Distribution of Win Shares


Synopsis: To be fair, the following post is geared towards “quant jocks” (ok, nerds) who have a reasonable knowledge of statistical distributions. In particular, I have used Weibull distributions to model different subsets of 1st round picks from over 40 NBA drafts. With different shape and scale parameters for each subset, the expected value of a draft pick can be estimated with statistical probability. Based on my analysis, I developed a methodology to define a bust objectively in order to overcome the bias which seems to be apparent in existing lists of all-time busts. If you work for an NBA team and came across this site, you should read this post.

If you made it through my last two posts and wondered why I wrote about two all-time greats (Oscar Robertson and Wilt Chamberlain) in the middle of a site about all-time busts, please excuse the digression but I needed to establish a credible scale that works for ranking all players from top to bottom. While win shares may not be an ideal statistic, it’s the best one available to compare cross-generational players on a common scale.


(Win Shares for Potential Busts in Bold)

Draft Pick Bottom 10% Bottom 25% Median Top 25%


1st Overall

16 39 64 107 273 – Kareem Abdul Jabbar
2nd – 5th 9 23 46 76

214 – Michael Jordan

6th – 10th

4 10 27 51 186 – Dirk Nowitzki
11th – 14th 1 5 18 41

235 – Karl Malone

15th – 21st

< 1 1 9 27 208 – John Stockton
22nd < 1 1 6 20

110 – Terry Porter


Not surprisingly, the table shows that earlier draft picks result in more productive players (i.e. players with higher win share totals). Just look down the middle four columns and notice that win shares decline for each subsequent group of 1st round draft picks. In contrast, the last column shows that the maximum win shares are not as strongly correlated to draft order. In essence, outliers exist throughout the 1st round, and their upside is not as dependent on draft order.

For those of you who aren’t too familiar with statistics, a Weibull distribution can be used to described a data set with a skewed one-sided tail. In real world situations, this type of distribution typically is used to describe product failure rates because there is a limit to the minimum time before breakdown (i.e. time=0 seconds) but the maximum time before breakdown can greatly exceed the product’s expected useful life. In addition, this type of distribution is versatile and can describe the operating characteristics of a dud or a well-engineered product. Depending on shape and scale parameters, it can represent a Jaguar (which might be equally likely to break down on the ride home from the dealer or last 100,00050,000 / 20,000 / 10,000 miles), as well as a Ford F-150 (which may be expected to last for 200,000 miles, but can last for well over 1 million).

The table also demonstrates that win shares are not normal (statistically, that is), but rather skewed to the right. Some NBA players will be complete flameouts (and have win shares close to 0) while others will accumulate many more win shares than expected. While the odds of a flameout are much greater for the 16th overall pick than the 1st overall pick, the upside potential for any one player is not much different throughout the top half of the first round. For example, John Stockton had 208 win shares as a 16th overall pick but Tim Duncan “only” has 195 win shares, which is the highest total for a #1 overall pick in the last 45 years. Based on the win share totals for every first round draft pick since 1970, I have been able to model the previously identified subsets by the following Weibull distributions.


Beta (shape parameter) = 1.3 / Eta (scale parameter) = 90

Note:  The area in red reflects the bottom 10% of the distribution

As shown previously, the median number of win shares for a #1 overall pick is 64 and the top quartile begins at 107. The distribution shows that the top 25% extends far to the right with a legitimate possibility for a player to exceed 200. For instance, LeBron is currently at 173 but should exceed 200 by the end of the 2016-17 season. The area in red reflects the lowest 10% of #1 draft picks. Just like the top 10% usually defines elite status, it seems reasonable to limit all-time busts to the bottom 10%. As such, potential players who were drafted 1st overall need to have fewer than 16 win shares to qualify as a Top 10 NBA Draft Bust.


Beta = 1.2 / Eta = 60

Note:  The area in red reflects the bottom 10% of the distribution

The median win shares of this distribution is 46 and top quartile begins at 76. Even though the graph stops at 130, you should note that there’s still a legitimate chance for a player taken with a 2nd to 5th pick to exceed 160 (1:25 odds) like Jerry West, exceed 187 (1:50 odds) like Kevin Garnett, or even reach 214 (1:100 odds) like Michael Jordan. As before, potential Top 10 Busts were limited to the bottom 10%, so draft picks selected between 2nd and 5th overall needed to have fewer than nine win shares to qualify.


Beta = 1.0 / Eta = 35

Note:  The area in red reflects the bottom 10% of the distribution

The median win shares for this distribution is 27 and top quartile begins at 51. The graph stops at 80, but you should note that there is still a legitimate chance for a player taken with a 6th to 10th pick to exceed 130 (1:40 odds) like John Havlicek or surpass 144 (1:60 odds) like Larry Bird. While it’s unlikely that a team will be able to duplicate a pick like Dirk Nowitzki with a 9th overall pick (win shares > 185 equate to 1:200 odds), he was a steal because foreign players were discounted heavily at that time. As before, potential Top 10 Busts were limited to the bottom 10%, so draft picks selected between 6th and 10th overall needed to have fewer than four win shares to qualify.


With respect to players drafted outside of the first 10 overall picks, there have been a handful of all-time greats (e.g. Kobe Bryant, Karl Malone, and John Stockton), but thousands of unproductive players. Whereas the probably of getting someone as productive as Kobe Bryant with a 13th overall pick is approximately 1:50, the probably of getting a flameout with the same pick is greater than 1:4. Furthermore, the probably of getting someone as productive as John Stockton with a 16th overall pick is approximately 1:250, while the probably of getting a flameout with the same pick is greater than 1:2. Statistically, these presumably conflicting data trends can be reflected by a beta measurement (i.e. shape parameter) which is less than 1. Based on this statistical difference, its makes sense to exclude all players taken outside of the top 10 overall picks from being considered Top 10 Busts. At the same time, there seems to be a symmetry to the restriction.

Even though the remaining 1st round subsets are not relevant for identifying potential all-time busts, I have included their distributions in case anyone is curious. More importantly, I did the work so why not show it. When looking at the following distribution, you should notice a difference in the shape of the graphs. Imagine the first three graphs as bunny slopes but the last three as increasingly steeper and taller sides of a half pipe. Which ones would you rather look down with a snowboard or pair of skies?

Shaun White Portrait Session
I’ll assume the Flying Tomato isn’t reading this post


Beta = 0.7 / Eta = 25

The median win shares for this distribution is 18 and top quartile begins at 41.  Even though the bottom 25% of draft picks taken 11th-14th overall have been completely unproductive with win shares < 5, there still have been a fair number of superstars taken in the middle of the first round. The most accomplished player drafted in this subset was Karl Malone, whose 234 win shares can be expected from only one out of every 125 players drafted 13th overall.  As mentioned previously, this subset was excluded from potential bust status because the odds of a flameout are too great. Furthermore, the bottom 10% from the group have win shares less than or equal to one, which is too restrictive. For instance, even Harold “Baby Jordan” Miner was able to dunk his way to four win shares.


Beta = .65 / Eta = 15


The median win shares for this distribution is nine and top quartile begins at 27. At this point in the draft, teams can expect that half of their picks will be unproductive with win shares below 10. In essence, these players will give a team less than a half-season of superstar production spread throughout their entire careers. Even though John Stockton was drafted within this subset, there are too many completely unproductive players at this point of the draft to distinguish any as all-time busts. Based on this distribution, you can stop watching the draft after the lottery picks are gone because it’s highly unlikely that there are any potential superstars whose names haven’t been called yet. In other words, the pundits are just winging it in order to try to keep your attention (just like Day 3 of the NFL Draft).


Beta = .65 / Eta = 10


The median win shares for players taken outside of the first 21 overall picks is six and top quartile begins at 20. Basically, any pick this late in the draft is a crap shoot. Teams are not likely to get a productive player, but they have a chance, albeit small, to draft someone like Tony Parker (97 win shares – odds of 1:50) or Terry Porter (110 win shares – odds of 1:70). It’s with these low draft picks that scouting teams can really prove their worth.

Since the Spurs drafted Tim Duncan with the 1st overall pick in 1998, they have made the playoffs every year and have won five titles so they routinely have drafted this late in the draft. Regardless, they seem to make the most of of their “crap-shoot” picks. In addition to picking up Parker with the 28th pick in the 2002 Draft, they selected Manu Ginobili with the 57th pick in the 1999 Draft, and George Hill with the 26th pick in the 2008 Draft. After three productive seasons with the Spurs, Hill was traded for Kawhi Leonard (the 15th pick in the 2011 Draft) showing how good they are at talent evaluation. Making any one of these picks might be considered lucky, but making all three (along with the trade for Leonard) shows that their scouting is truly special.

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