NBA Draft Lottery

[Boom. This is awesome. Bumped from the Fanposts - R]


As the trade deadline looms closer and closer, teams will start to realize where they belong between the two groups: the playoff hopefuls and the lottery hopefuls. It is around this time when teams start realizing what their team is made of, what the team still needs, and what the market is based on those two groups. Playoff hopefuls will be willing to risk their immediate future a little bit (I say a little bit because of the HUGE luxury tax penalties that are coming in 2013) and lottery hopefuls are hoping to be the market for this playoff hopefuls.

For lottery hopefuls, these are the times when they stockpile on young talent they deem worthy of the risk (not JUST young talent) and also jockey for the picks of the playoff hopefuls. One strategy though that seems to be lost in all this hocus pocus that is called the trade deadline is, how it affects draft position JUST by virtue of a team's record. Usually, when a team acquires a pick, it has a certain estimation of what position that pick will be on when draft night occurs, especially if its outside the lottery. Teams such as the Bulls, OKC, MIA will end up in some order of 30,29,28 in the 2012 draft (if they still own their own), and teams such as the Magic, San Antonio, 76ers, MEM will muddy up the 27,26,25 in some order. And so on and so forth..

One very difficult thing though is when you own a pick that's one of two things - it's neither one or the other (not a playoff hopeful, but not also a lottery hopeful) or it can be one or the either (a playoff hopeful that also has the chance of entering the lottery). Unfortunately for the Hornets, they own one of those - the MIN unprotected pick.

Now, for arguments sake, let's put in the Hornets own pick in the equation (Hornets probably finish in the top 5 worst records). A question everyone wants to be answered is - What draft position would ANY team want to be in to maximize its value? This is not a question of which picks historically resulted in the best players(a different study), but rather in the win-loss column, which position (1st worst?2nd worst?3rd worst? etc..) maximizes its value?

The Draft Lottery

To begin, let's discuss briefly the draft lottery in place. the draft lottery makes use of 14 number ping pong balls to select the pick. The league chooses 4 random numbers (example 1/5/7/14) for a total of 14C4(14 choose 4) = 1001 combinations.

From these 1001 combinations, one combination is disregarded (when we mean disregard, if the randomizer picks that certain combination, there will be a re-drawing of lots) , and the other 1000 are distributed to the non-playoff teams: 250 to the 1st, 199 to the 2nd, 156 to the 3rd, etc etc. When the lottery commences, the team with the winning combination (in our case, the team which owns combination number 1/5/7/14) wins the 1st pick. Afterwards, all of the team's combinations are disregarded, and another lottery occurs with the remaining 1000-x total combinations (x = total combinations of winner in 1st lottery). This continues on, until the 1st,2nd and 3rd pick are determined. Afterwards, the 4th to 14th pick are arranged by the W-L column and you have you're ACTUAL draft position.

Now, in understanding how to maximize the value of a pick, we need to know how much is the increase in odds from the 1st to the 2nd, from the 2nd to the 3rd, etc.. We use the formula (x-y)/y to denote the percentage change in outcome from the worst record to the 2nd worst record. For an example, we note that the worst record has a 25% chance of getting the 1st pick, while the 2nd worst record has a 19.9% chance of getting the 1st pick. Thus, moving from the 2nd worst to the worst record improves my odds by 25.63% that is, the worst record is 25.63% better than the 2nd worst record in getting the 1st pick. Calculating this for all 14 positions, we have the following:

  1. 25.63% (2nd to worst)
  2. 27.56% (3rd to 2nd)
  3. 31.09%
  4. 35.23%
  5. 39.68%
  6. 46.51%
  7. 53.57%
  8. 64.71%
  9. 54.55%
  10. 37.5%
  11. 14.29%
  12. 16.67%
  13. 20%

Notice that the lottery is heavily skewed in the middle (the jump from 9th pick to 8th pick is a whopping 64.71%!!). Off course, this is not taking into account sample size. a 50% increase is better from 50 to 75 than for 2 to 3, so we also need to consider the weights of these percentages. This number tries to answer the question - how good is the jump from pick x to pick y as unbiased as it can (we take into account percentage change and sample size). This number is obtained by multiplying the percentage change to the total number of combinations the position has. Lastly we do this for the lottery for the 2nd and 3rd pick, taking into consideration the conditional probability of a position i.e. (what is the probability that the worst record gets the 2nd pick given that it did not win the 1st pick). Finally, we sum the weights to get a complete picture of which positions have the best value to get a top 3 pick (not saying BEST chance, but best value). Here are the numbers (ranked from largest to smallest)

  1. 3rd worst record - 113.86
  2. 2nd worst - 113.28
  3. worst - 110.21
  4. 4th worst - 106.41
  5. 5th - 95.39
  6. 6th - 82.57
  7. 7th - 64.83
  8. 8th - 53.82
  9. 9th - 26.93
  10. 10th - 12.68
  11. 13th - 3.91
  12. 11th - 3.74
  13. 12th - 2.94
  14. 14th - worst value to get a top 3 pick

Real World Explanation

Mathematical Analysis is nothing if it can't be explained - at least intuitively - in real life. As such, in every study, we need to know WHAT it means in the long run, and HOW to apply it.

The results are obviously surprising, because the lottery SHOULD value the 1st pick higher, followed by the 2nd pick, followed by the 3rd, etc etc. This is because the percentage changes are heavily skewed in the middle i.e. mid lottery picks experience the most increase in odds just by moving one spot. An example is jumping from 9th pick to 8th pick, adds almost 64.71% in your odds. This is mitigated by sample size (17 combinations) so the system tries to balance sample size and percentage change. In fact, it is not surprising that the 1,2,3 and 4 are jumbled together because they are the 4 positions that have combinations of greater than 100 (next is 88). As such, percentage change plays a HUGE role.

What does this mean for us Hornets fans?

Personally, it means that if the Hornets draft board is Davis/Robinson/Sullinger, then being at the 3rd worst record isn't such a bad thing to happen - theoretically speaking, we are at the best position to acquire a top 3 pick because of the weighted score system(although it's not that big between the top 4). However, this does NOT in any way assure us that the Hornets WILL pick in the top 3. It just says we gain the most value for our pick if it were there.
For the MIN pick, we should pray it lands on that 9th spot, because value wise, it's a HUGE jump from 10th (26.93 compared 12.68). And does it have a good chance of getting there? No. I mean its close to zero. HOU, UTA and POR could end up with better records than MIN (pushing MIN out of the playoffs). but even in that scenario, MIN still is the 12th worst record among non-playoff foddlers. So that's a lost dream.

Overall, take this with a grain of salt. the Draft is such an inexact science of economics, statistics and psychology that it's nigh impossible to come up with ONE definite research on how to maximize the draft. However, as human beings, even though we know we can't achieve perfection, we always strive for it, failure is always a part. Disect this analysis, add on to it. As the immortal Michael Jordan said

I can accept failure, everyone fails at something. What I can't accept is not trying.

This is me trying. I might have missed a variable here or an interpretation there, but this is a step towards something. This is a step towards helping us fans (and possibly the Hornets) understand the draft more.

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