The 76ers Can Tank All They Want, But They Still Need Lottery Luck

Tuesday night marks the NBA’s draft lottery, the annual spectacle in which 14 franchises hitch their futures to a sack of pingpong balls. (And not the kind Michael Jordan plays with these days.) Although the process is weighted toward giving better picks to teams with worse records, it’s also an exercise in pure luck as to where the picks are ultimately distributed within that setup. So we decided to take a look at how much effect luck has had, and which teams have benefited from it in recent lotteries.

First, we have to quantify the value of an NBA draft pick. Last summer, ESPN’s Kevin Pelton developed a draft value chart on a similar scale to the NFL’s famous Jimmy Johnson chart, based on the net wins above replacement value of the typical player picked in each slot (relative to his salary). Here were Pelton’s values for lottery picks:

Armed with those pick values — and the lottery probabilities for the past three years — we can run a series of simulations to figure out how much value each team was expected to glean from the draft before the lottery balls bounced, and how that value changed after the picks were finalized. I included lottery-protected draft-pick trades in this accounting, so situations where a team’s pick would or would not be traded depending on the outcome of the lottery are reflected — and, as we’ll see, can make a pretty big difference.

It’s no surprise to see Cleveland at the top — the Cavs won the lottery from the third slot (despite 16 percent odds) in 2013, when they drafted Anthony Bennett, then won it again the next year from the ninth slot (a 1.7 percent proposition!) and drafted Andrew Wiggins. Bennett’s awfulness aside, in recent lotteries no team has seen the balls bounce in a luckier direction than the Cavs.

To underscore that point, here’s a look at the possible distributions of Cleveland’s draft outcomes, and where they actually ended up:

Meanwhile, the next-luckiest — and the least lucky — teams are linked through a trade conditional on where a pick landed, which Cleveland’s stroke of luck also influenced. In 2014, the Detroit Pistons’ first-round pick was top-8 protected, and they finished in the No. 8 lottery slot, with an 83 percent chance the pick would not be conveyed to the Hornets. Instead, because the Cavs won the lottery and everything else played out according to the pre-aligned slots, Detroit fell outside the top 8 and lost the pick, which Charlotte used on Noah Vonleh. (It almost certainly would have been conveyed to Charlotte anyway the following season, but it illustrates how one team’s unexpected lottery luck can have ripple effects for numerous other teams.)

Finally, since we all love focusing on the tank-tastic Philadelphia 76ers, here’s that same distribution chart for their past three lotteries:

Notice that the entire x-axis of their distribution is shifted far farther right than, say, Cleveland’s — because the Sixers were so bad, their drafts had an enormous amount of expected value. But given that, they essentially hit on exactly the median expected value of those picks — with average luck, multiple years of tanking only carried them to the fourth-most valuable set of picks after the balls finished bouncing.

Tuesday night, Philadelphia will have the highest probability of picking No. 1 — albeit with only a 25 percent chance. Let’s see if they can exceed the straight-down-the-middle lottery luck they’ve had the past few seasons.

CORRECTION (May 18, 11:03 a.m.): A previous version of this article misstated the years in which two Cleveland players were drafted. Kyrie Irving was drafted in 2011, not in 2013, and Anthony Bennett was drafted in 2013, not 2014.