What Warhammer taught me about football Whether in politics or football, we create narratives about chance events

The idea is simple enough – your Necron Warrior’s Gauss blaster might shoot 24” and hit on a three, so you measure the distance, crouch down to see if it can see its target, and then roll. Then, if you hit, you roll the other dice to see if it does any damage. Or for your fang-toothed, green-skinned, cleaver-wielding Ork Boyz, you might roll to see if they successfully charge into combat, and then roll again to see how many times they hit their opponents.

The game is all about dice-rolling. It is explicitly random – dice are the archetypal random-number generator. The game is about understanding and managing randomness, about surfing uncertainty; the skill is in navigating the luck. Your big, tough Terminator has good armour; you can probably expect him to shrug off most shots from normal guns. But if you get shot enough times, you’ll probably roll a few ones. Do you dare put him out in the open where everyone can see him, but where he can quickly close with the enemy and do the most damage? Or do you try to sneak him around behind cover, which takes more time but is safer?

We struggle, sometimes, with randomness and uncertainty. We struggle with it in the sense that we don’t enjoy it – we don’t like not knowing what’s going to happen. We struggle with it in the sense that we are bad judges of how likely or unlikely things are, of thinking in more complex shades than “will happen, won’t happen, might happen”.

But we also struggle with it in the sense that we don’t recognise it: after the fact, contingent facts seem inevitable; randomness dissolves into fate. We judge decisions not by whether they were made using the best information available at the time, but by what actually happened – a mistake known as “outcome bias”. Say I charge my Terminator out into the open and he gets 15 lasgun shots in the face, with three of them sneaking past his armour, killing him: did I make the wrong decision? Maybe – but maybe I made the right decision and rolled a few bad dice. 

Years ago, I used to play poker, very occasionally and very badly: I tended to get drunk and go all-in on bad hands. Once, I played at a casino against a pro for a feature for the Telegraph. As usual, I played my signature move, betting very heavily on useless cards after a few pints; but for once, I drew exactly what I needed on the river, and won. Very obviously, I had made bad decisions, but got lucky. But from the inside, it felt as though I had played brilliantly. 

I spoke to a financial trader for that poker piece, who uses poker to teach decision-making; he said that in games of uncertainty, like poker (or like Warhammer, he did not in fact say but could have), you can only detect the role of skill over a long time. Even after a new player has played 100 hours of poker, he said, still, “we don’t feel that we have a good handle on truth;” there’s so much noise, so much luck, that the (very real) skill can be drowned out except over the very long term. “If you win a single hand,”, I wrote at the time, “it’s meaningless to attribute it to skill. If you’re in profit after 100,000 hands, you can say with reasonable confidence that you’re a skilled player.”

In Warhammer, too, it feels as though the outcome of the decision is what determines whether a decision was the right one. But these are games of chance – explicitly random. That is, I think, why games of chance are important. Because you know they’re random, it’s easier to detach the outcome from the process. In other areas of life, without the training that games of chance give you, it’s not so easy.

A stock trader might become a billionaire off a few lucky trades. Are they good? We don’t know: millions of traders make trades every day; some of them will be lucky. A company runs a huge profit for a couple of years: is that because it’s well-run? We don’t know; it could just be survivorship bias. Warren Buffet clearly is genuinely skilled: we have years of data to show that. But if someone has one good year, that might just be fluke.

We have an inbuilt need to explain success and failure. And sometimes that’s important. But in some situations, huge outcomes hinge on tiny moments; a dice-roll, in essence, but a hidden dice-roll. The recent Batley & Spen by-election, for instance: Labour won it by 323 votes. In an electorate of 80,000, that’s essentially coming down to a coin-toss. If Labour had lost by 323 votes, it would have been a huge blow to Keir Starmer’s leadership; he might have faced a challenge. But in reality it would have told us nothing different about his success or otherwise.

Or football. As I write this, the memory of England going out on penalties is still fresh and painful; Gareth Southgate is being criticised for bringing Marcus Rashford and Jadon Sancho on in the last minute of extra time to take penalties, and for asking Bukayo Saka, a teenager, to take the last one. They all missed.

But before the shootout, Jermaine Jenas, the BBC co-commentator, was saying that Sancho was probably being brought on because he had the fearlessness of youth. The outcome was negative, but was the process wrong? As this guy says, in 1996 people got angry with Terry Venables for leaving penalty-takers like Robbie Fowler on the bench; in 2021 we get angry with Southgate for doing the opposite. And it works both ways: at 1-0 up against Germany, Thomas Müller ran clean through after a misplaced pass from Raheem Sterling; he should have scored but put his shot just wide of the post. He would probably make that shot five times out of six; he rolled a one. Sometimes you do.

People then make narratives about it. If the Tories had won Batley & Spen, we’d have been told it was because the Hancock affair wasn’t cutting through, or because “woke” issues were alienating the Labour base. Labour won, so the ground game was strong, or Kim Leadbetter was an engaging candidate. 

Likewise: if Müller scores, our defence isn’t good enough; if Rashford does (and his penalty sent the keeper the wrong way and was only a couple of inches wide), then Southgate’s plan worked. But if you’re trained by games of chance, then you can think: OK, sometimes you roll a one; sometimes the coinflip comes up heads. 

There’s an obvious counter-argument: dice actually are random, whereas football and politics are not. But that’s wrong. Technically, dice are not random: when you throw them, you impart a certain amount of spin, you give them a particular velocity, they will bounce a certain way. The face they show when they land is not randomly determined: it is determined by how you threw them, by the surface they land on, by how sharp or rounded their corners are, by their density and elasticity. A Laplace’s demon, an all-knowing God, could in theory predict how they bounce, limited only by the apparently true randomness at the quantum heart of the universe. But in reality, as chaos theory tells us, tiny changes in the input make it fundamentally unpredictable.

Similarly, tiny, unnoticeable differences in reality can have major impacts on your outcome. David Foster Wallace, writing about tennis in 2006, talks about the minuscule details a tennis player has to pay attention to: the tiniest difference in the angle of the racquet’s face; hitting a ball a millisecond earlier or later. Tennis players repetitively, obsessively hit the same shots thousands and thousands of times in training, so that it is second nature, so they can hit it 999 times out of 1,000. But still, a minor irregularity in the court’s surface can change a bounce; a momentary slip can make a shot fail. The difference between a bad player and a good one is that the good one is more able to control randomness, to put the ball into the area they want to more often. But the randomness is still there. If, in Batley & Spen, a few Labour activists had had to self-isolate for Covid, or if the weather had been different, that might have changed the result. 

If you want to draw conclusions from these things — to say that England should have done X or Labour should have done Y — there are hard limits on how much you can say, from a single data point like a by-election or a cup final. Too much of sports and politics journalism, I think, is finding narratives after the fact, “analysing” events by looking at the results. As in poker, you need more data than a single hand can provide. 

We suck at spotting randomness. The whole enterprise of science is a careful, and only partially successful, attempt to get past our innate human need to see patterns where they often are not. But one way of training your own ability to think about processes, not outcomes, to see the hidden dice rolls behind the events that shape our world, is to play something with real dice rolls. It doesn’t have to be Warhammer; Dungeons & Dragons will do, or poker, or bridge; cards do the job just as well as dice. But I do recommend Warhammer, because you can learn about randomness while also smashing someone to pieces with a gigantic poisonous scythe. Which makes it a lot more fun. I’m going to preorder the new edition.

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Tom Chivers is a science writer. His second book, How to Read Numbers, is out now.

TomChivers