Draft

Knicks and Nuggets finish 7th and T-8th in lottery, Raptors have roughly 1-in-604 chance at No. 2 pick

The Toronto Raptors have roughly a 1-in-602 chance of landing the No. 2 pick in the 2016 NBA Draft.

The Raptors finished 56-26, good for the fourth-best record in the NBA. That means their own first-round pick will be the No. 27 overall pick.

But the Raptors are also owed a first-round pick from the New York Knicks from the infamous Andrea Bargnani trade. The Denver Nuggets, however, have the first claim on that pick, owning the right to swap with the Knicks from the Carmelo Anthony trade. So the Raptors get the lesser of the two picks. Which would be simple, except that Denver gets to decide whether or not to swap after the lottery, so projecting exactly where the Raptors’ pick will land is a little murky.

We know this much: The Knicks finished with the seventh-worst record in the league. We know that they have 43 of 1,000 ping-pong balls as a result, and that the most likely landing spot of their pick is seventh overall (a 59.9-percent likelihood).

We also know that the Nuggets finished in a three-way tie for the eighth-worst record in the league. Tiebreakers don’t exist when it comes to the lottery, and so those three teams will split the ping-pong balls for the Nos. 8, 9, and 10 position. A three-way coin flip will determine which two teams have 19 ping-pong balls and which unlucky team has 18. That same three-way coin-flip will also determine who is Nos. 8, 9, and 10 – essentially, the chances of jumping into the top-three are balanced out by the ball split, but the coin flip still determines the most likely lottery position.

(Note: I am not 100 percent clear on the machinations of said three-way coin flip. I’m imagining it’s like odds and evens, but my only experience with such a flip is from Friday Night Lights.)

Last year, said coin flips occurred two days after the end of the regular season, which would be Friday.

So determining the Raptors’ odds of landing in each spot would be tough even if Denver had the swap rights before the lottery. But they don’t, and so we’re left with some messy conditional probability work. It’s not as easy as the Raptors having 1.8-percent odds at the No. 1 pick because “Denver’s 1.8 percent is worse than New York’s 4.3 percent” and so on for each potential pick slot – we have to account for which pick jumped to which spot, and how many ping-pong balls are leftover as a result, and calculate the odds of every combination of scenarios. It’s difficult and tedious to do, and the value just isn’t there, so I’m not calculating the odds of each spot, just the odds of landing at No. 2 and a range of possible outcomes.

So, with no more preamble:

If the Nuggets win the coin flip, the Raptors will have a 0.1687-percent chance of landing the No. 2 pick, or roughly a 1-in-593 chance. They would be most likely to pick eighth but could conceivably pick at Nos. 2, 3, 8, 9, 10, or 11.

If the Nuggets are second in the coin flip, the Raptors will have a 0.1687-percent chance of landing the No. 2 pick, or roughly a 1-in-593 chance. They would be most likely to pick ninth but could conceivably pick at Nos. 2, 3, 9, 10, 11, or 12.

If the Nuggets lose the coin flip, the Raptors will have a 0.1597-percent chance of landing the No. 2 pick, or roughly a 1-in-626 chance. They would be most likely to pick 10th but could conceivably pick at Nos. 2, 3, 10, 11, 12, or 13.

Averaging those three scenarios out, the Raptors have a 0.1657-percent (1-in-604) chance of landing the No. 2 pick before the coin flip. They’ll have a slightly higher chance of landing at No. 3. Their most likely draft range is 8-13, and if my rough math is correct, their most likely landing spot is No. 10 (slightly higher than No. 9).

The Raptors will convey their second-round pick, No. 57 overall, to Memphis, completing their obligation from the multi-team Hedo Turkoglu sign-and-trade of 2009.

The draft lottery will take place May 19.

(Note: If you are a giant nerd and want to run the conditional probability matrix for all of the lottery scenarios, please @ me.

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