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.

HoopIdea on tanking

• Tanking: Far worse than you think

• OKC is not a role model

• Jeff Van Gundy's tanking fix

• Rig the draft

• The five-year lottery

• Get rid of the draft

• Better lotto logic

• The M.I.T. Sloan solution

• Thorpe: Teams can make players better.

• Bill Simmons vs. tanking

• Tanking is like pornography

• Tanking hurts fans

• Parity through paying rookies more

• Does tanking even work?

• Fix tanking: Grading on a curve

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:

• This system hurts a team that is in a playoff position before the deadline, then nosedives out of contention at the end of the season (Utah and Phoenix last year). Such a team would have fewer lottery chances than if it were bad for a while and then got better (Milwaukee last season). My answer to that is: any system is going to favor some situation and hurt another. But in this case: aren't we getting what we want? Teams that get better during the season are rewarded? That makes the product more exciting. That sells tickets. It is sad if a team's best player gets hurt and they bottom out at the end of the season, but those are the breaks (literally). Hurray for the team that got better.

• This system has the potential to misalign the team's incentive to play young, maturing talent over veterans. If you really want to go all-in for the most chances, at the deadline you should stop playing your young, developing players and switch over to playing all experienced veterans who can scrape out a few more win. My response to that is: if management thinks that a few extra ping-pong balls are worth not trying to develop their young players, they probably should move those young players at the break anyway since they aren't investing in them. And, as I mentioned above, we don't have to give a large benefit to winning games at the end.

There are also some hidden benefits:

• If teams are incentivized to win games down the stretch, the lottery teams will be more likely to try to build good combinations of young players and veterans that work. Imagine a lottery-bound team being a buyer at the deadline because they want to get the right chemistry to try to pull together some wins. If they think that this will help their team and they aren't giving up too much, doesn't that sound like fun? This will mean that, to a degree, quality teammates or good practice habit guys and the like will have their value increase, in both the trade market and in free agency. And, hopefully, we'd see fewer situations where the team amasses too many bad teammates or clueless players.

• The lottery TV show would be much better, with more suspense and fewer cat-out-of-the-bag moments. Looking at last year's standings, once the Clippers and Cavaliers were not among the lower picks, we knew that they were in the top three. In my system, every envelope would be a surprise.

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