# NBA Draft Lottery: Index of pain and gain

Though it may seem far in the distance right now, the 2016 NBA Draft is fast approaching. The first step in the process is the NBA Draft Lottery, which occurs tonight. The 14 teams that did not make the playoffs will be entered into the lottery, with the worst teams receiving the best chances at higher picks. It is in fact a lottery, however, and the worst-placing team (this year’s Philadelphia 76ers), has only a 25 percent shot at winning the first overall pick. In fact, the Minnesota Timberwolves winning the first overall pick last year was the first time the worst-performing NBA team had won the first overall pick since 2004.

A common misconception of the NBA draft lottery structure is that each team has a shot at winning any of the 14 picks. In reality, the lottery is just determining the order for the top three picks. Each team has a shot at winning one of those but once that order is decided the rest is filled in by the reverse order of the standings. So every team in the lottery has a chance to jump into the top three, but no one should be pushed down by more than three spots. If the Philadelphia 76ers were to get leapfrogged by three other teams, they would pick no later than 4th, no matter what.

The most exciting part about the lottery is that it can move NBA teams up or down the draft board, for no reason other than luck. The Cleveland Cavaliers have notably had the first overall pick three times in the last five years without ever being the most likely team to land the pick, and this is in no way a reflection of anything other than randomness, sorry conspiracy theorists.

The lottery is distributing advantages and disadvantages either through a team moving into the top three, or a team getting pushed down as someone with lower odds leaps over them into the top three. The advantage and disadvantage that teams obtain from their random lottery movement can be quantified. To do that, however, one must quantify the value of the picks, and by extension, the players drafted by them.

There are many ways to quantify player value. Some are better than others. In quantifying player value for the purposes of quantifying draft pick value, it is important to use a metric that summarizes the impact of players, rewards players who sustain that impact for a larger share of minutes, treats players with different career lengths equally, and perhaps most importantly, summarizes multiple seasons in one number. A two year peak of VORP (Value over Replacement Player) derived from BPM (Box Plus Minus) is well suited for this goal. BPM is one of the more predictive of one number player-value metrics and VORP values players that play more. The two year peak methodology condenses careers to one number while at the same time treating different career lengths equally, and is the preferred method of choice for summarizing a career in mine and other draft projection models.

Using seasons going back to 1980, the list of top players by this number includes some very recognizable names.

Using these numbers as the value assigned to each player, the value of each lottery pick can be assigned, and subsequently, averaged across all draft classes since the unequally weighted lottery system began. These averages are not plain averages, they reflect a weighting system that gives less weighting to the players that have been drafted in the last four years, as these players have not yet had a full chance to develop and reach their peak. The value of each lottery pick is expressed below in both expected VORP and the approximate number of wins that amount of VORP equates to.

Each team enters the lottery with an expectation. That expectation is the pick they would receive based on their record over the past year, if the lottery were not held. By comparing the expected value of the pre-lottery position of each team to the expected value of the actual pick of the NBA draft they received throughout the years of the NBA draft lottery, one can understand which teams have profited most from the hands of randomness. The values below are expressed as wins derived from the VORP metric used to assign player value, and the appropriate measures have been taken to assign value for each team (The old Charlotte Hornets are the New Orleans Pelicans here, etc).

It is important to remember a few caveats when digesting this table. The first is that some teams are much more frequent lottery visitors than others, even over a long span of time. For example, the San Antonio Spurs have gained 1.97 expected wins by moving up in the draft lottery since 1990, but that value is the result of one draft lottery, the one in which their position improved enough to enable them to draft Tim Duncan.

Another important consideration is that the values here are reflective of an overall average value of each lottery pick since 1990 as defined by the two-year peak VORP, and are not reflective of each individual draft class, so the year-to-year varying value of moving up in position is glossed over here. Thirdly, the value of position improvement is assigned to the team that held the pick before draft night, so that value or loss of value may have been transferred onward to another team via trade. (Which is valid, because one would assume the return for that pick appreciated or depreciated in the trade market accordingly,).

Over the long run, the gains and losses of lottery teams tends to balance themselves out. As is the case in all statistics, shorter runs (fewer lottery trips) produce more extreme values, and this is evident when comparing the expected wins gained by each team since 2010 to the expected wins gained by each team since 1990.

Many NBA fans might have expected the Cleveland Cavaliers to have been at the top of the luck list here. While they have been the luckiest team since 2005, their more normal luck between the years of 1990 and 2005 serves to dilute their overall average and pull it back to the center, making them just the fifth-luckiest team since the draft lottery as we currently know it began, at least by this definition. People are quick to forget that the Cavaliers have not only been gainers in the last few years; the picks that became Tristan Thompson and Dion Waiters were both Cavalier lottery picks that fell in value thanks to the bounces of the ping pong balls.

The current New Orleans Pelicans (former Charlotte Hornets) are an organization that enjoyed repeated good fortune during the 1990s, nabbing the No. 1 and No. 2 pick from the fifth and eighth position in 1991 and 1992, respectively, and also moving way up the ranks to grab the No. 3 overall pick with the 13th lottery position in 1999 — the pick that eventually became Baron Davis.

On the other side of the coin, the Memphis/Vancouver Grizzlies have been to the draft lottery many times and repeatedly been denied good fortune by the lottery gods. Since moving to Memphis, the Grizzlies have had a position improve in the NBA draft lottery only once, in 2009, when they drafted Hasheem Thabeet with the No. 2 overall pick. Since the inception of the franchise in 1995, they have been to the draft lottery 13 times, and have only improved their position three times. A lot of this is due to the structure of the lottery however, as the Grizzlies had the first overall position four of those times, a position which either falls or stays the same. The Grizzlies failed to secure the number one overall pick all four times they had the leading chance to do so.

The matrix below may serve as an interesting reference. Like the first table, it shows the possibilities of the upcoming NBA draft lottery. Unlike the first, which represented the chances of each team landing each respective pick, this matrix shows the expected gain and or loss in value of each team moving up or down in this year’s lottery.

While draft lottery luck evens out for the most part over the course of 25 years, there are real, significant benefits for moving up in order, just as there are real, significant detriments for moving down. Time will tell which teams will play which role this year, a year when it might be especially important to sneak into the top two.