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Pelicans' Draft Lottery Probabilities

A look at more draft intricacies


I have a thing for playing with numbers, statistics. This is why Excel is my best friend - with all the number crunching and manipulation possible therein, it's held a special place in my heart.

And so here are 2 studies I did on the draft:

The first looked at the relative value of draft position -- how much better is the 1st slot compared to the 2nd slot at getting a top 3 pick? And so forth. What it revealed was that the drop off in value was minimal between the first four picks. You will however experience a great drop-off once you go down to the 5th pick. This means the 5th slot is far less valuable than the 4th slot, in terms of increasing your odds at a top 3 pick.

The second one looked at the history of the draft and which picks yielded the best players in terms of production per minute, ability to stay on the court, and longevity. I used Win Shares -- Win Share per 48 as the basis of my analysis, and it showed that the top 5 picks yielded near quasi-stars. Of course, the 1st pick was way ahead of its top 5 pick counterparts as they produced at a near superstar level. Just revisit the articles if you want to. For what it's worth, the 9th pick mystique still holds true. Kemba Walker and Andre Drummond -- both top 5 material that fell because of multiple reasons (size for Walker, production for Drummond). Should we not trade our pick (whatever it is) for the 9th pick (currently owned by Minnesota) for Pekovic and Budinger? (I kid. I kid).

Today, I'm going to look at a far simpler aspect -- the ability of each slot to increase in draft position, stay put or decrease in position, and lastly the expected value of each pick and how it relates to initial seeding.

The Draft Matrix

Here is the draft matrix for the draft. (Note these are unconditional percentages meaning there is no longer any basis required for the percentages. The probability that the 2nd seed gets the 3rd pick given that the 4th seed won the 1st pick. These are already built into the calculations).

#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14
1st 25% 21.5% 17.8% 35.7%

2nd 19.9% 18.8% 17.1% 31.9% 12.3%

3rd 15.6% 15.7% 15.6% 22.6% 26.5% 4%

4th 11.9% 12.6% 13.3% 9.9% 35.1% 16% 1.2%

5th 8.8% 9.7% 10.7% 26.1% 36% 8.4% 0.4%

6th 6.3% 7.1% 8.1%
43.9% 30.5% 4% 0.1%

7th 4.3% 4.9% 5.8%

59.9% 23.2% 1.8% 0%

8th 2.8% 3.3% 3.9%

72.4% 16.8% 0.8% 0%

9th 1.7% 2% 2.4%

81.3% 12.2% 0.4% 0%

10th 1.1% 1.3% 1.6%

87% 8.9% 0.2% 0%
11th 0.8% 0.9% 1.2%

90.7% 6.3% 0.1% 0%
12th 0.7% 0.8% 1%

93.5% 3.9% 0%
13th 0.6% 0.7% 0.9%

96% 1.8%
14th 0.5% 0.6% 0.7%


Up, Down or Stay?

For most of us, these are the pertinent questions (especially since we're at the precarious position of not being guaranteed a top 5 pick in a top 4 or top 5 heavy draft). The question is "what are our odds of going up and/or staying on our position?". With that in mind, here are the numbers.

Seed Pr (Up) Pr (Stay) Pr (Down)
25.0% 75.0%
2nd 19.9% 18.8% 61.1%
3rd 31.3% 15.6% 53.1%
4th 37.8% 9.9% 52.3%
5th 29.2% 26.1% 44.8%
6th 21.5% 43.9% 34.6%
7th 15% 59.9% 25.0%
8th 10% 72.4% 17.6%
9th 6.1% 81.3% 12.6%
10th 4.0% 87.0% 9.1%
11th 2.9% 90.7% 6.4%
12th 2.5% 93.5% 3.9%
13th 2.2% 96.0% 1.8%
14th 1.8% 98.2%

A couple of notes:

- The only sure thing is that the probability of moving down gets lower and lower. That's not surprising since in order to go down, people below you need to win. And due to the process of the lottery, the lower your seed is, the lower the chances of someone leapfrogging you because you have less competition. The 1st seed has to compete with 13, the 2nd has to compete with 12, the 3rd with 11, and so forth.

- The 3rd pick and 4th slot are very valuable because of their ability to move up.

- The slot that are lower than 5th (6th downwards) are valuable in that they have the highest possibility of staying in their position.

Of course, we need to have a sort of measurement for how we want to value these percentages.

If we take set the value of moving up at 2 (remember, moving up here means getting a top 3 pick only. A 5th seed can never draft 4th, 6th can never draft 5th and 4th, and so on and so forth. Hence the +2 value of moving up), the value of staying is at 0 (you literally did not gain anything) and the value of going down (-1). Then the value of a 1 seed is (according to unconditional probability, which is entirely different from the value of increasing odds, as the first study suggested) 0*2 + 75*-1 = -0.75. Here are the rest of the numbers (along with ranking).

Seed Value Rank
1st -0.75 14
2nd -0.22 13
3rd 0.10 3
4th 0.23 1
5th 0.14 2
6th 0.08 4
7th 0.05 5
8th 0.02 8
9th 0.00 10
10th -0.01 12
11th -0.01 11
12th 0.01 9
13th 0.03 7
14th 0.04 6

As you can see, the 5th spot holds the 2nd best position in terms of expectation of an up, stay or down. It's also no surprise that the 1st spot is the worst position since it has nowhere to go but down. The 1st spot has 13 teams that can leapfrog it, some more probable than others but the fact that the odds are not stacked against it is quite funny (and depressing maybe).

However, that assumes "staying" and going "down" is equal for most teams (here, valued as 0 and -1, respectively). The value of a "stay" for the 1st seed means it claims the #1 pick, which is better than a "stay" for the 14th pick. So what I did instead was use the theory of expected value. The average pick for moving up for the 2nd seed is 1 (since it can only go up to the 1st pick). The average pick for a move up by the 3rd seed is therefore 1.5 (1+2 = 3/2 = 1.5). The value of an up for the 4th down to the 14th seed is 2 (1+2+3 = 6/3 = 2).

The value of a stay for the 1st pick is 1, the value of a stay for the 2nd pick is 2, and so on, until the value of a stay for the 14th pick is 14.

The value of a move down for the 1st pick is 3 (2+3+4 = 9/3 = 3). The value of a move down for the 2nd pick is therefore 4 (3+4+5 = 12/3 = 4), continuing until the value of a move down for the 13th pick is 14 (since 13th can only go down to 14th and no further).

In this case, lower means better.

The numbers:

Seed Expected Value Difference Rank
1st 2.5 -1.5 14
2nd 3.027 -1.027 13
3rd 3.5925 -0.5925 12
4th 4.29 -0.29 11
5th 5.025 -0.025 10
6th 5.832 0.168 7
7th 6.743 0.257 1
8th 7.752 0.248 2
9th 8.825 0.175 6
10th 9.872 0.128 9
11th 10.867 0.133 8
12th 11.7965 0.2035 5
13th 12.776 0.224 3
14th 13.784 0.216 4

This was however looking only at the expected value of an up, stay or down. What about the expected position value (or the draft equivalent of "expected" value)?

Well, in order to calculate this, we'll just multiply the unconditional probability with the position and then add them for each seed. So the 1st seed's (or the team with the worst record) expected position value is 1*0.25 + 2*0.43 + 3*0.534 + 4*1.43 = 2.6 which is -1.6 from his seed (1-2.6)

Here's the expected position with value and ranking:

Seed Expected Value Difference Rank
1st 2.642 -1.642 14
2nd 2.979 -0.979 13
3rd 3.407 -0.407 12
4th 3.965 0.035 11
5th 4.688 0.312 4
6th 5.546 0.454 2
7th 6.526 0.474 1
8th 7.595 0.405 3
9th 8.710 0.29 5
10th 9.788 0.212 9
11th 10.808 0.192 10
12th 11.78 0.22 7
13th 12.779 0.221 6
14th 13.786 0.214 8

What can we derive from all of this and what does it mean for the Pelicans?

  1. The draft is an inexact science. As you can see, there are multiple ways of looking into the draft and how it should be valued. You can value it against the pick before it (my first study). You can value it against the individual probabilities (what I did in the 3rd part) or you can value it on the probability of an up, down or stay (what I did in the 1st or 2nd part).
  2. What does this mean for the Pelicans? Well, glass half full, if you think of this draft as a "top 5" draft (Noel, McLemore, Porter, Oladipo, Burke) then we have a good chance of getting one of those 5 simply because the odds of us getting a top 5 pick is at 55.3% (probability of a move up or probability of a stay). That's probably why the 5th seed ranks as the 4th best in terms of individual expected value (we increase our position by 0.312 since our expected position is 4.688). Glass half empty, the odds of New Orleans going down (6,7,8) is very debilitating. That 10.5% difference between a good outcome (up or stay) and a bad outcome (going down to 6,7 or 8) can mean the difference between a prospect we like (Noel, McLemore, Porter, Oladipo, Burke) and a prospect we don't like (Len, Adams, Bennett) or even a trade out. That 9th pick suddenly seems great, huh?
  3. It's too bad New Orleans didn't get the 4th seed. One thing that's becoming obvious through these write-ups is that the 4th spot is a really great spot to be in a draft lottery. This is because not only is the 4th slot clumped with the top 3 in terms of value over the pick before (the first study), it also has the largest move-up probability (37.8%) and has had a good history of picks in that spot (2nd study).
  4. For what it's worth, the fifth pick has yielded quasi-stars (2nd study). The problem is that the spectrum is so wide. It's produced superstars like Wade, Garnett, Allen, Love and Carter. It's produced quasi-stars (or players that look like quasi-stars-to-be) like Cousins, Rubio, Valanciunas, Harris (for a time) and maybe Jeff Green. It's also produced good role players like Mike Miller, Felton (yes, he is), Battie, Jason Richardson. But it's also produced duds like Shelden Williams (um, Anthony Bennett?), Isaiah Rider (Shabazz?), Jonathan Bender (Alex Len?) or worse... TSKITISHVILI (Saric?).
All in all, even in a class that's supposedly as weak as this one, I'm holding on to that 29.2% (i.e. the probability of going up for us). We're hoping against hope, yes, and odds say we're probably picking somewhere between 5 and 6. But the difference between picking 5 and 6 can be the difference between picking one of Noel/McLemore/Porter/Oladipo/Burke) or picking someone else.

What's the point of this article? Well, plain and simple. Rohan said we won last year in part because of my pre-draft post, Monty being there, and whatever voodoo you guys did. So we're doing that again (I'm going to rock my New Orleans jersey again and will wear a flat top along with it) in hopes of recreating some of the conspiracy magic of last year. Yes?