Explaining The NBA Draft Lottery

Winning looks like this. - Derick E. Hingle-US PRESSWIRE

Hey, Suns fans. Quick intro - for anyone that doesn't recognise me, I'm that other Mike from down under (the younger one, too - sorry Motherwell) and I'm a long-time reader, occasional commenter. I've noticed in the comments throughout the season a common topic - the NBA draft lottery. I've also noticed that in some cases, there is a lack of understanding of how it works. After reading this, you will hopefully have a better grasp of how the lottery works.

The Situation

A quick look at the standings will tell you why as Suns fans we're talking about the lottery - the team currently stands at .347 (17-32), which is good for 12th in the Western Conference and 23rd overall. However, we also (quite famously) own a first round pick from the Lakers for this season. The Lakers pick has a weird protection on it, but the gist of it is if the Lakers miss the playoffs, we get their lottery pick - at the time of writing, the Lakers are 3.5 games out of the 8th playoff spot, good for 10th in the West and 18th overall. If the Draft Lottery were held today, the Suns would be slotted 7th and 12th.

How It Works

This is where it gets complicated. We know already that only teams that missed the playoffs qualify for the Draft Lottery, and we know that the prize is to improve Draft position. However, there seems to be a lack of understanding when it comes to how the Lottery actually works.

Of course, this is all understandable - if you're not a big maths kind of guy like me, then you'll just be lost in a sea of jargon if you try to understand Wikipedia's explanation of the process. It's a good place to go if you're interested in a more advanced understanding of what goes on.

The easiest way to understand it all is to look at this table:

Seed Chances 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th 14th
1 250 .250 .215 .178 .357
2 199 .199 .188 .171 .319 .123
3 156 .156 .157 .156 .226 .265 .040
4 119 .119 .126 .133 .099 .351 .160 .012
5 88 .088 .097 .107 .261 .360 .084 .004
6 63 .063 .071 .081 .439 .305 .040 .001
7 43 .043 .049 .058 .599 .232 .018 .000
8 28 .028 .033 .039 .724 .168 .008 .000
9 17 .017 .020 .024 .813 .122 .004 .000
10 11 .011 .013 .016 .870 .089 .002 .000
11 8 .008 .009 .012 .907 .063 .001 .000
12 7 .007 .008 .010 .935 .039 .000
13 6 .006 .007 .009 .960 .018
14 5 .005 .006 .007 .982

(Props to Wikipedia for the table - and yes I feel dirty citing Wikipedia more than once)

Now, this table tells you a few things. First, you'll notice that the 14th pick for example, can only be the 1st, 2nd, 3rd or 14th pick. There's a very good reason for this - the Draft Lottery only determines the top 3 picks. Once the top 3 is set, the draft is ordered by record, from worst to best. Take a good look at this table, and let it be your reference point - not only for the value of our draft picks, but for what they CAN and CAN'T be.

Potential Outcomes

This is where we come back to the Suns. I mentioned earlier that if the Draft Lottery were held today, the Suns would be slotted 7th and 12th. If our position holds true, then a few things are certain:

1. The Suns pick will be no worse than 10th; the Lakers pick will be no worse than 14th
2. It is only possible to move up to the top 3 - the 9th pick can not become the 5th pick, for example.
3. The Suns will have TWO separate shots at moving up in the lottery. There is no rule preventing a team from 'winning' the Lottery twice, although it is unlikely.

So, what are the possible outcomes?

1. The Phoenix and LA picks both 'win' the lottery and move into the top 3; fans get to wear out their vocal chords asking "U mad bro?" (for the first time in a while...)
2. The LA pick moves into the top 3, and the other top 3 picks go to teams worse than Phoenix. This would give us a top 3 pick and the number 8 pick.
3. The Phoenix pick moves into the top 3, and the other top 3 picks go to teams worse than LA. This would give us a top 3 pick and the number 12 pick.
4. One or more teams better than Phoenix move into the top 3. This would worsen our pick to 8th (if one team with a better record moves up), 9th (if two teams with a better record move up) or 10th (if three teams with a better record move up).
5. One or more teams better than LA move into the top 3. This would worsen both the Phoenix and LA picks.

Aaaaand... a ton more. I tried to list a few of the desirable and not so desirable scenarios, but none of them really deal with probability very well. For that, I'd recommend checking out Chad Ford's Lottery Game. The 2013 version hasn't been released yet, but you can still play with the 2012 version to get an idea of how the picks can move around.

So... should we tank?

Maybe. The Suns are fairly convincingly removed from the playoff race, so there's little point in trying to win as many games as possible. But, and again referring to the table, we can see moving from 7th to 6th in the lottery only slightly imrpoves our chances at moving up. So why bother? What's there to gain other than a few extra balls in the draw?

The answer: worst possible outcome. The higher the Suns are slotted, the better our worst case scenario. Where the 7th slot can fall no lower than 10th, the 6th pick can fall no lower than 9th, and so on.

Obviously, losing has a psychological affect on personnel - none of the players or coaches will enjoy losing. We'd want to avoid poor locker rooms reminiscent of recent Wizards and Kings teams. My personal solution would be to find the balance between improving our lottery standing, developing players and being competitive enough to avoid a toxic environment.

Easier said than done.

Key Points (basically a tl;dr)

  • The Lottery only determines the top 3 - the other 11 teams are ordered from worst to best in terms of record
  • The Suns have two separate chances at landing in the top 3
  • The Suns can pick no worse than 10th and 14th as it currently stands
  • Tanking (and rebuilding in general) is tricky business
  • The real value in worsening your record is not the increase in potential gain; rather the decrease in potential loss (the higher your lottery slot, the better your worst case scenario)

I'll end with an interesting fact - only once in the history of the Draft Lottery has the team with the worst record kept the first pick: the 2004 Orlando Magic.

Quick update:

It was pointed out in the comments below that there is some potentially conflicting text in the Wikipedia article. I said that a team can 'win' the lottery twice, and jc79 countered with the following:

"In the event that a combination belongs to a team that has already won its pick (or if the one unassigned combination comes up), the round is repeated until a unique winner is determined."

Thankfully for us as Suns fans, this section DOES NOT refer to a situation in which a team owns multiple picks in the lottery. Rather, it is referring to the number combinations assigned to one individual pick. Let me explain in greater detail.

The lottery uses a standard lottery machine with fourteen balls number 1-14. Each lottery pick is assigned a number of combinations of those numbers, 1-14. The first pick gets 250 combinations, the 14th pick gets 5. There are 1001 possible combinations - one is always exlucded, leaving 1000 combinations to be divided among the 14 teams.

Carrying on with the example, the first pick might have the combination 1-2-3-4 and the combination 2-3-4-5 as part of its 250 combinations. If the first combination drawn is 1-2-3-4, then the first overall pick will go to that team. If the next combination is 2-3-4-5, then the lottery will be re-drawn until one of the 250 combinations belonging to the first pick is not drawn.

This is important. Every pick is assigned a different set of combinations. A team owning two lottery picks does not see its combinations added together - they are still separate. At this time, the Suns have a 4.3% chance to win the first overall pick with their own lottery pick and a 0.7% chance to win the first overall pick with the pick from the Lakers.

Since there was some confusion, I went to the trouble of getting an answer from somebody with knowledge and authority on the topic - enter Larry Coon, CBA and Salary Cap expert:

Hope that clears up any doubt, folks. Enjoy your dreams tonight.

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