# the tombstone proposal for the NBA draft

fivethirtyeight recently did an interesting crowd-sourced exercise on looking for ways to fix the NBA draft and address the issue of tanking,
http://fivethirtyeight.com/datalab/the-6493-best-ideas-to-prevent-tanking-in-the-nba/

The purpose of this post is to look at the proposal to award draft position by wins-after-elimination, or the so-called tombstone proposal. Specifically, the tombstone proposal says , weight the draft picks according to wins achieved after being eliminated from the playoffs. This was a popular choice, and, evidently, was discussed at the Sloan conference a few years ago,
http://www.sloansportsconference.com/?p=5496

My gut reaction is that, it’s a great idea! It achieves the fundamental goal of taking away the incentives for teams to lose late season games. It also ties draft order directly to performance, which is aesthetically appealing.

What about the other fundamental goal of the draft lottery; to preferentially give high picks to poor performing teams? Logically, the tombstone proposal addresses this since the teams that are eliminated first – although they are generally worse teams and have less chance to win any given game – have more chances to bank wins towards their draft position.

Quantitatively, it’s less clear. My first inclination was to go to basketball-reference and start munging around with data; but then I realized that the basic question here, i.e. what kind of team benefits most from this proposal, is fairly easy to model.

Specifically, say a team, has a true talent $t$. Also, say that teams that loses $L$ games are bubble teams, so practically speaking you are eliminated when you lose your $L$-th game.

Losing your $L$-th game will occur (on average) in game $N_L = L/(1-t)$. The number of games you play after that, $N_W$, is $N_W = N - N_L$, where $N$ is the total number of games in the season. The number of wins that go toward your draft position, $N_p$, are,

$N_p = t \cdot N_W = t \cdot (N - \frac{L}{1-t})$.

To find the best possible true talent to have under this system, take the derivative with respect to $t$, and set the result equal to 0, and you get,

$\frac{d}{dt} N_p = N - \frac{L}{(1-t)^2} = 0$,

or

$t_x = 1 -\sqrt{\frac{L}{N}}$

So far I haven’t specified $L$, or $N$, but for basketball, basically a $0.500$ team is a bubble team so,

$t_x = 1 - \sqrt{\frac{1}{2}} = 0.293$.

Over an 82 game season, this means 24 wins. This seems to me a really reasonable place to set the line!

Overall this proposal still has the potential downside of letting teams tank early on and pick up wins later in the season; but orchestrating a 24 win team is harder than orchestrating a 10 win team, and with the added randomness of the lottery itself, this seems like a very good inflection point to set.

For the record, I made a submission, which is #162 in the spreadsheet (the surrogate method),

that idea is essentially the same one I floated on Tom Tango’s blog about a year ago when this topic came up,

In summary, the tombstone method favors teams that have poor performance at the beginning of a season, and that have true talent around 0.300. The surrogate method favors teams that have poor performance a year prior, and that have good projection systems. My description of the surrogate method is given below.

— the surrogate method —

A team’s draft pick is determined, not according to their record, but according to the record of a surrogate team. The surrogate team is picked at the beginning of the season, and the order of choice of surrogate is determined by record. For example, last season the Milwaukee Bucks had the worst record, so they get first chance to pick a surrogate. Let’s say they pick Philly. Then for the next draft, they get the pick determined by Philly’s record (which I’m assuming is still some kind of weighted lottery). Philly had the second worst record last season so they get second choice of surrogate, and on down the line.

The main pro for this plan is that it takes away the incentive to lose any particular game. A loss never directly benefits you, and always directly benefits some other team (the team that picked you as a surrogate). It rewards teams that have good projection systems and therefore do well at picking a surrogate. It sets up extra drama, both in the picking of surrogates, and in the cases when the team that picked you comes to town.

Potential cons are that it could in principle set up some convoluted situation where a team is incentivized to lose (to their rivals surrogate) in order to hurt their rivals draft odds. It could also lead to a strong team getting a lottery pick if the surrogate performs drastically worse than their expectations, and some people may object to this. For example whichever strong team had Oklahoma City as a surrogate coming into this season would get a lottery pick in the upcoming draft. On the other hand, Oklahoma City, which is a strong team that was mainly derailed by injuries, will end up getting it.

## 3 thoughts on “the tombstone proposal for the NBA draft”

1. Joe says:

Seems to me one major downside for the surrogate method would be teams at the end of an era. Imagine the Spurs win the title next year (2016), and Duncan, Pop and Manu decide to go out on top and retire. And Kawhi leaves for somewhere in free agency. Under the current method, the Spurs would be horrible the following year, and pick in the top 10. Under the surrogate method, they would pick last, and get a pick in the high 20s. They couldn’t even be smart about projecting, because they would just literally get the last team left that no one else picked.

1. Yes, good point. Cleveland, the year LeBron left for Miami, is a good example of that also.

2. orion says:

one fix could be that if non-lottery teams can only have non-lottery surrogates and vice versa. For example, in the Lebron scenario (since it already happened). Lebron leaves Cleveland picks one of the last ten surrogate teams left because that’s what their position dictates. Assuming the cavs surrogate pick is in the playoffs the next year the cavs get the worst lottery slot. Meanwhile, a team that was a lottery team and picked a surrogate that did poorly wouldn’t get a lottery pick, they would get the best playoff pick.

Definite some down sides to this method too but I think it’s one way to at least even out the playing field for those teams mentioned.