Determining NBA Draft Pick Values

How do we answer ‘What is the value of each NBA Draft pick?’ Going back over time, we can pull data from each draft, aggregate it, and perform some mild analytics to come up with our version of NBA draft pick values. Many people have considered this problem before – and why not? It is entirely natural to wonder how much more valuable the first pick is than the third. How much should the Hawks have asked for to trade back from the third pick to the fifth pick of the 2018 draft?

Our main conclusions are threefold:

• That without post-processing the gathered data, the results are relatively meaningless and certainly incorrect
• Assigned NBA draft pick values should be handled differently depending on if your picks are very early or relatively later on
• The top 3 picks constitute roughly 38% of the total draft value while the lottery (picks 1-14) contains about 78% of the value.

In this article I study NBA draft pick values in two different ways. First, I simply use win shares as a surrogate for ‘player value. Those players with large win shares necessarily had some combination of a long career and high productivity, either of which should be deemed a successful pick. However, if we consistently pick slightly-above-league-average players, our team will be stuck in mediocrity for forever. To win a championship, a team needs stars. Thus, for my second metric, I use number of All-Star games a player appeared in to determine their value. In this way we can accurately capture NBA draft pick value in two different, meaningful ways.

Raw Data and Unfiltered NBA Draft Pick Values

The first step in this analysis is to pull the raw data from basketball reference. In order to maintain some semblance of the modern NBA and the changes that have happened over the years, we choose only to use the drafts dating back to 1980. For each of these drafts, we noted the number of All-Star game appearances and the total win shares for each player as well as where they were drafted overall. Then, we computed the average number of All-Star game appearances and the average win shares at each draft position. This is our first iteration on the way towards determining the value of each NBA draft pick. Shown below is the raw data which will lead to our NBA draft pick value determination. First, here is our raw estimate for pick value based on win shares.

Notice that if we use win-shares as our metric, 26% of the raw number of win shares are inside the first five picks. 42% of the win shares are inside the first five picks. The median pick, where half the win shares come before and half come after, sits at the 13.5^th pick. That is, half the win shares on average come in picks 1-13, the other half of the win shares exist in picks 14-60. The entire second round is worth roughly the equivalent of picks 1-4. There is definitely something fishy about this. I would always rather have picks 1-4 than 31-60 (even if you give me all the roster spots for those 30 new players to fit onto my team).

What if we look at All-Star game appearances? Using All-Star appearances as our surrogate for ‘value’ of a pick paints an entirely different story. Now, 54% of the value exists in the first 5 picks while 70.5% of the value is in the top 10 of the draft. The median pick is 4.5 with roughly 45% of the value coming before this point and 55% of the value coming after this point. Pick 1 is worth about three times the entire second round, according to this metric.

Which NBA draft pick value metric is correct? The answer is neither and both. I suggest that the correct metric to use is context dependent. If you are drafting roughly in the top 10, you don’t just want an average player, you want an All-Star, a superstar even. However, if you are drafting towards the end of the first round and into the second round, your goal with every pick isn’t necessarily to find the next Nikola Jokic, rather it is to find excellent role players to be the 3^rd-5^th best guys on championship teams.

Processing the Raw NBA Draft Pick Values

Staring at the charts in the last section should cause some discomfort to the reader. No way – there is simply no way – that the third pick is worth more than the second. This is simply a fact, not up for debate. Every player who is available at 3 is available at 2. The fact that pick 3 appears more valuable than pick 2 is simply a statistical anomaly. With more and more data, I am confident that the second pick would emerge naturally as the more valuable pick.

However, we don’t have the luxury of more and more data. In the meantime, we as the analysts need to figure out the correct mathematical machinery in order to impart our wisdom onto the data. Sometimes this process can be a source of bias or error itself. However, in this case when the claim (that higher picks are more valuable) is incontrovertible. It is natural and correct for us to force the value of each pick to be non-increasing as the picks go on.

The next two pargagraphs (and no more, I promise) will discuss the mathematics going into solving this problem. There are many conceivable ways one could accomplish the task of solving for values in a way that match the observed values but are non-increasing. The first two that might come to mind include penalized optimization and fitting the data to a pre-selected decreasing model. These have been done before. Penalized optimization can lead to sub-optimal solutions depending on the penalty. Pre-selecting a model is rarely a good idea because you are biasing the results significantly. For us, we determine NBA draft pick values via the constrained optimization route. We want to solve the following problem: Assign values to each draft pick so that (1) the computed values match the observed values since the 1980 draft as closely as possible and (2) the value of picks does not increase from one pick to the next.

Generally, constrained optimization is difficult and nigh on intractable. Many techniques exist including Lagrange multipliers and projected gradient descent. However, luckily our problem is quite simple. If we choose to minimize the squared error between assigned values and observed values subject to the constraint that the value of each pick is non-increasing, we are actually solving a quadratic program. Moreover, we aren’t solving any random quadratic program, we solve one in which the quadratic matrix is the identity – which is trivially positive definite – and so a solution is guaranteed and quickly. In the next section, we present the result of our quadratic programming solution for NBA draft pick values.

NBA Draft Pick Values with Quadratic Programming

The result of our analysis is a list of values for each draft pick. In both cases – using All-Star Game appearances and when using total win shares as our metric for determining value – the numbers presented are our best guesses for ‘average value you can expect in the future when drafting from this position’. First let us start with the simpler, more direct metric: win shares.

This looks much more like what you would expect ‘NBA draft pick values’ to look like. It clearly breaks into tiers: 1, 2-3, 4-5, 6-11, and so on. This matches fairly well with intuition. But, we still see some undesirable behavior. Indeed, even though we forced the values to not increase from pick-to-pick, we still get regions where the value is determined to be constant. This does not match with our mental model of what should be true. What about if we use All-Star game appearances?

Again, we see similar behavior when it comes to “tier-ing” the players. Clearly the picks can be grouped into 1, 2-3, 4-5, 6-10, etc. As one might expect, after pick roughly 19, the odds of finding an All-Star in the draft are exceedingly low. For example, at pick 20, the predicted number of All-Star seasons for someone drafted is 0.14 seasons. While these charts seem to fairly well approximate NBA draft pick values, I suggest that we may be able to do a bit better.

As I mentioned above, an analyst needs to be careful every time they add something extra to their model. Every time something is added, the model may lose some accuracy. For us, the assumption that NBA draft pick value decreases as the picks get later on is both reasonable and necessary. However, in the following, we’ll actually assume that the pick value decreases by at least 5% from pick to pick. While this seems like a small amount and may be a reasonable assumption, it is important to be aware of and wary of any time one bakes assumptions into a model. I think we are OK here.

So what happens if we force our quadratic program to pick numbers that decrease by at least 5% from pick to pick? Well, when we look at expected value when it comes to win-shares we get the following:

This seems to be a fairly strong model because:

• The value decreases from pick to pick which we know to be true, and
• When comparing this model with ‘extra baked in assumptions that we need to be wary of’ to the other curves which assign win-share values to draft picks in an unbiased way, the values match fairly well but this curve decays more smoothly

If we do the same thing by computing NBA draft pick values in terms of expected All-Star games, the result is:

The commentary I could make regarding this graph is almost identical to the commentary I made above, so I won’t repeat it.

NBA Draft Pick Value Charts

I wanted to take this last opportunity to summarize all of the above into one source. The below is my best estimate to assign relative values of NBA draft picks incorporating all of the following:

• The value of draft picks should decrease as the draft goes on
• In the lottery, average All-Star game appearances is a good measure of relative value
• After the lottery, average win shares is a good measure of relative value.

With all these things in mind, the table below gives the relative NBA draft pick value for the first round. The first pick is assigned a value of 100 and all others are measured relative to this.

Pick (1-15)	Value	Pick (16-30)	Value
1	100	16	10.0
2	51	17	9.5
3	49	18	9.0
4	39	19	8.6
5	37	20	8.1
6	18	21	7.7
7	17	22	7.4
8	16.2	23	7.0
9	15.4	24	6.6
10	14.7	25	6.3
11	13.7	26	6.0
12	12.3	27	5.7
13	11.7	28	5.4
14	11.1	29	5.1
15	10.5	30	4.9

And, pictorially, the same information in a graphic:

Final Thoughts

If you are working in an NBA front office, are trying to evaluate the quality of a trade your team just made, or are interested in how to apply some mathematics to solve problems in sports, you might be interested in assigning values to NBA draft picks. There is one important caveat to this entire analysis: prospects aren’t just numbers. You cannot simply use these numbers to assign values to draft picks when these picks have probable players associated with them. Let’s consider a few scenarios. First, the infamous 2018 Hawks-Mavs trade.

The Mavs received Luka Doncic (3^rd) and the Hawks received Trae Young and Cam Reddish (5^th and 10^th). Simply adding the values of each of these players you see that the Hawks won the trade because they received 52 points of relative value (5+10) versus 48.5 points of relative value (pick 3). I am not taking sides on this trade, but the numbers call this a fairly fair trade. After watching the Hawks and Trae in the 2021 playoffs, many NBA fans would agree just from the eye test.

However, this will not always be the case. What about in 2003? The pure numbers tell you that pick 1 is almost exactly equal to the value of picks 2 and 3 combined. However, because Lebron James was seen as a once-in-a-generation talent, Cleveland could have been offered the rest of the first round and I bet they would have said no. Just looking at picks 2 and 3 for pick 1, no way is Darko Milicic + Carmelo Anthony = Lebron James.

However, in the 2020 NBA draft the general consensus that there were three players who were almost equal in value: Anthony Edwards, James Wiseman, and LaMelo Ball. If I am the Timberwolves and somebody offers me picks 2 and 3 for the first overall pick, I snap accept and go home with 2 of the top 3 picks.

The point is this: these values are best used in a vacuum. Especially near the top of the draft, the relative value of picks will have to be adjusted for the specific players being scouted. If anything, these NBA draft pick values should be used as a starting point, as a baseline for determining the relative value of picks. Then, it is the job of the scouts, the college basketball aficionados, and the talking heads to determine the actual value of the players available at these spots.

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