And the winner goes to ...

Short-term update: liked on social media by William (bill) Watts, the markets editor for Wall Street Journal's MarketWatch.  And most viewed and enjoyed for a week on KDNuggets.

It’s Oscars weekend in Hollywood.  In this 88^th and queerly controversial Academy Awards, there are over 120 nominations, across 24 motion picture categories.  To be straight, box office revenues for the 2016 Best Picture nominees were not the highest-ever, and equally interesting among this so-so ticket sales performance is that the movie with the most nominations this weekend (The Revenant) is not even the highest grossing among these nominees.  While there are many dazzling nominees and delightful films competing this weekend, there is much attention given to the Best Actor and Best Actress awards.  Eddie Redmayne is nominated 2-years straight, including a win in 2015.  And both Leonardo DiCaprio, and Cate Blanchett have each been nominated an admiral >=3 times before (Blanchett winning twice!)  What do probability models on both the frequency of nominations, and conditional probabilities based on past performance, and gender "equality", have to say (if anything) about all of their chances of winning a coveted statuette this weekend?  Read on (especially if your name is Steve Harvey), and we’ll happily tell you.

When actors and actresses compete in a cavalcade known as the Academy Awards, often the analysis will turn to any prior nominations and an opinion about how the Academy’s judges may try to “engineer” the winners to spread out the winners and cultural film themes over time, and also across various demographic segments and individuals.  Bear in mind that while pressure is on the Academy for diversity, it is respectable to note that they are not narrowly reflective of the directors and casting agents.  In passing, these accolades eventually in 1939 were officially marketed as Oscar by the Academy of Motion Picture Arts and Sciences, as opposed to the more elite and foreign-press society's Golden Globes that started more than a decade afterwards in 1944 and now given out in the ritzy city of Beverly Hills.  Now is this all just silly chittychat, or is there some rigorous calculations behind those talking points?  Some had concluded -for example- that Russell Crowe was edged out of the 2001 award, for his portrayal of the late Nobel-laureate John Forbes Nash, Jr., since Crowe had won the year prior for playing the gladiator, Maximus Decimus Meridius.  And yet others have concluded that DiCaprio is edged closer to winning an award this year, since it is his 4^th nomination (the first being in 2004) and so “he is due” to win this first Oscars trophy.  It turns out that there is a great deal of randomness relative to the signal, in both this dynamic and the others we discuss here.

Luckily for us, there are very many repeat nominations over the Academy’s 88-year history.  We’ve assembled the most important nominees over this history for this analysis (anyone with 4 or more nominations including for 2016) and analyzed the consecutive nominations in the Best Actor or Best Actress categories.  The 59 results were statistically equivalent between these two categories, so the consolidated results are shown here:

	Following year’s loss	Following year’s win	Win %
Of 48 prior year's loss	33	15	31%
Of 11 prior year's win	8	3	27%
Total	41	18	31%

We see that in the case of Russell Crowe for example, his winning probability for his role in “A Beautiful Mind” was 27%, however that is statistically similar to the probability of winning, even if he had lost for his prior year’s nomination for his role in “The Gladiator”.  Of further interest is that this probability of winning for the lead actor or actress award, if any one of these (coincidentally also) 59 top nominees through history, is 20%.  Obviously random luck for any nominee is also usually 1 in 5 for the Academy Awards, or 20%.  So the probability Russell Crowe winning in 2002, for example, would according to this analysis actually be enhanced -more than usual- due to the fact that he was nominated the previous year.

This year, the back-to-back phenomenon may apply for only Eddie Redmayne.  Nominated for his role in “The Danish Girl”, while winning last year for his role in “The Theory of Everything”.  Though as we’ll appreciate through this analysis (similar to other popular articles on data mining risks here, and here), the probabilities are only useful when appreciated in a vague sense. 

For the case of DiCaprio and Blachett, it is interesting to see what is the probability of these 59 leading nominees in winning on their 4^th and 5^th nominations, respectively.  The chart shows that in the general case of someone being nominated 4 or 5 times, on those nominations they have a high 20’s% probability of winning.

  

Nearly as high it turns out, as the likelihood we earlier gave to Redmayne!  Note that once the number of nominations exceeds 7 or so, the number of actors or actresses who have ever received so many nominations dwindles to a statistically small sample size.  And the resulting probability becomes too unstable to be useful.

For all of the arguments brought up about the unfairness of women to get great acting opportunities as they age, it is breathtaking to observe how well the finest actresses fare in sustained Oscar wins, even as they age and with nominations for them that have happened a generation more recently.  33 women have been nominated 4 or more times in the Academy's history and winning 10 of those times so far (30% win rate).  With only 26 men achieving the same nomination milestone and winning only 8 of those times so far (31% win rate).

The most triumphant actresses (Meryl Streep, and Katharine Hepburn) have been nominated a total of 27 times, with 6 wins among them (22% win rate equalling a toss of a 5-sided die such as a triangular prism).  These women received their first nominations earlier in life (typically in the late 20s) and their last nominations late in life (typically in their late 60s).  The most triumphant actors on the other hand (Laurence Olivier, and Spencer Tracy) have fared worse by being nominated a total of 18 times, with only 3 wins among them (dropping to a lower, 17% win rate).  These men received their first nominations later in life (typically in their mid-30s) and their last nominations just as similarly to when women do (typically in their late 60s).  Given the much larger number of women versus men with repeat nominations, with again no core performance difference on a per-nomination basis between the two segments, the actor and actress categories were merged for this analysis.

But also here, context is important.  Just knowing that DiCaprio and Blanchett have been nominated so many times is interesting but what’s more critical is knowing the probability of winning, given a certain number of prior nominations and wins.   See the table below.

	w/ 0 prior wins	w/ 1 prior win	w/ >=2 prior wins	Total
2016 winning probability	26%	17%	11%	21%
Sample size	129	106	27	262

The pattern is fairly strong, with our manually collected history of 262 total nominations.  We see that DiCaprio having been nominated but winless has a 26% probability of winning this year.  A little less again than what we saw earlier, given his 3 previous winless nominations (though here Redmayne with 1 prior win would appear even weaker). Blanchett, with a stronger performance of having won 2 Academy Awards already has simply 11% chance of winning now.  This is less than what we saw before (and less than the 1 in 5 random chance among 5 candidates), but merely reflects the historical odds of someone with already so many winning nominations.  Incidentally no one has ever won more than 4 times (hence someone such as the late Katharine Hepburn and Daniel Day-Lewis would have an uphill battle winning additional nominations).

The bottom line is statistical models, even based on a decently large sample size, can sometimes be mined to provide interesting results.  Here we see probabilities of winning the Oscars, given performance considerations for these nominees, and the probabilities are fairly similar to one another.  In a range of between 10% and 30%, reflecting some random error in the estimate.  That's all.  Certainly not >>50% or something you would want to confidently wager on.  The only nominee discussed above that seems interesting, from a probability perspective for this weekend's Academy Awards, is Blanchett.  With so many winning nominations she is among a small sample size that has tended to likely underperform a random 1 in 5 chance.