The NBA Draft Lottery is the ping-pong-ball-centered game the league plays with the four worst teams from the previous season to determine the order of selections for the next player draft. It’s basically beruit/beer pong with millions of dollars instead of Keystone Light, and, like timid lightweights, the winner doesn’t want to stay on the table for the next round.

The positions are selected in descending order, and the number of balls a team has in the hopper is inversely proportioned to how well the team finished the prior season. The ostensible idea is to give the last-place team the best shot of getting the first overall pick (i.e., the best chance at improving its lot in the future). Why not just award the worst team the first pick as a rule? I suppose the idea is to avoid the sort of tanking that allegedly is a problem in the NFL, where such a rule is in effect. Injecting an element of chance means it’s harder to game the system in a way that’s detrimental to the game– losing on purpose– although it can’t fully do away with the incentive to lose so long as it maintains its rehabilitative goal.

This year, the Charlotte Bobcats had the worst season in NBA history. The New Orleans Hornets, recently late of league ownership, merely had the fourth worst of the 2011-2012 season. This year’s draft lottery thus was arranged with the stated goal of giving the Bobcats the best shot at the first pick and the Hornets the worst.

Of course, once everyone saw that the Hornets would be in the mix for this year’s draft lottery, the conspiracy theorists, folk singers of my literary heart, rolled out their obvious prediction: the league was going to rig the lottery so that the Hornets got the top pick. Why would the league be motivated to do this? Before the season started, you may recall, the league did pretty bad by NOLA when it severely intervened in the team’s handling of Chris Paul. (If you don’t recall, here‘s my assessment of the situation, with totally appropriate and obvious references to the Founding Fathers and Monty Python.) When the league later convinced someone to buy the Hornets from them, the conspiracy theory goes, NBA Commissioner David Stern promised the new owner the first overall pick in exchange for his agreement to take ownership of a foundering franchise that had just dealt away the best active point guard in the game.

Seemingly confirming evidence came in the form of this photograph, which surfaced last night and allegedly was taken three weeks prior to last night’s lottery:

What did Anthony Davis know, and when did he know it?

Anthony Davis, he of the unibrow, has been the consensus number one pick since consensus first was formed about who would be the number one pick. There’s a pretty steep falloff after the first pick, though. Davis’ college teammate, Michael Kidd-Gilchrist, ex-Jayhawk Thomas Robinson, and Harrison Barnes will comprise the top four picks, and after that, this year’s picks rapidly diminish in value. All this is to say that the first pick is really valuable this year in absolute terms because of Davis, and it’s really valuable this year in comparative terms because of the quality of rest of the field.

_______________

On his radio show this morning, Mike Golic tried to stem the rising tide of conspiracy angst by arguing that he didn’t believe last night’s results– Charlotte with the fourth pick, New Orleans with the first– provided any evidence of conspiracy. In fact, he said, the odds actually were against Charlotte getting the first pick. How’s that? Golic pointed to the fact that in eighteen years of draft lotteries, the worst team only received the top pick three times. Therefore, Golic said, the odds were heavily against Charlotte getting the top pick, even though it had the most balls in the hopper.

I’m not totally on board with the general concept of probability, but this idea immediately struck me as incorrect, and the investment disclaimer that past performance is not indicative of future results jumped to mind. Each draft lottery is an independent test. What happened last year, or for the past eighteen years, has nothing to do with what happens this year. Charlotte had the most balls in there. They were supposed to have the best chance to win this year. That should be the end of the story.

But then I started thinking about that dang Monty Hall/Let’s Make a Deal problem. I don’t pretend that I ever will understand that thing, but the track record of outcomes from repeated testing of a particular event is difficult to discount. Given the variables at play in the draft lottery, I don’t know what a statistically significant number of tests would be, but it almost certainly is (many) more than eighteen. That said, 3/18 seems quite low if the deck supposedly is stacked in favor of the last-place team.

When Rosencrantz and Guildenstern flip their coin and the former wins ninety-two consecutive times, betting heads every time, we start to question our assumptions about either the coin or reality more broadly. I don’t think that the seemingly peculiar results of the NBA draft lottery are a signal that we’ve tumbled into some dark, alter-Shakespearean parallel universe. I do think they raise questions about our assumptions about the mechanics of the draft lottery itself, though.

Draft lotteries may be independent tests, but the four selections within a single lottery most certainly are not, because each team can only be selected once, and the selections are made at different times, in a particular order. Charlotte, the worst team ever, had the most balls in play at the time of the first test– which was for the fourth overall pick– so we shouldn’t be surprised that that’s the result that obtained; indeed, it was the most likely result. Had another team’s ball come up in the first test for the fourth overall draft pick, that team would be out of the running for the subsequent tests, meaning that it then (but not at the outset) would have been even more likely that Charlotte would’ve been chosen for the third overall pick. And so on.

(One complicating feature for me in scenarios like this is the fact that, while Charlotte had more balls in the hopper than any of the other three teams individually, the other three combined had more than Charlotte individually. Looking at things this way, it was more likely that not-Charlotte, rather than Charlotte, would be selected first (for the fourth draft pick). I’m going to set this aside until it serves my purposes, which it currently does not.)

What conclusion, then? Besides the fact that I now demonstrably have a sub-elementary understanding of statistics and probability? It’s that the NBA draft lottery is rigged, but it’s rigged against all last-place teams, and not, as the conspiracy theorists argue, in favor of or against any particular team. I therefore agree with Golic’s conclusion that Charlotte was unlikely to receive the top pick, but the 3/18 historical statistic simply serves as confirming evidence of that conclusion, not as the reason to draw it.

The assumption that the way to achieve the lottery’s stated goal– to give the worst team the best chance at the top draft choice– is to give that team the most balls in the hopper looks to be incorrect. To find out, and to test my conclusion, the NBA should either (but not both) give the worst team the fewest balls or draw the draft positions in descending order.