The Martian
Matt Damon in "The Martian." Damon has never been directed by a woman on the big screen.

When the Academy abandoned its short-lived experiment with 10 Best Picture nominees in 2012, the arcane system it adopted promised a changing number of nominees each year—as few as five, as many as 10. The Academy even ran tests of the new voting procedures using previous years' ballots, and assured observers that in at least one (unnamed) year, the number of nominees would have been five. But that hasn't come to pass. Neither has a total of six, seven, or 10 nominees. Of the three rounds of Oscar nominations since the switch, there have been eight or nine films in the race for Best Picture each time. 

This strange Oscar season may change that.

The conventional wisdom has it that a wide-open field increases the chances of 10 films receiving a Best Picture nomination—voters spreading the love—but the math suggests otherwise. And yes, with preferential ballots and 6,291 eligible voters and "surplus reallocation" and "the 5% rule," predicting the Oscars now requires math. (If you want to know more, read our step-by-step breakdown of the complicated Best Picture nominating process.)

READ MORE: "Guillermo del Toro, John Krasinski, and Ang Lee to Announce Oscar Nominations Thursday" 

Before Thursday morning's Oscar nominations announcement, we explain why this year could see seven, six, or even five Best Picture nominees:

#1 votes are key. Though each Best Picture ballot may contain up to five titles, ranked in order of preference, it's the first-place votes that matter most. As The Wrap's Steve Pond calculates, if all eligible voters submit a ballot, a film needs 571 first-place votes (one-eleventh of the total, plus one) in the initial round of tabulation to earn a Best Picture nomination. This becomes more difficult with more films receiving #1 votes. The average number of first-place votes earned by the top nominee between 2001 and 2011, per the L.A. Times, was 20.5%.

This year, there are more films in contention overall—and fewer clear frontrunners—than usual. To give a generous estimate, 20 or 25 films might be in the race, which any experienced Oscar observer will tell you has been idiosyncratic throughout. As a result, each individual film faces a harder climb to cross the minimum threshold of 5% (315 votes, using Pond's example) required to land a Best Picture nomination.   

READ MORE: Oscar Predictions 2016       

In a wide-open field, lack of consensus may be more likely down the ballot, too. The more films that receive #1 votes, the more films will be below 5% after the first round of counting, much less surpass the magic "one-eleventh plus one" barrier. This is where "surplus reallocation"—and thus #2 votes—come into play. If #2 votes are as fragmented as we expect #1 votes to be, it becomes even harder for films with 3% or 4% support after the initial count to meet the 5% requirement. (Remember, a second-place ranking is worth less than a full vote, though the exact fraction varies.) Films need to garner both passionate support and consensus to land a Best Picture nomination, and the sheer breadth of contenders limits the potential of any one title to check both boxes. 

Here's an example. Let's say the current leaders in the Oscar race, "The Big Short" and "Spotlight"—which have the support of the actors, writers, and producers, if the guild nominations are any indication—are the only films to receive more than 10% of the #1 votes after the first count. In that case, they're in. (The only other film to be nominated for Best Ensemble by SAG, Best Original or Adapted Screenplay by the WGA, and end up in the PGA's top 10 is "Straight Outta Compton," which until recently was on few analysts' radars.)

For the sake of argument, let's say "The Martian" and "Mad Max: Fury Road" also receive between 5% and 10% of the #1 votes in the first round. If the rest of the field is as fragmented as we expect, it's possible that many films receive only 2-4% of the #1 votes, making a down-ballot consensus choice (say, "Bridge of Spies") the only additional film able to cross the 5% threshold after surplus reallocation. That would make five Best Picture nominees for the first time under the new rules. 

We predict between five and seven Best Picture nominees, for the first time under the current system. The unexpected inclusion of "Ex Machina" and "Sicario" on the PGA list of 10 nominees confirms that support is spread out among many films. And the fact is, with more titles competing for the same, finite number of votes, it will be more difficult for the eight or nine films of recent years to reach 5%. The exact number will depend on just how divided the voters are on their #1 and #2 choices, but this year's math—and its unpredictable twists and turns to date— point in a clear direction: a shorter, not longer, list of Oscar suspects.