The hammer rang once. A spark jumped off the anvil and did not go out. It waited. They followed.

The games club met on Thursdays in the old science lab, the one with the gas taps nobody was allowed to touch, and it had a rating site.

Bayard had built it the summer before. It was a plain page with every game on the club shelf listed down the left-hand side, and after each club night anybody could give any game they had played a score out of ten. The page added up the scores, divided by the number of them, and sorted the list from top to bottom. It was the first thing anyone looked at when they arrived. It was how the club decided what to play when it could not decide, which was most weeks.

For six years, the game at the top had been Harbour Lights. It was a slow, clever game about fishing boats and lighthouses that a former member had designed and printed at the library, and it lived in a battered box held together with tape. Sixty different people had rated it. Its average was 8.1. People who had left the school years ago still came back at Christmas to play it.

Then Ellis joined.

He arrived in October, from a school three hundred miles away, halfway through the term, which is the worst possible time to arrive anywhere. He was small and polite and slightly too formal, and for the first week he ate his lunch in the library because he did not know where else to sit. Tara noticed him because she ate her lunch in the library too, for different reasons. On the second Thursday he came to games club with a shoebox under his arm.

Inside was a game he had made himself. It was called Bramble. It had hand-cut cardboard tiles and a board drawn with felt-tip pens, and rules on two sides of lined paper. He asked, very quietly, whether anybody might like to try it.

Two people did: his cousin, who was in Year Ten, and a boy from his form who had been kind to him. They played twice. They loved it. That night, they each gave Bramble a ten.

On Friday morning Bramble was at the top of the club's rating site. Its average was ten. Harbour Lights, with sixty ratings and six years of Christmases, was second.

By lunchtime it was an argument.

"It's ridiculous," said a Year Thirteen called Marcus, who had been in the club since Year Seven. "Two people. His cousin, for one. Harbour Lights has sixty. You can't put a game two people have played above a game sixty people love."

"So what do you want to do?" said Bayard, a little defensively. He had built the site in the summer holidays, mostly at night, and he did not enjoy hearing that it was ridiculous. "It just takes the average. That's what an average is."

"Then the average is stupid."

The committee met after school: Bayard, Marcus, a quiet Year Twelve called Vera who kept the club's tallies, and Dunna, the treasurer. Tara was there because she was the club secretary, which mostly meant writing things down and not being asked her opinion.

Marcus had a fix ready. "Hide everything with fewer than twenty ratings," he said. "Don't show it on the list at all until twenty people have rated it. Then it can't jump to the top on two votes. Problem gone."

It sounded tidy. Bayard could add it to the site in ten minutes. Dunna started to nod.

Sol was sitting on the side bench by the sink. He had been club captain three years before, and now he studied at the college across town and came back on Friday afternoons because, he said, the club made the best tea in the county. He did not run anything anymore. He mostly asked questions.

"Can I ask what that does to Bramble?" said Sol.

"Hides it," said Marcus. "Until it's earned its place."

"How does it earn twenty ratings if nobody can see it?" said Sol mildly. "Hiding it doesn't help it grow. Everyone picks games off the list. If it isn't on the list, nobody plays it, so nobody rates it, so it never gets to twenty. You won't have fixed the rating. You'll have fixed the new kid's game out of existence." He sipped his tea. "And every new game after it."

"Fine," said Marcus. "So two votes is proof, then?"

"No," said Sol. "Two votes is something, but not everything. What does three votes really tell you? A bit. Not nothing, and not a lot. The question is how much a bit should count." He put his mug down. "Right now, the site counts two people exactly as much as it counts sixty. That's the bit that's wrong. Not the fact that the game is new."

Nobody said anything for a moment. Bayard, Tara noticed, was looking at his own site on his phone as if it had betrayed him.

The next Thursday Priya brought a whiteboard pen.

Priya was the person in the club who explained things. If you lost a game and did not know why, Priya would sit down and replay it for you, move by move, until you did. She had heard about the argument and wanted to have a go.

"Forget Bramble for a second," she said. She drew a blank box on the whiteboard. "Here's a game nobody has ever played. It's in a shrink-wrapped box. Nobody's voted. What score should it have?"

"None," said Marcus. "It hasn't got one."

"But if you had to guess," said Priya. "If I made you write a number down. Where do we start before anyone's voted?"

People thought about it. Ellis, who had come in quietly and was sitting at the end of the bench with his shoebox, said nothing.

"Ten?" somebody said, and laughed.

"Why would you guess ten for a game you know nothing about?" said Priya. "Most games aren't tens. Zero, then?"

"No," said Vera. "Most games aren't zeros either."

"Exactly," said Priya. "You can't start from nowhere. If you know nothing, the honest guess is the middle. Every game starts at the middle: five and a half, on a scale of one to ten." She wrote 5.5 in the box. "That's the prior: what you'd guess knowing nothing. It's not a judgement of the game. It's a confession that you haven't got any evidence yet."

"So Bramble starts at five and a half," said Bayard slowly. "And then the votes move it."

"Start in the middle, then let the votes move you," said Priya. "The question is how far."

Danya, who had come with Tara and was eating crisps on the floor, said, "That's what people do with new people too. They guess."

Priya laughed. "Yes," she said. "They do. And the good ones don't start at ten or zero."

Ellis looked up for a second, and then back down at his shoebox.

Dunna took the pen. Dunna was the treasurer, which meant she counted the club's money in a notebook with ruled columns and wrote every single thing as a sum. She said that if you could not write something as a sum, you did not understand it yet.

"Write it as a sum," she said. "Here's how I'd do it. Count the pretend votes too. Imagine that before anyone plays a game, it already has ten pretend votes, all of five and a half. Ten votes of five and a half, sitting there first. Then the real votes get added on top."

She wrote it out.

"Bramble. Ten pretend votes of 5.5 is 55 points. Two real votes of 10 is 20 points. Add them up, then divide. Fifty-five plus twenty is seventy-five. Divided by twelve votes altogether." She did it on the board. "Six and a quarter."

"Six and a quarter," said Bayard. "Not ten."

"Now Harbour Lights. Same ten pretend votes, 55 points. Sixty real votes averaging 8.1 is 486 points. Add them up, then divide. Five hundred and forty-one, divided by seventy votes." She worked it out. "About 7.73."

She stepped back. On the board:

Bramble: 6.25. Harbour Lights: 7.73.

"Harbour Lights is back on top," said Marcus, satisfied.

"Yes," said Dunna. "But look what happened. The two tens still count. Bramble went from five and a half up to six and a quarter, because two people loved it. That's real. It just didn't jump past sixty people's opinion on the strength of two." She tapped the board. "How many real votes to move the block? With two, not very far. With a lot, a long way."

"And the pretend votes," said Bayard. "With Harbour Lights, they hardly matter."

"Ten pretend votes against sixty real ones," said Dunna. "They barely move it. Against two real ones, they're most of the answer. It's a blend, and the bigger pile wins."

Bayard was writing in the corner of the board. "It's a blend, not a switch," he said, half to himself. "Weigh it by how many there are." He looked up. "I built it the obvious way, and the obvious way was wrong."

On the Monday something happened that made the whole thing real.

A Year Eleven who had lost badly at Bramble on Friday, and had sulked about it all weekend, logged in to the site and gave Bramble a two.

On Bayard's old site, with its plain average, Bramble fell off a cliff. Two tens and a two: twenty-two points over three votes. The average dropped from ten to about 7.33. One bad mood had knocked nearly three points off.

Ellis saw it at lunch. Tara, two tables away in the library, watched him look at his phone and then put it face down on the table and not pick it up again.

Vera found Tara at the end of lunch. Vera was the person who kept the club's tallies: who had played what, who had won, how many times. She was steady in the way that very few people at school were steady, and she did not get excited about anything.

"I ran it through Dunna's sum," said Vera, and showed Tara her notebook. "With the pretend votes. Ten of five and a half, plus ten, ten and two. Seventy-seven over thirteen." She had circled the answer. "About 5.92. It went down from 6.25 to 5.92. A bit. Not a cliff."

"So one angry vote can't wreck it," said Tara.

"And two happy votes can't make it," said Vera. "That's the point. Three friends aren't a crowd. A lot of ordinary votes beat a few loud ones. Volume moves it, not volume of voice."

"So what would it take," said Tara, "for Bramble to actually beat Harbour Lights?"

Vera had worked that out too. Of course she had.

"Thirty people," she said. "Thirty ordinary people playing it and giving it nine on average. Ten pretend votes of 5.5 is 55. Thirty votes of 9 is 270. Three hundred and twenty-five over forty is 8.125." She showed the circled number. "That beats 7.73. So if it really is that good, it'll get there. It just has to get there the slow way, like Harbour Lights did." She closed the notebook. "Give it time and votes."

Tara looked across the library at Ellis, who was sitting very straight and not looking at his phone.

"Does he know that?" she said.

"I don't think anyone's told him anything," said Vera, "except that his game was top and then it wasn't."

On Friday Ms. Varga came to the club. She was the teacher who unlocked the lab on Thursdays and signed the forms, and she had a problem.

Every year, the club's top-rated game went to the regional games fair in March, where clubs from all over the county brought their best home-made and favourite games. It was the club's big outing. The form had to be in on Monday, and it asked for one game: the one at the top of the list.

She was not a villain either. She had looked after the club for nine years without being paid for it. She had a principle she said every September: the club ran on rules everyone could understand, so nobody could ever say anything was fixed. A plain average was a rule anyone could check with a calculator. A formula with ten imaginary votes in it was, she said, "the kind of thing that makes people think someone's cooking the books." And she had watched the plain average fail twice in a fortnight, once in each direction. People had stopped trusting the list. That was worse than either.

She sat on a stool by the whiteboard, where Dunna's sums were still faintly visible under a smear.

"Here's where we are," said Ms. Varga. "Bayard says he can switch the site to Dunna's blend tonight. Marcus wants new games hidden until they've got twenty votes. Sol thinks hiding things is the worst choice of all. Ellis" — she nodded at him, kindly — "has a game that two people adore, one person hates, and nobody else has played. And on Monday I have to put one name on a form."

She looked round them all. Bayard with his laptop open. Vera with her notebook. Priya with the whiteboard pen. Sol on the side bench with his tea. Marcus, arms folded. Ellis, with the shoebox on his knees. Danya, cross-legged on the floor by the gas taps that nobody was allowed to touch.

Then she looked at the table by the window, where the secretary sat.

"Tara," she said. "You've written down every meeting this term. You've played every game on that shelf, including Bramble, on Thursday, when nobody else would. And you haven't said a word about any of this." She folded her hands. "How should the list work? And what goes on the form?"

The lab went quiet. A radiator knocked. Somebody's dice rolled off a table and nobody picked them up.

Tara thought of the blank box with 5.5 in it. Two tens from a cousin and a kind boy. A two from a Year Eleven in a bad mood. Sixty people and six Christmases of Harbour Lights. Thirty ordinary votes, the slow way. Ellis eating lunch in the library in his first week, before anybody had decided anything about him at all.

Everyone in the room was partly right.

Tara opened her mouth.

 

 

(Write the sentence Tara says.)

 

The spark dimmed to a warm dot and settled back on the anvil. The Green was just the Green again.

Back on the Green

A new girl moved into the flats by the Green in the spring. On her first day she knocked over the community fridge's milk and cried.

"She's a bit of a disaster," said a boy on the steps.

Danya, who was sitting next to him, thought about it.

"That's one vote," he said. "Ask me again after ten."

She went over and helped mop up the milk.

Afterword. The idea in this case is a prior. Before you have any evidence, you already hold a starting guess, and the sensible starting guess, when you know nothing, is somewhere in the middle. Then evidence moves you, and it should move you in proportion to how much of it there is: a little evidence a little way, a lot of evidence a long way. A rating that blends a prior with the real votes in this way is called a Bayesian average, and the same idea sits underneath much of modern statistics. It is also, the case suggests, a fair way to meet a new person. You can play with priors, pretend votes and the volume that overcomes them in PriorForge.