A Little Oscar Math

One of the stories going around this week was that several black celebrities — including Spike Lee, Will Smith, and Jada Pinkett Smith — had announced they would not be attending the Academy Awards ceremony this year in protest of the lack of black acting nominees. Or as director Spike Lee put it in his oddly-capitalized Instagram rant:

How Is It Possible For The 2nd Consecutive Year All 20 Contenders Under The Actor Category Are White?

Let’s do the math.

When looking at racial statistics in the United States, it’s important to remember that black people really are a minority. I’ve seen complaints of the form “It’s outrageous that only 10% of <whatever> are black!”, but that’s actually not too bad. According to recent census estimates, approximately 12.6% of Americans are black, so 10% isn’t too far off. Depending what we’re talking about, the 2.6% difference could easily be explained by benign cultural and environmental differences.

Given that 12.6% of Americans are black, and assuming for purposes of the calculation that academy award voters are not racially biased in any way, what are the chances that not a single acting nominee is black? Could it just be random chance?

If there was only one nominee, then there would be a 12.6% chance of picking a black actor, which is the same as saying that there would be a 100% – 12.6% = 87.4% chance of picking a non-black actor. Expand the selection to two nominees, and there’s an 87.4% chance that the first one will be non-black, and then another 87.4% chance that the second one will also be non-black. So the chance of both of them being non-black is 87.4% * 87.4% = 76.4%. More generally, every time we add another person to the sample, that’s another 87.4% chance to keep the non-black streak going. So if we choose a group of N people at random, the chance of all of them being non-black is given by

From this, we can get the odds of all five nominees for Best Actor being non-black,

So we’d expect the Best Actor category to shut out black actors about half the time, even if the nomination process is completely colorblind. Add in Best Actress — raising the size of the sample to 10 nominees — and that works out to about 1-in-4 chance of a black shut-out:

Two years in a row makes it 20 people, and the odds get worse:

In other words, pure random chance will deliver an a slate of Best Actor and Best Actress nominees with no black nominees about 7% of the time.

I was just about to conclude that it’s not unreasonable that completely colorblind Academy could give black actors a two-year shutout entirely by chance, but then I noticed that Spike Lee says “For The 2nd Consecutive Year All 20 Contenders Under The Actor Category Are White.” At first I thought Lee made a mistake — I counted 20 Best Actor and Best Actress nominees over both years, i.e. two consecutive years of 10 nominees, not 20 — but then I realized Lee is also including the Best Supporting Actor and Best Supporting Actress categories, which also haven’t had any black people for two years. That’s a 40-person-long streak of non-black nominees. The odds of that are pretty low:

That’s less than a 1-in-200 chance that this could have happened entirely by random selection. That’s not impossible, but it’s pretty unlikely. By comparison, in the social sciences, any result that has a less than 1-in-20 chance of arising under random chance is considered significant enough to publish. The lack of black acting nominees is very unlikely to be random chance. Something is going on here.

These simple statistics alone, however, cannot tell us what that something is. All we’re doing is comparing the racial composition of the population of acting nominees to the racial composition of the entire population of the United States. There’s a lot of room between those two populations to explain the differences, which could be caused by a number of factors other than racist voters in the Academy. For example, just making stuff up off the top of my head,

• Perhaps cultural and environmental conditions make black Americans 10% less likely to think of acting as a legitimate career choice, and
• Perhaps racial bias in acting schools makes it 10% less likely that blacks will get in, and
• Perhaps racial bias in acting schools cause blacks to receive 10% less effective educations in acting, and
• Perhaps cultural and environmental conditions make black Americans 10% less able to devote time and energy to their acting careers (e.g. because of a greater need for a paying day job), and
• Perhaps racially biased casting directors are 10% less likely to cast black actors in the bit parts that will give them experience and exposure, and
• Perhaps racially biased screen writers are 10% less likely to write major parts for black characters, and
• Perhaps racially biased studio heads devote 10% less promotional effort to movies with black leads (possibly in response to racially biased audiences spending less on those movies), and finally
• Perhaps racially biased Acedemy voters are 10% less likely to vote for black actors and actresses.

Combine all of those elements, and the calculation looks something like this:

So if there’s a 10% drag on blacks at eight different places along the way, then the odds of a two-year shutout for the acting categories is about 1 in 9. That means this explanation is statistically plausible.

I should emphasize, however, that I totally made up those explanations and the numbers to go with them, merely as an illustration of the kinds of things that might influence the acting nominations. These are the kinds of things we might want to look for if we are serious about figuring out what’s happening. It could turn out that all of the bias is indeed at the Academy voting stage, in which case a boycott might be a sensible response. Or it could just be that there is just an accumulated drag on black actors which builds up enough over their careers to keep them out of the nominations. I have no idea.

But I can do the math. And at 1-in-200 odds…something is going on.