Hello Reader!

 

Right now, across the United States, Canada and Mexico, millions of people are behaving in ways they would never admit to at the office.

Norwegian fans are rowing on an escalator like it's an Olympic final. Dutch fans are doing 'naar links naar rechts' in the street, a whole crowd swaying left, then right, as one. Egyptian fans are dancing through the streets of Vancouver after Egypt's first ever World Cup win, Mo Salah and the whole squad right there with them.

This is the World Cup. The largest, loudest, most joyfully chaotic party on Earth.

 

I Smuggled a Dutch Dance Across the Border

The Netherlands is practically next door to where I live. So back in 2017, my own football team took a teambuilding trip to the Dutch North Sea coast. We came back with sand in our boots and a new obsession: 'naar links naar rechts', that left-right dance you just saw the Dutch fans doing up top.

We imported it to our German Sunday league pitch immediately. We loved it. We did it everywhere, constantly, with the devotion of true converts.

Our coaches did not love it. For reasons that remain a mystery to me to this day, our enthusiasm annoyed them.

So they did what coaches do. They turned our joy into punishment.

Pre-season football is already brutal. Endless running, fitness drills, the kind of endurance work that makes you question your life choices. One day, after a long run through the woods, legs already gone, the coaches lined us up and made us jump along to the entire Snollebollekes song. Not the chorus. The whole thing. If we loved it that much, we could have all of it.

I have never looked at that dance the same way since.

But here's what stuck with me: all that fan joy sits on top of something far less spontaneous than it feels. Somebody had to decide who plays whom, in which city, on which day. That's a sports scheduling problem. And we happen to have a gloriously detailed example of one: not from soccer, but from American football, where the puzzle is arguably even bigger than a World Cup's, and where Gurobi published how it actually gets solved.

 

The Schedule Everyone Loves to Hate

Every spring, the NFL releases its schedule for the coming season. And every spring, like clockwork, every team finds something in it to complain about. A brutal travel stretch. Too many strong opponents bunched together. A run of away games at the wrong moment.

The complaints are practically a tradition. But behind them sits one of the hardest scheduling problems around.

At first glance it sounds almost trivial. A small team of people, around ten weeks, a few hundred games to slot into a season. Plenty of time, surely.

Then you count the options. The number of possible schedules runs into the quadrillions.

The constraints are merciless. Stadium availability. Travel. Competitive equity, which is their term for fairness. Television viewership, because the games that pull the biggest audiences need to land in the right slots. Thousands of these conditions, with more added every year.

So in 2013, the NFL turned to mathematical optimization. They run Gurobi, one of the world's leading solvers.

Here's the part that surprises people. They didn't buy one powerful computer and press go. They outgrew that almost immediately. Today the NFL runs a room full of servers, breaking the one giant problem into many smaller sub-problems spread across a pool of machines, all sharing what they learn as they go.

And even with all that horsepower, the solver doesn't hand back 'the answer'. It produces tens of thousands of valid, complete schedules. Then human beings sit down and choose.

That last sentence is the whole point. Hold onto it.

 

When "Best" Has No Single Definition

Finding a legal schedule is not the hard part. The solver can produce tens of thousands of them. The hard part is deciding which one is best. And "best" turns out to be a surprisingly slippery word.

It helps to split what the schedulers juggle into two very different kinds of requirement.

• Hard constraints. These must hold, no exceptions. A stadium is unavailable that weekend. A venue is double-booked with another event. Local police need two high-risk matches kept apart on the calendar. Break one of these, and the schedule is simply invalid.
• Competing objectives. These are the things you want more of, and they refuse to agree with each other. Fairness is made of dozens of small patterns: how often a team plays two away games back to back, how its rest days line up against its opponents', how its tough matches are spread out. And here's the catch: you cannot hand every team a clean deal. Two away games in a row, for instance, are mathematically impossible to avoid for at least some teams. In any realistic schedule, almost everyone ends up carrying a few. So fairness isn't fair against unfair. It's a balancing act between many small unfairnesses, spread as evenly as you can manage. And sitting on top of all that is another objective entirely: making the schedule attractive for TV, getting the biggest matchups into primetime.

You cannot maximize all of it at once, because the goals disagree. This is the heart of multiobjective optimization: not one summit to climb, but a whole landscape of trade-offs where every good option gives something up.

And it gets harder still. Some of these goals resist being turned into a number at all.

Take those unfairness patterns. The NFL knows which ones sting: back-to-back away games, awkward rest gaps, a run of strong opponents bunched together. So the planners penalize those patterns in the objective, telling the solver to avoid them where it can. But how much should each penalty be worth? There's no natural unit for unfairness. You can't look up the exchange rate between one extra away streak and one missed primetime slot, because no such rate exists.

So here's what the NFL planners actually do, and it's the detail I love. They can't pick the perfect penalties up front, because the schedule is far too tangled to predict. Instead they choose some penalties, run the giant computation, look at the schedule that comes out, and judge it by eye. Too harsh here, too soft there. Then they adjust the penalties and run the whole thing again. Much of that enormous compute isn't spent solving the problem. It's spent discovering what "good" even means, through trial, inspection and judgement.

That's the real lesson hiding inside a football schedule. Computers are brilliant at finding the best solution once you tell them what "best" means. The expensive, deeply human part is deciding what you actually want, and turning those messy, competing, half-spoken wishes into a single honest objective.

That translation, business into mathematics and back again, is most of what I do for a living.

 

Confess Your Team's Worst Ritual

Now I'm curious about you. What's your favourite goal of the tournament so far? Or, better yet, the most ridiculous ritual your team ever talked itself into. I'm always in the market for new dance moves, so hit reply and tell me. I read every one.

 

Until the next iteration! Tim Varelmann ​Bluebird Optimization​ Complicated Decisions - Simply Automated! Follow me on LinkedIn​

 

P.S. My favourite goal of the tournament so far? Nene Brown's, the one that made it 5-1 for Germany against Curaçao. For my money it's the best assist-and-finish combination of the group stage: watch it here. Honourable mention to Mbappé's opener against Senegal: Olise's pass, that first-time turn, almost as gorgeous.