- the value of penalty goals in rugby league*;
- when Melbourne would overtake Sydney as Australia's largest city;
- how Melbourne Cup betting works; and
- the Commonwealth Games medal tally, per capita
A look at the NBA Draft Lottery...
*and the NRL has totally caught up to this thinking in the 2018 season, I'm taking all the credit for it.
I've never written about basketball before - I did have an article half-done about the 2016 Olympic tournament, but kiboshed it when the Aussies lost their semi-final. But ever since I got Fetch TV a couple of years ago, I've watched a lot of basketball on ESPN. I think I even know what I'm talking about! Yet it's only when it's more about maths rather than the game that I felt comfortable writing something.
What Is A Draft Lottery?
All major American sports, and the AFL domestically, have a draft. The aim is to disperse new players entering the league to different teams. A draft typically favours giving the first pick to the worst-performed team, second pick to the second-worst team, and so on, as a talent equalisation measure.
The draft is important in all sports, but most important in basketball. In basketball, a star player can make a much bigger difference than in almost any other team sport.
This is where the 'lottery' element of the draft comes in. To counter accusations that the NBA draft incentivises bad teams to play even worse ('tanking') to guarantee the top draft pick, a lottery element was introduced that meant while the worst team still has the best chance, they aren't guaranteed the top spot.
History
The NBA draft lottery has had a few iterations in its attempts to find the right balance between talent equalisation and tanking avoidance.
Initially it was quite a crude process - one envelope for each of seven worst-performed teams in a barrel. This was then reduced to the top three teams.
From 1990 to 1993, things got a bit more sophisticated. The top three draft selections would be determined by a lottery opened to all 11 teams that failed to make the playoffs, but the lottery would be weighted to favour the worst of these teams.
Table 1 shows the probabilities of getting the first pick on the left. It is adjusted on the right columns to show how it would work in the current NBA, which has three more teams.
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| Table 1. Past NBA Draft Lottery |
The Magic won the first pick when they were the second seed, having a 10 in 66 chance. It was Shaq, and with their star rookie, they improved to nearly make the playoffs. The system works.
But then the next season, they won again, as #11 seed (1 in 66 chance).
As a result, odds were skewed more to bottom ranked teams, in the NBA draft lottery model still used today. Table 2 provides a comparison:
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| Table 2. NBA Draft Lottery - Past vs Current |
The Current NBA Draft Lottery
In terms of avoiding lower seeds, the new model worked. An 1 in 66 chance became 5 in 1000 (1 in 200), and as a result a bottom seed has never received the highest pick.
Having said that, from 1994 to 2014, only two top seeds ever won the lottery. This is half as many as have won top pick from 5th seed, and the same number as from 9th seed. So the results at the top end are still quite random.
Despite this, and the fact top pick is not a guarantee of success, tanking became a real concern. The final straw was perhaps the Philadelphia 76ers undertaking "The Process", where they constantly traded players for future draft picks, deliberately accepting poor results now with a view to rebuilding in the future.
Now for every Embiid and Simmons, there is a Okafor and (maybe) Fultz. But The Process has worked well enough that from next season it will be the top four picks chosen by lottery, and the current probabilities will be flattened as shown on Table 3:
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| Table 3. NBA Draft Lottery - Current vs Future |
Old is New
To show the cyclical nature of this, Table 4 shows a comparison between the original weighted NBA draft lottery and the future one:
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| Table 4. NBA Draft Lottery - Past vs Future |
If another team pulls off an Orlando Magic, say back-to-back draft picks where the second years comes as seed lower than 10th, it will be interesting what the next NBA move is.
Alternative Draft Models
There are a lot of NBA draft ideas out there: at least 6,493.
Some of these are mathematically sound but ridiculously complicated, like assigning the probability of the top draft pick using the formula p = (L-41)sq, or the wheel, or the "tombstone date", or NBA futures.
Others are just ridiculous, like "then, [NBA head honcho] Adam Silver will ride a bear into the pool..."
There are two simpler options.
Firstly, have the lottery apply to more picks than just the first three or four. This wouldn't change the probability of the worst team getting the first pick, but it would be change the probability for other picks. For example, in the upcoming NBA Draft Lottery, the worst team cannot pick lower than 4th, which is a 35.7% chance of happening. If you apply the lottery to all 14 non-playoff selections, that 35.7% is distributed across picks 4-14 instead. There is slightly more risk in tanking.
Secondly, a triangular weighting, hereafter referred to as the Rob's Blog model. This is similar to the current and future NBA Draft Lottery formats, in that probabilities are assigned based on past season performance, but it's much easier to understand the probability distribution.
The 14th seed (best team to not make the playoffs) gets one ball
13th seed gets three balls (1+2)
12th seeds gets six balls (1+2+3)
The top seed (worst record) gets 105 balls (1+2+ ... +14)
Table 5 compares the probabilities here against the current and future NBA Draft Lottery models:
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| Table 5. NBA Draft Lottery - Current vs Future vs Rob's Blog |
Note that the Rob's Blog model provides lower odds to the current model, but better odds compared to the future model, for almost all lottery teams. It seems like a sensible middle ground.
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