Finding the perfect NFL schedule is a crusade that may be infinitely more difficult than unearthing the Holy Grail itself. There are exponentially more potential permutations to the league's 256-game regular season — the 2019 lineup will be revealed tonight — than there are atoms in the universe. Literally. Consequently, the NFL, which transitioned about 15 years ago from a manual approach to schedule design to a heavily automated one, has enlisted outside help while attempting to streamline and optimize the process. "This is, by far, the hardest mathematical thing I've ever done," Dr. Mark Karwan, a professor of operations research at the University at Buffalo, told USA TODAY Sports. Karwan explains the NFL's puzzle is much harder to solve than, say, a field like airline management — which includes vast variables including gate changes, crew scheduling and aircraft maintenance. Apples to Granny Smith apples, Karwan says the NFL schedule is drastically more complex than those of the NBA and Major League Baseball, even though those leagues play far more games. Why? The NFL has more constraints — perhaps more than 10,000 — including logistical considerations like stadium availability and broadcasting rules as well as individual team requests — up to 200 per year league-wide, not all of them possible to fulfill. The league's network partners often have mutually exclusive objectives, all of them seeking the most alluring matchups — especially in prime time slots. Factor in hardwired parameters installed by the league while attempting to maintain competitive balance and fairness, and one only begins to grasp the scope of the conundrum. Just one team's schedule — minus any influencing factors — can be constructed roughly 60 trillion ways when merely considering the sequence of 16 opponents. "If we cured cancer," quipped Karwan, "we wouldn't get as much press as coming up with a better NFL schedule." Maybe you're thinking this task can't possibly be that onerous. After all, since realignment in 2002, the NFL's scheduling formula has elegantly forecast 14 of each team's opponents ad infinitum (the final two matchups every year determined by each club's corresponding divisional finish to two other divisions within its conference). Yes, this is a task one person performed in the past. In the 1940s, then-Commissioner Bert Bell used a matrix on his dining room table and his children's dominoes (affixed with team labels) to create dozens of prospective schedules, an undertaking that required weeks of tireless effort. But that occurred when a 10-team league employed a 12-game schedule, largely unrestrained by competitive rules and logistical issues that exist today. Bell's successors used some variation of his methods, often sequentially slotting and tinkering until a solution came into existence. But NFL vice president of broadcasting Michael North told USA TODAY Sports that it was basically "a miracle" the schedule ever got done by hand, and previous versions were certainly never efficient solutions — and weren't forced to account for ever-growing considerations, including an increasing number of stadium blackout dates. League venues are increasingly booked (up to 40% conflicting with potential game dates) for concerts that occupy days of usage, college playoff games, even occasional marquee NHL events, all things that provide revenue streams to individual owners, which the NFL doesn't want to impede. So, at North's recommendation, the league has funded a three-year project at Buffalo led by Karwan, Zach Steever (it's actually his doctoral project) and assistant professor Chase Murray. Their vision sprouted from a paper the university presented at the 2015 MIT Sloan Sports Analytics Conference, the objective to alleviate competitive imbalance using a mathematical approach following a year when the Bills played an inordinate number of opponents coming off bye weeks. Karwan and Steever got North's attention when their methodology managed a 20% optimization to the 2017 schedule after it was released. That quantification came by reducing "penalty points" invariably associated with any schedule. For example, no team is allowed begin the year with three consecutive road games. However penalty points can be assessed to a schedule requiring a team to open on the road the first two weeks. Clubs cannot play more than two road games against a team coming off a bye week. They cannot be forced to take their bye week in the earliest window in successive seasons. They can, for instance, play a road game the week after a Monday night appearance, but that will incur penalty points. There's a laundry list of other examples, many arcane, not to mention the reality that CBS probably doesn't want to lose a bunch of Patriots games any more than Fox likely wants to sacrifice Cowboys dates to prime-time windows not on their air. All schedules contain penalties, but the Buffalo team is trying to build a mousetrap that minimizes them. In layman's terms, Karwan and Co. are seeking avenues allowing the league to set a core of games numbering 40 to 50 — the schedule initiates with approximately a dozen "fixed" games (the Week 1 opener, Thanksgiving and international dates among the examples) — while allowing the remainder to slot into some logical order while determining where flexibility lies and where it doesn't. North would be thrilled if the UB project, which is housed in a secure lab while plugged into the league's hardware, produces results that can be applied in 2020 and 2021. At present, he rents hundreds of servers for cloud computing that basically run 24 hours a day for 10 weeks until the NFL finds a solution. "They're looking into an infinite space," says North, "I'm still not sure we're seeing more than one-tenth of 1 percent of the total solution space." League vice president and scheduling czar Howard Katz analyzes potential schedules for weeks, banning specific outcomes so they don't appear in subsequent editions, while adding what amounts to artistry to the proceedings. Per North, Katz is looking for "that magical, mythical one schedule that is going to be as good as possible for everybody — and there's no such thing, nobody's ever completely happy." Katz may scan 50,000 versions while closely dissecting perhaps 500 schedules in the midst of his quixotic quest. "Howard gets to throw every one of them away except for one," says North, a luxury Bell never had. Even with Katz's keen eye and all that computing power, the software just can't solve the schedule sometimes if a certain variable is introduced. There simply may not be a schedule that exists that allows the league, for instance, to stage this year's NFC Championship Game rematch between the Saints and Rams in Week 11 at the Los Angeles Coliseum on NBC's flagship "Sunday Night Football" telecast. And there may actually be no "perfect" schedule, one that contains zero penalty points, even if the league searched for it indefinitely — which is why the annual release date requires every bit of allotted time during the 10 weeks following the Super Bowl. "We can't say with 100% certainty," said Steever, "but we would be willing to wager that no schedule exists with a penalty score of zero." But he'll continue chasing it while ultimately hoping Buffalo's Center for Computational Research, which includes a supercomputer, becomes a test bed for North during the nine months of the year he's not renting server space all over the world. If North wants to ponder a schedule, for example, that had all 32 teams playing an international game one year, the UB team wants to provide that option. "If we can get a bunch of really smart people thinking about this, we can only be better," said North. "The more math and science we can marry with his art, the better we're going to be." *** Follow Nate Davis on Twitter @ByNateDavis If you love talking football, we have the perfect spot for you. Join our new Facebook Group, The Ruling Off the Field , to engage in friendly debate and conversation with fellow football fans and our NFL insiders.