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Thursday, March 29, 2012
Fix Tanking: A logical lottery

By Sandy Weil

NBA lottery odds
Chart by Sandy Weil
Current lottery odds give a huge benefit to being the worst team in the NBA.

It is universally acknowledged that there is something odd about teams being rewarded for playing badly, as we have discussed when HoopIdea first addressed tanking. But it's not a simple problem to solve. In that spirit, we present a number of different proposals. This one comes from Sandy Weil, Director of Analytics at Sportsmetricians Consulting and the researcher behind groundbreaking hot hand research.

The NBA lottery generates some excitement. But with a little tweaking, it could be both more compelling and provide better incentives to teams to win as much as possible during the regular season.

The first thing that stands out is that too much is weight given to the being the first worst as compared to the second worst. Minnesota has two more losses than Cleveland. Should that really account for 25 percent more ping-pong balls? What about Toronto's 60 losses versus Sacramento's 58? Why should Toronto should have a three times better chance of getting the number one pick? That just doesn't feel right.

Here’s my three-part proposal to fix all this.

Part One
The number of chances should not be allocated on an ordinal basis (worst=25 percent, second-to-worst=19.9 percent, etc.) but on a semi-continuous basis: the number of chances you get should be related more directly to the number of losses. It is OK to give more weight to more losses (so, not linear) but this distribution looks too skewed to me.

But valuing losses that way doesn't take away the incentive to lose the last game of the year, does it?

Hold on.

Part Two
What if you got more ping-pong balls for games you lost before the trading deadline but then the equation flips and, after the trading deadline, you start getting more ping-pong balls for each win?

Here’s how it would work: The league would take the standings as of the trading deadline, and allocate a set of ping-pong balls. Then, at the end of the season, they look at the incremental standings after the deadline, and allocate another set of ping-pong balls, based on the a similar equation, just entering wins instead of losses. The size of the benefit at the end of the season for wins doesn't have to be particularly large. It can be a much smaller pile of additional ping-pong balls given out in that last third. We just need to incentivize winning.

The implementation of this equation (functional form, coefficients) could go in a number of ways, but the general idea is that, if management wants to get the best chance to get Anthony Davis, at some point, they would need to show improvement during the season.

We’d probably want there to be little benefit in the before-trade-deadline period for being historically awful as opposed to just plain bad. The equation (sigmoid function, I think) would treat the bad teams pretty evenly (say in the 20-30 percent winning percentage range) and would also treat evenly teams that are decent (40 percent to 50 percent winning percentage range). That is, if you are on pace to win only 16 games instead of on pace to win 26, you shouldn't get much additional benefit for that.

Notice that even after we have fixed the incentives around the lottery, we still have some residual incentive to lose games. It comes from the fact that the current lottery system allocates only the top three picks and then the picks revert to the order of reversed winning percentage. So using last year as an example, Washington, with one more win than Toronto, will always pick behind Toronto, unless Washington gets lucky and wins one of the top three picks. By losing that last game, Toronto's expected pick number moves up about a half a pick (from 3.97 to 3.40).

How can we fix that?

Part Three
Now that we have allotted ping-pong balls to properly align incentives during the regular season, why would we stop the lottery after three picks? Let's just keep picking the entire bottom of the draft using the lottery. If we draw the same team's pick again, we just skip it and keep picking until we have our picks.

This system has a marginal incentive for teams to win games at the end of the season while still likely sending the potential franchise players to the worse teams.

The potential problems here that I can see are:
There are also some hidden benefits:
You can give us your ideas and talk with us and other fans in the following places: