Now that we've reached the point where the Suns would have to win games by accident to finish ahead of the Nets, I decided to look into what the Celtics should expect given that fourth seed in the Draft Lottery. Here is Q&A-style look at some of what I've learned.
What draft pick should the Celtics expect to get?
The expected value of Boston's draft position is approximately 3.97. This means that if this year's Draft Lottery hypothetically were repeated many, many times, the average position of the Celtics' picks would be 3.97 – that is, Boston would choose extremely close to fourth on average.
Does this mean that planning on that fourth pick makes sense when talking about the players we'd like to pursue?
Sort of... but not really. While in a statistical sense we expect the Celtics to pick fourth, it turns out that the Celtics actually getting the fourth pick is a pretty unlikely event, as Boston has less than a 10% chance (~9.9%) of choosing fourth. (If this seems counterintuitive, think about rolling two dice. If you rolled many, many times and averaged the results, you'd get something very close to seven. That doesn't mean, however, that rolling a seven happens most of the time, or even particularly often.)
So, the Celtics aren't really likely to get the fourth pick. What is likely, then?
I hate to say it, but coming in at approximately 35.1%, the C's are more than three-and-a-half times as likely to get the fifth pick as they are to get the fourth. That's more than a one-in-three chance, and by far the most likely single outcome for the Celtics. In fact, if you took that hypothetical where you repeated the Draft Lottery a bunch of times and lined the results up from best to worst, the result(s) in the middle – the median – would be the fifth pick.
Ugh. Does that mean we really should plan on the fifth pick?
I have some good news here: Despite the relatively high probability of getting the fifth pick, the Celtics remain even more likely to land in the top three! It's close, but Boston has about a 37.8% chance of a top-three pick, compared to that 35.1% chance of the fifth pick. In fact, each of the first three draft positions taken individually is a more likely outcome for the Celtics than choosing fourth! (For those of you focused on Simmons and Ingram, it's pretty close to a one-in-four chance of making the top two at 24.5%.)
Alright. Top three or fifth, with a slight chance of fourth. That doesn't sound so bad. What aren't you telling me?
Unfortunately, sixth and seventh are possibilities for the Celtics as well. At about 1.2%, seventh is pretty unlikely barring the jinx I'm laying down right now. Sixth, though, can't be dismissed out of hand; at 16.0%, it's more likely for the Celtics than any of the top four positions taken individually. Yuck.
That's a lot of possible ways to look at the draft, and some of them seem to almost contradict one another. How should I be thinking about this?
Personally, I enjoy that the different ways to think about expectation run afoul of one another here – it just makes the process much more interesting to me when optimism, pessimism, and pragmatism can all be justified. I'd say simply thinking of the pick in terms of its central tendency at the fourth or fifth position isn't wrong exactly, but if you're putting a lot of time into thinking about potential players to take, you should also take a more nuanced look at where the Celtics' pick might land.
Submitted April 06, 2016 at 12:15PM by SpanishInfluenza