Searching NBA Lottery Results for Evidence of Tampering

Published: May 30, 2012

Some people claim to believe that the NBA Draft Lottery is rigged . . . is there any evidence of such rigging or do we just have evidence of empty claims?

It is human nature to look for explanation for events, and it is the nature of random events to defy explanation. So what happens when the immovable object of human, all too human, tendency to assign causes meets the irresistible force of chaos?


The following is work generated in response to those who believe the NBA draft lottery is rigged. We look at the construction of the lottery, generate the probabilities, and compare the actual results to expectations to evaluate informal allegations of tampering. We try to accomplish this in just about the least boring way possible.

The NBA instituted a draft lottery in 1985 after years of determine drafting order based on win-loss records with some procedural cha-cha-ing thrown in. The impetus was the perception that teams were losing games in droves to obtain a better draft pick.

Since then, the lottery system has been modified. We use the system during the eighteen years since the “1994 system” was instituted as our data set. Before this, the lottery had a different weighting system early on.

The results in the following are based on calculations that account for the ties that have occurred over the years rather than the theoretical probabilities and the changing number of teams. These adjustments are small. Also, expansion deals sometimes forced teams into and out of certain picks. These had no effect on the lottery, but it makes comparing the slot at which a team chooses and whether they won, or were even in, the lottery difficult. Lastly, the assumption is made that the lotteries are independent from one another and work according the published procedures whose execution is witnessed by auditors.

The sources of conspiracy stem from two pools of teams getting the top pick: top seeds and near-bottom seeds. We do not reproduce the claims here. They exist. Just go look for them if you need to satisfy your curiosity on that front.

Top Seeds

The team with the most chance to get the top pick has received it exactly twice in this era. The top seed getting the top pick twice or fewer in eighteen tries has about a 14% chance of happening. Adding in the “or fewer” is important here we are trying to determine if an event is extreme. Thus, we examine not only the chance of an event occurring, but also something even more `alarming’.

In this case, the observations do not constitute evidence for any sort of tampering. An event would have to be rarer than one with a 5% chance of occurrence to be considered so, at least in these highly quantifiable situations. This is interesting since the two teams what won the lottery from this position were Orlando in 2004 (Howard) and Cleveland in 2003 (James).

In the latter case, allegations of rigging surfaced since Mr. James was from near Cleveland. Why send Mr. James to Cleveland rather than Dwight to Orlando, I don’t know. Why when the NBA has franchises in 20 states, D.C., Canada, and those states include the 10 most populous states, that the top pick being used on a player from near the city that drafts him is evidence that the NBA conspired against itself (the however many other teams), I’ve yet to figure out.

And is the NBA feeding these good players to the top seed too often? Then why is it happening less than expected? Does it need to reward the worst team more often? Then why complain about Mr. James going to Cleveland instead of holding it up as how things are supposed to work? Which is it?

And so on.

The top seed has advantages besides being the most likely to garner the top pick with a whopping 25% chance, discounting ties. The top seed has gotten a top three pick 13 times. This happens at this rate or higher around one time in three drafts, not at all alarming in either direction.

Near-Bottom Seeds

At the other end of the spectrum is the rare event causing a stir. This happened in the 2008 NBA Draft when Chicago won the lottery and selected Derrick Rose.

There is no disputing that Chicago had a 1.7% chance to get the top pick, and them winning is a rare event. However, we have to take an 18-lottery perspective here. Over the course of these 18-lotteries, three teams have won the lottery with less than a 5% chance of winning: Cleveland with the Clippers’ pick in 2011, Chicago in 2008, and New Jersey in 2000.

While these particular teams were all unlikely to win the draft, the collection of teams slotted seventh or worse have over a 12% chance of winning the lottery. For eighth or worse this changes to around 8%, and then 5% for ninth or worse. In this light, a team slotted ninth or worse is more likely to have won at least one lottery than to have won none. Which team should win from which slot does not matter, only that a team winning once from such a position was more likely to appear in our data set than it was not to appear.

Considering either and worse and seventh and worse, similar results are obtained.

Again, no evidence of any rigging.


There is more analysis that could be done (I’ve done some, especially with later picks), and I’m sure a small percentage of properly done analyses would show some evidence of statistical anomalies. As it turns out, a dataset this large without one those would be an anomaly itself.

We pause while you bend your mind back the right way . . .

So, either the NBA is employing mathematicians to help them bamboozle themselves into placing key draft choices with teams where they won’t win titles (too soon?) while they figure out what exactly the criteria are for when to do this manipulation so it is undetectable, or it’s just random.

I believe the latter.

Or maybe they work for free . . . I know one math guy stupid enough to do such a thing for a blog . . . and the hours are atrocious . . .

If you have a particular item you wish discussed, detail your concern in the comments, and I’ll do my best to address it.

At any rate, Hornets fans should not be holding out for any deux ex machina here. It’s all up to Fortuna. You can check out her handiwork here.

I do encourage everyone, nonetheless, to work your gris-gris, your mojo, your talismans, and have some fun with this lottery. We’re getting assets here, and they just may be good ones. Bring them and the fun to Manning’s (519 Fulton) from 6 – 8 with Jason Smith, Xavier Henry, Lance Thomas, and Jerome Dyson. Joe and I will be there, along with many of your fellow Hornets fans.

I’ll start with the declarations.

I’ve been rocking the unibrow for decades.