player produces per 48 minutes of gameplay.

Virtually every advanced statistic contains flaws associated with it, and WS/48 is no exception. The problem with WS/48 lies primarily in its DWS calculation because it relies too much on the team’s performance, rather than the individual performance of the player we are assessing. As mentioned before, the Marginal Defense calculation includes multiplicative factors of the player’s minutes relative to their team’s minutes and the number of their team’s defensive possessions. This method assumes that every defender contributes the same defensive impact at each defensive possession. For example, a poor defender on a team of excellent defenders will be awarded the same multiplicative factor as the rest of their teammates, given that they play equal minutes. In this case, the poor defender will have a greater DWS than they deserve. OWS is a much more refined calculation and minimizes some of the inconsistencies in DWS, and based on how we define the value of a draft pick, we believe WS/48 is an appropriate metric of assessment.

However, another issue of using WS/48 is that it is less reliable when calculated for players who have played minimal minutes in their career. Players in this category have an exceedingly volatile WS/48 because it is a rate dependent on the total minutes a player has played and their performance within these minutes may not be enough to truly gauge how valuable a player is. Let’s consider an extreme example with a player who has an 80% field goal percentage on 4 made shots out of 5 attempts in their entire 10 minutes of an NBA career. Their estimated points produced would be exorbitantly high, leading to an incredibly high WS/48 that does not accurately reflect their value. We can observe WS/48 as a function of average minutes played per year (min/yr) below.

We can see that WS/48 is extremely volatile around 0 min/year and becomes much more stable as it approaches 250 min/year. From then on, it appears to be relatively stable. You may be pondering why we used average min/yr as the metric. Well, let’s assume we used the more frequently observed metric, average minutes played per game (min/game), instead. Our goal is to filter out cases in which WS/48 is a poor indicator of value. We may approach this by only excluding players who have played fewer than X min/game (where X is an arbitrary number). However, if a player has played X+ min/game but has only played 3 games in their career, they would still be included in our analysis even though their statistics are unlikely to be representative of the value they add to the team. Additionally, they have not materially contributed to their team’s performance. The same applies for a player who has played fewer than X min/game, but has played many games and accumulated a considerable number of minutes in their career. They would not be included in our analysis by this metric even though they have likely contributed significantly to their team. By using average min/yr, we overcome this issue because we are factoring in the number of games played in addition to the minutes played in each game. Another potential method would be to use total career minutes played as the metric, however, this would be disadvantageous for newer players in the league and favor veterans.

To help us decide where to establish our minimum average min/year such that our analysis outputs accurate results, it would be convenient to include a graph illustrating just the volatility of WS/48 as a function of average min/year. We will use the standard deviation of WS/48 to represent this. The graph below depicts the cumulative standard deviation, which is the standard deviation of the entire sample of WS/48 with average min/year (the x value) set as the minimum average min/year a player must have played to be considered into the sample. This explains why the volatility increases as it nears the maximum limits of average min/year, as fewer players qualify for the sample.

Initially, it would seem ideal to set our minimum at 750 min/year because that is when the standard deviation of WS/48 starts to reach its minimum value. However, we do not want to set our minimum average min/year too high because this will exclude too many players (especially those picked in the 2nd round) and reduce our sample size. Statistics derived from a small sample size are usually less credible than their larger-sized counterparts. We are already working with a more limited sample size for picks 55+ because there were some years between 1989-2004 in which those picks were never drafted. It is also more common for players drafted in those picks to witness very few minutes or never to have played an NBA game at all. Our decision of setting a minimum average min/year is a tradeoff between the size of our sample and the volatility of WS/48.

To address the issue of low sample sizes, we decided to assign a WS/48 of zero to players who were drafted but never played in the NBA. This would lead to results with lower volatility when calculating the average value of each pick. This method also follows intuitively, as these players used up a draft pick but never contributed towards their team’s wins. For players who played in the NBA but were excluded from our analysis (players that played less than the minimum average min/year we set), we calculated the average WS/48 among them and assigned each of them this value as their WS/48. This drastically reduces the volatility while also rewarding an appropriate value for these players. We decided to use the WS/48’s of players drafted from 1980 to 2019 to give us a sufficient sample size to conduct our analysis.

With all this mind, the analysis below considers the WS/48’s of players who played, on average, 250+ minutes per year throughout their career. We designated this boundary because we believe the volatility within this range is low enough to generate credible results without sacrificing too much data in our sample. The graph displays the average WS/48 at each draft pick, which we interpret as the average value each draft pick brings to their team.

Before we take this visual as the final result, we must admit that it is a little misleading. For example, we observe that there is a 29.3% increase between the 8th and 9th pick. Does this mean that the 9th pick is more valuable than the 8th pick? No, it does not. We have to remember that these values were generated with historical data, and it just so happened that from 1980 to 2019, the average 9th pick has had a higher WS/48 than the average 8th pick. Every pick should be valued higher than the ones following it, but historical deviances arise because drafting isn’t a perfect science. By taking the average WS/48 at each draft pick over a span of 40 years, we attempted to minimize these inconsistencies; however, we are still missing a step. Now that we have the raw data above, we must also “average” this out to achieve a more accurate and comprehensible result. We applied LOESS (Locally Estimated Scatterplot Smoothing) regression to our data as seen below.

Each data point calculated by the regression is determined using the weights of nearby data points of the training data, with larger weights assigned to closer data points. However, this means that the regression value for the 1st pick is determined only using data points of subsequent picks, making it more heavily weighted to one side than any other pick (besides the 60th pick). To adjust for this, we assigned a 50% weight to the actual WS/48 of the 1st pick and dispersed the remaining 50% weight to the subsequent picks to arrive at the regressed value of the 1st pick observed in the graph above. From now on, we will be referring to the WS/48 produced by the LOESS regression when we mention WS/48. To analyze trends in our result, the table below helps by listing the change in WS/48 across each pick and is color coded by severity of change. The “WS/48 Change” of each pick is calculated by taking the difference between its WS/48 and the WS/48 of the pick before it. For example, the “WS/48 Change” of the 2nd draft pick can be interpreted as: The WS/48 from pick 1 to pick 2 changed by -0.00629.

The first item you might perceive is the abrupt drop in WS/48 between the 1st and 2nd pick as it seems that the 1st pick lives up to its name. From pick 2 to pick 8, we observe a steeper decline in WS/48 than any other range. After the 8th pick, we see that the decrease in WS/48 is still relatively steep until the 18th pick. From then on, the degree of decrease is marginally less with occasional ranges in which there is very little change from pick to pick. Specifically, picks 40-48 and 52-60 both exhibit lesser decreases in value than the other ranges. While it is always beneficial for a team to acquire an earlier pick, this observation implies that receiving a later pick between two close picks in those ranges is not very concerning. However, our table does inform us that receiving a random pick from the top 8 picks is rather significant as value drops off quickly from the 1st to the 8th pick. This suggests that on average, each draft consists of 6-10 players that make up their own tier of top talent and 1 or 2 players that significantly excel above the rest. To give us more insight when assessing trades, we included some numbers that act as a multiplier of a pick’s worth relative to that of other picks in a table below.

To interpret this table, we first note an entry from the blue column and then compare it to an entry in the red row. For example, we see from the first row and second column of the data that the average 1st Pick is worth 1.30x the average Lottery Pick. Similarly, the average Lottery Pick is worth 0.77x the average 1st Pick from the second row and first column.

Using our WS/48 values, we were also interested to find out which players drafted from 1980-2019 brought the best value to their team for their pick. We determined this by finding the marginal WS/48 for each player, which is calculated by subtracting their individual WS/48 by the average WS/48 for the pick they were drafted at. For example, 1987 draft’s 1st pick, David Robinson, has a WS/48 of 0.25 and the average WS/48 for 1st picks is 0.115. Thus, his marginal WS/48 is 0.25 - 0.115 = 0.135, leaving him with the largest marginal WS/48 out of all the 1st picks. Below are the charts displaying the player with the largest marginal WS/48 and their marginal WS/48 at each pick.

A few standouts from these graphs include Robert Williams at the 27th pick, Mitchell Robinson at the 36th pick, Nikola Jokic at the 41st pick, and Manu Ginobli at the 57th pick, each with a marginal WS/48 exceeding 0.18. It is an essential distinction to note that these are not necessarily the best players to have played (from 1980-2019) at their pick. These players are simply the ones that contributed the most towards their team wins per 48 minutes at their respective pick. Everyone has their own definition of what it means to be the best, but for now, let’s assume it describes the player that is the most individually skilled in basketball. By nature of WS/48, it directly correlates with the team’s total wins. Imagine a scenario in which there is a skilled player on a historically losing team versus a lesser-skilled player on a historically winning team that both average the same minutes per year. The lesser-skilled player will likely receive a smaller portion of their team’s Win Shares than the skilled player receives from their team; however, since the lesser-skilled player’s team has more Win Shares, their individual Win Share may be greater than that of the skilled player. For this example, it is more straightforward to picture the lesser-skilled player as someone who is not as talented overall but is a crucial role player for their specific team. Hence, it may not be accurate to say that a player is “better” than another player solely because they have a greater WS/48. WS/48 is more fitting to determine titles like who are the best MVPs, which could be found by dividing the player’s WS/48 by their team’s total WS/48, resulting in the proportion of wins they are responsible for.

Until now, we have only discussed the value that a player yields based on how much they contribute to their team’s wins. Other than wins, we believe another attractive component for a team is having an All-Star on their roster. A team with one or multiple All-Stars are more likely to have increased viewership, fans supporting their franchise, and all the other perks that come with stardom. Some teams want a star player to be the face of their team, and it is conventional for championship teams to boast one or more All-Stars leading the pack. Intrigued by this concept, we decided to explore the relationship between All-Stars and the pick they were drafted at.

## All-Stars

The graph above displays the percentages of players drafted from 1980-2016 who have made an All-Star Roster in the years 1981-2020. The percentage is calculated by taking the number of All-Stars at each pick and dividing by the number of players taken at that pick from 1980-2016. The reason for the upper bound differential in years we used is that the average player achieves their first All-Star appearance during their 4th season, given that they will become an All-Star. To permit players a fair amount of time to develop into an All-Star caliber player, we fixed the upper bound of the draft years to be 2016, 4 years before the most recent 2020 All-Star game.

It is vital to note that these represent the percentages, not probabilities, of a draft pick making an All-Star appearance at least once in their career. Once again, it seems that the 1st pick is heads and shoulders above its counterparts with a 75.7% All-Star rate. After the 1st pick, there is an incredibly steep decline in this rate until we reach a staggering 27% increase from the 8th to 9th pick. The only other change in All-Star rate more severe than this is the 37.8% decrease from the 1st to 2nd pick. We find that the average All-Star rate for lottery picks is 27.4%, with the rest of the 1st round picks averaging a 7.4% rate. Entering the 2nd round, it appears that the rate is somewhat random and sparse, with only 2% of these players having ever been named an All-Star. While it is always pleasant to be hopeful, the rate of drafting an All-Star falls off rather quickly as draft night progresses and players in the 2nd round rarely get named an All-Star. However, it appears that if you do have a 2nd round pick, it does not matter too much how deep the pick is if your goal is to land a future star.

There have been cases where a player has one breakout season and is named an All-Star that year, but then struggles to maintain this level of play later on. Although an invaluable asset, these players are usually unable to garner the attention and fame some teams seek. Instead of just one All-Star appearance, we were interested to distinguish how the percentages of players who have made at least three All-Star rosters fare at each pick. The graph below exhibits this comparison.

The data considered in this graph is slightly different from the one before because we adjusted the range of years we considered. For this graph, the percentages represent the number of All-Stars at each pick divided by the number of players taken at that pick from 1980-2013. We reduced the previous upper bound of 2016 by 3 years because we want to provide a fair amount of time for players to be able to achieve 3+ All-Star appearances. Note that we are still considering All-Star games that occurred from 1981-2020.

There appears to be a large drop-off when we compare 1+ and 3+ All-Star appearances for picks drafted after the lottery, with a 65.1% decrease in appearance rate, a 23.3% greater drop when compared to the lottery picks. Even with the new constraint, the 1st pick still holds an impressive 55.9% rate, which means that the majority of #1 overall picks have been selected as an All-Star at least 3 times! Another compelling observation is that the difference in rates between the 1st and 2nd pick have stayed relatively similar among the two criteria, with the gap between them only closing by 7.8% in the 3+ All-Star condition. The other vast difference in rates was between the 8th and 9th pick, but the gap here has closed by 60% when considering 3+ All-Star appearances. Intuitively, one might assume that the quality of players between the 1st and 2nd pick are close. Under this assumption, it might make more sense that a reason the gap between the 1st and 2nd pick was so large when looking at 1+ All-Star appearances was that there were many more 1-time and 2-time All-Stars who were drafted #1. In a parallel line of thinking, it would make sense that many of the 2nd picks considered in the 1+ All-Star appearances were actually recurring All-Stars. However, we can see that this is not the case as we still observe a drastic difference in 3+ All-Star rates between the 1st and 2nd pick. The notable increase from the 2nd to 3rd pick adds more intrigue to this mystery. Is it merely dumb luck that this anomaly came about or is there an underlying reason?

If there is an underlying reason, the most susceptible one would be that drafting agencies with the 2nd pick are poorly assessing the value of players left. This may be due to a combination of pressure to carry out the proper decision from possessing a top pick, increased incentive to gamble on players who demonstrate impressive potential but still need development, or placing too much significance on specific metrics like size of a player over a well-rounded individual. Hindsight is 20/20 and this does not prove anything, but notable examples of this case include 7’0”+ bigs like Hasheem Thabeet, Darko Milicic, and Shawn Bradley who were all drafted at the 2nd pick over future stars and led less than impressive careers. This does not diminish the value of the 2nd pick as it will always be more valuable than following picks, which suggests that the reason the 2nd pick has historically underperformed may be due to a specific framework of decisions made at the front office.

Finally, we’re interested to see how draft picks fare in action. The ultimate goal of a franchise and its players is to be crowned as champions at the end of the season. How frequently do we see players at each pick significantly contributing to their team’s efforts in fighting for the title? We will now proceed to examine the rate at which draft picks appear among championship contenders, where we define a contender as a team who has at least reached the Conference Finals of the playoffs (top 4 teams).

## Championship Contenders

We will first define which players have materially contributed towards their team’s performance because we are not interested in players who did not have significant play time. In order to exclude players who did not contribute considerably in the playoffs, we decided to use their average min/game as our metric of filter. Our analysis only includes players whose average min/game exceeded the median of the average min/game of all players in each respective round. Below, we have a scatter plot of Conference Finals games played from 2000-2020, executed with our metric in place.

For Conference Finals, the x-axis is given by draft pick number (undrafted players are represented by the 61st pick), and then y-axis is given by playoff year. To help us interpret the scatter plot, we grouped the number of appearances by draft picks in the mini table above. From our data, we noticed that the number of appearances of players from picks 1-10 was significantly more substantial than any other group. We also observed that player appearances and pick numbers have an inverse relationship-- as pick number goes up, number of appearances of players go down. Another striking observation is that there were more undrafted players (48 players) present than the aggregate number of player appearances from picks 41-50 and 51-60 combined (37 players). There was also only one more appearance of players from picks 11-20 than players from picks 21-30.

In this graph, we applied the same metric as stated before for Finals games from the years 2000 to 2020. As seen in the graph, there is a less accumulation of scatter plot points in general compared to the Conference Finals graph. This makes sense because there are fewer players and teams that make it to Finals. The data in this scatterplot also indicate an inverse relationship between picks and appearances. There were more undrafted players (25 players) present than total players from picks 35-60 (23 players).

This particular scatter plot above displays appearances of Champions, the players who won it all. From our data, we see that there is the same number of undrafted players present as total players from picks 35-60. In a similar fashion as the Conference Finals data, there is only one more appearance of players from picks 11-20 (22 players) than players from picks 21-30 (21 players). In this scatter plot, we noticed that there was no consistent pattern in appearances from 2nd round picks 31-60 in the data table. Interestingly, if we only look at the number of unique players from 2nd round picks, there are 2 players from picks 31-40, 5 players from picks 41-50, and only 1 player from picks 51-60. The sole appearance from picks 51-60 is Manu Ginóbili, who exclusively makes up the majority of appearances among picks 51-60 for these 3 stages of playoffs. This suggests that the inverse relationship seen in the Conference Finals and Finals data is not as prevalent in the Champions data. Considering that some picks in the range 55-60 were never drafted from 1989-2004, this reveals that the appearance of a championship-caliber player in the 2nd round of the draft is arbitrary and exceedingly rare.

We have noted the prevalent appearances of undrafted players in comparison to 2nd round picks throughout these observations and would now like to provide more context as to why this may be the case. In the Conference Finals data, we saw that there were 48 undrafted players while there were only 37 players from picks 41-60. This discrepancy occurs primarily because 513 players undrafted from 1999-2019 ended up playing in the NBA while there were only 407 players drafted from 1999-2019 at picks 41-60. If we compute the percentage of players in these groups who played significant minutes in the Conference Finals, we have 9.36% of the undrafted players and 9.09% of the 41st to 60th picks represented. We also calculated that the average WS/48 of undrafted players (who played more than 15 min/year to avoid data issues) is 0.025, making it approximately equal to the average WS/48 for the 40th pick. We can conclude that undrafted players bring similar value as players selected in the later stages of the draft and are on average even slightly more valuable than players chosen in the last 20 picks. However, we do not find this very surprising as we restricted our analysis to only consider undrafted players who were selected to play in the league.

## Key Takeaways

At the end of the day, each pick is more valuable than its following picks. There isn’t a specific pick that is “lucky” and secures a player much more talented that its neighboring picks. We may be tempted to believe that when we first saw that the 8th pick had a low raw average WS/48 relative to close subsequent picks, but we have to remember that every player chosen after the 8th pick was available during the 8th pick. The main results of this analysis demonstrate how quickly player value drops off from the 1st pick.

Based on our results, the difference between the very top picks and the rest suggests that there are usually two or three players that greatly excel among the rest in each draft. We find this to be very interesting because even though the draft class consists of the best of the best of young prospects each year, there are still two or three players that are considered outliers of talent among them. The distinction of value in the 1st pick is exaggerated when compared to the poorly performing 2nd pick. With even the 3rd pick significantly outperforming the 2nd pick, it seems that the outline of risks and factors teams are considering when drafting the 2nd pick is not working very well. Decline in value is most significant within the lottery picks, thereby revealing that the data does support upset fans when they get unlucky in the draft lottery.

When we reach the 2nd round, players are much more level with each other in terms of value, implying that rights to swap 2nd round picks do not hold much merit when included in trade packages. The 2nd round is somewhat of a crapshoot when it comes to drafting players that will have an integral role in a winning team. As shown in both the All-Star percentage graphs and the scatter plots for championship contenders, the appearances of players drafted in the 2nd round witnesses a dramatic decrease compared to player appearances at the end of the 1st round. The players that do appear are players who have defied the odds and predictions of scouting experts; hence, it would be expected that they show up very infrequently.

The months and days leading up to each year’s NBA Draft provide an extensive challenge to teams as they try to agree on a ranking of players that best fit their franchise among a pool of extremely talented individuals. Drafting is not a perfect science since no draft is ever the same, but teams are more likely to benefit when they possess a firmer grasp on the value of each pick. These results should not be considered with absolute certainty, but we hope it may signal teams towards the appropriate direction when they bet on their futures with trade packages and give fans a more realistic expectation going into the draft.

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