Saturday, March 10, 2012

How to Fix Lottery Tanking

The NBA draft lottery is set up to help less talented teams gain more talent through new players. Over the years it's been tweaked and adjusted so that strong teams don't have much of a chance to win the lottery as it's seen as unfair and to minimize the power of intentionally losing games to gain the first overall pick. Before 1985, for a number of years the worst teams in each division would literally flip a coin for the rights for the first pick, meaning you were guaranteed a great pick if you were the worst in your division. The year before people accused Houston of tanking their games in order to draft Olajuwon, who later won them two titles. It was also such a deep draft with the Bulls taking Jordan third and Stockton and Barkley later that it was reasonable to assume there was a high enough incentive to lose games that teams would do it intentionally. And the year before that Houston also won the first overall pick and took 7' 4" center Ralph Sampson, whose career was ended short by injuries. There is no guarantee the first pick will be a great player, but you have a much better chance than picking 12th.

A Brief History

The modern lottery system was started in '85 when the league gave every non-playoff team an equal chance to win the top pick. This led to the Knicks landing Patrick Ewing (third worst record in the league), which created a conspiracy theory that commissioner Stern and company planted the top pick for the Knicks since it would put a big star in their biggest market. Obviously, the problem with giving teams who just missed the playoffs and cellar dwellers the same probability is one of unfairness. The worst teams need more help than the ones with near 0.500 records. Also, starting in 1987 the lottery determined the first three picks, rather than every lottery pick. After the third pick, your record decides your place in the draft. The consequence is that the team with the worst record in the league can do no worse than fourth in the lottery.

In 1990, the league decided to give the worst teams more odds to win the lottery. This was done in a way that the worse your record was, the better your odds. However, in 1993 the Orlando Magic won the rights to the first pick despite having the best record out of any lottery team and odds of winning at 1.5%. This was a year after they drafted Shaq first overall, mirroring the back to back Houston picks in the 80's. The league responded by lowering the odds for the best teams and increasing them for the worst. Since 1994, the worst team had only a 0.5% chance, while the worst 25% instead of 16.7% the year before. Each probability is shown in the table below. Interestingly, the team with the worst record has never had the first overall pick, but don't mistake that fact with any decreased probability of winning the first pick. Odds are odds.


Lottery seed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Odds (out of 1000)
250
199
156
119
88
63
43
28
17
11
8
7
6
5


The top prizes in the draft over the years since 1994 have included Tim Duncan, LeBron James, Kevin Durant, Carmelo Anthony, Dwight Howard, Jason Kidd, Elton Brand, Derrick Rose, and Blake Griffin. This year it's Anthony Davis, a long-armed defensive star shooting 66% from the field who can handle the ball surprisingly well for a player for his size and is averaging a staggering 4.8 blocks a game with only 1.9 fouls. With how much a single player can transform a team from the bottom of the league to a perennial contender there is a very high incentive to land these players, many of whom are seen as franchise players while still in high school or college. There is also no question that some teams have performed in tanking, intentionally skirting the team's chances for the rest of the season after it becomes apparent the playoffs can't be reached with some maneuvers like placing a healthy player on the injury list (I doubt Eric Gordon would have missed as many games on the Bulls) or trading away all their talent (the Bobcats have started looking for a starting small forward on Craigslist.) The problem is that the organization is throwing away the season for the fans too. You don't just hit "simulate the rest of the season" and hope for a better season next year; people have to watch your terrible games.

Looking back at the history of the draft and why it's developed into the current version, there are two contrasting problems -- tanking to get better draft odds or good teams unfairly winning the top pick. An ideal solution thus balances between the two mechanisms.

The Solution

Here's mine: the bottom seven teams all have the same odds of winning the lottery, and the top seven have odds that decrease with their win total. It would nearly eliminate tanking because if you're bad, there's no incentive to be any worse, and the teams that have lower odds are close enough to the playoffs that they would be much more unlikely to punt the season. The odds linearly decrease after the worse seven teams. If the odds were to plummet at a nonlinear rate with, for example, exponential decay, whose curve sharply drops off then levels, then there would be too much of a difference between the odds for the seventh worse team and the ninth worst, inducing tanking once again. The other flavor is a curve that only gradually declines until the very end, but that arguably gives too many odds to the "best" lottery teams.

Only a little math is needed to distribute the odds. With the current lottery system, the odds are out of 1000, so a team with a 25% chance of winning has 250 hypothetical ping pong balls. Know this, it's a simple algebra equation to create your own system. My proposal calls for even odds for seven teams and linearly decreasing for the rest. Call the highest odds "x" and base everything on that variable.

The straight line that connects the odds for the 14th place team and the seventh has eight different "steps" to reach the top, hence the team with the lowest chance has x/8 odds, the second lowest 2*x/8, etc. It's eight rather than seven because one of the seven teams with the highest odds is included in this imaginary line. Then set it up into a tidy equation and solve:

1000 = 7*x + x/8 + 2*x/8 + 3*x/8 + 4*x/8 + 5*x/8 + 6*x/8 + 7*x/8

1000 = 7*x + x(1/8 + 2/8 + 3/8 + 4/8 + 5/8 + 6/8 + 7/8)

1000 = 7*x + x/8(1 + 2 + 3 + 4 + 5 + 6 + 7) = 7*x + x/8(28)

1000 = 7*x + 28*x/8 = x(7 + 28/8)

x = 1000/(7 + 28/8) = 95.24

The next step is to distribute the odds to each place and round appropriately to ensure the total odds equal 1000. Seen in the table below, the odds are calculated for each lottery team based on how poor their win-loss record was. To convert to percentage, simply move a decimal point in between the numbers (95 to 9.5%, 83 to 8.3%, etc.) Even the worst team only has roughly a ten percent chance of snaring the top. The odds increase by 11 or 12 as you move up in the lottery seeding, but the great thing about that system is that increasing by 11 is more important when you're a 14th seed than an eighth or ninth. You're double you're odds at 14th, but only increasing them by around 14% from eighth to seventh, meaning there is higher motivation to tank to increase your odds the closer you are to the playoffs, which cancels out the effect.

Lottery seed
Odds out of 1000
1-7
95
8
83
9
72
10
60
11
48
12
36
13
24
14
12

With the draft lottery, it's not just the top pick that's decided by the odds; it's the top four. Higher odds means you also have a higher chance of getting the second, third, or fourth pick, and the rest of the draft is ordered by team record (i.e. lottery seed.) I would argue that it would be better to expand that to the first eighth or so picks decided by the odds to similarly discourage tanking. If the league can't figure out how to manage that, how can they run a multi-billion dollar sports business?

Final Thoughts


Rewarding the worst teams with substantially higher chances of landing the top pick creates a league complacent with bad management and unfairly sticks the best players on dreadful teams. Additionally, organizations have an incentive for throwing away entire seasons in the hope of landing a franchise-changing force of nature like a LeBron James or Dwight Howard. By skewing the odds, you can eliminate most of tanking, which punishes fans who pay for the games. A successful lottery system knows how to balance motivation to encourage better played games and the advantages of  better draft lottery chances.

As a last note, in comparing the proposed lottery odds with the current one, the new method spreads the odds more evenly throughout the worst teams. The cumulative odds mean that at lottery seed two it's the sum of the first and second lottery seed, at number three it's the sum of first, second, and third, etc. The five worst teams in the league have over an 80% chance at receiving the top pick, while in the propose system it's  only 47.5%. This is not a tragedy for small-market teams because even if you have little money to pay and attract players with good management you can at least be sixth or seventh from the bottom, which from the lottery standpoint is the same as last place.

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