Buckball Abstract

by Pineta

Chapter 1: Sabermetrics for ponies

“Isn’t havin' an alicorn on the team goin' to give us an unfair advantage?” Applejack asked Rainbow Dash as they walked towards Twilight’s castle.

“Well the way I see it,” said Rainbow Dash, “if she stays on the ground and doesn’t buck anything or flap her wings, nopony can call it cheating. And alicorn or unicorn she’s the best pony at magic, so we totally need her on the buckball team if we want to crush Appleloosa. I told her all about it yesterday—she said she wanted to read up about it—but she seemed keen.”

“All the same, it doesn’t seem quite right havin’ a princess playin' for us. I guess Rarity could do it—she’s good at levitatin' things—but she would spend all the time worryin' about what colors we were wearin'.”

“No. Not Rarity,” agreed Dash. “If Twilight won’t do it, we can ask Starlight—she's just as awesome at juggling loads of stuff in the air.”

“I guess,” said Applejack.

They walked through the door of the castle and into the throne room. At the central table they could just make out the horns and manes of Twilight Sparkle and Starlight Glimmer behind piles of books. Both were frantically scribbling notes with their quills.

“…I would say that the earth pony on the Fillydelphia team has been the strongest player in the league this season,” said Twilight. “She has a bucking average of .347.”

“She has a serious weakness,” said Starlight, “she tires too easily—her performance always drops after the first rounds, and she underperforms when playing away from home. But her on-buck plus hugging percentage comes to .850. That compares well to the team from Baltimare.”

“This is so much fun,” exclaimed Twilight, looking up from the table where copies of Hayesian Statistics and The Historical Buckball Abstract lay open. She clapped her hooves together, “I think buckyball just might be the best game ever!”

“It’s buckball,” said Starlight. “A buckyball is a type of fullerene molecule.”

Rainbow and Applejack reached the book-covered table, and pushed a pile of Buckball Almanacs to one side so they could face the unicorns. Copies of Probability Theory, The Discrete Unicorn Distribution, and Bitball fell onto the floor.

“So you’ll join the team?” asked Rainbow Dash.

“Oh—Hi Rainbow. Hi Applejack,” said Twilight, looking up from her scroll and noticing and pegasus and earth pony for the first time. “Come and join us—were discussing sabermetrics. It’s so exciting!”

“Saber—what now?” said Applejack.

“The metrics used in Serious Analytical Buckball Research,” said Twilight. “It’s the study of buckball statistics, using mathematical methods to make academically rigorous statements on subjects such as who is the best bucker. It’s absolutely fascinating. I went to collect some books from Canterlot, and it turns out Moondancer had been collecting data from the Canterlot games. We’ve put this together with other studies Starlight found and we’ve been doing a meta-analysis.”

“I don’t care much that fancy mathematics,” said Applejack. “But we need a good unicorn for the team.”

“We can help.”

“You will!” Rainbow smiled enthusiastically.

“Sabermetrics can help by providing the best metric to judge the performance of a player. You have to be careful. Simple measures don’t work very well. For example if you just count the error statistic of the times a unicorn misses a ball, that would favor the slow unicorns—who don’t make many attempts—over the faster ones who dive in wherever they can even if they risk missing.”

Applejack was not convinced by this approach to buckball management.

“But how can you just reduce a pony to a number? That ain’t doin’ anypony justice.”

“Of course there is an inherent uncertainty on the metric for any single player, but if you have enough statistics then the uncertainties will tend to cancel out,” explained Twilight. “And using statistical methods you can get an accurate estimate of that uncertainty. So we can say with 97% certainty that the Appleloosa team will field a player with a bucking average of at least .32, so you’d better pay attention if you want to have a probability of winning above 67%—”


“—meanwhile there’s another way we can help. Starlight’s also been working out the physics of ball flight to help your bucker send the ball along a winning trajectory.”

Starlight lifted up a scroll showing a diagram of the air flow around a ball.

“If you can buck the ball so the air flows faster on one side then its path will curve due to the pressure difference,” she said. “This makes it more difficult for the pegasus defender to intersect the ball. The trick is to get a smooth laminar flow on one side, and a turbulent flow on the other. I’ve been working out a new technique of reverse swing bucking which will work at faster speeds and is sure to give your team the advantage. I just need to work out some of the details and maybe do some experiments.”

“Right…” said Rainbow.

“Well…” said Applejack.

The unicorns had stopped paying them any attention and had returned to scribbling numbers on their scrolls.

“We’ll... err… leave you two to… err… figure out the details,” said Rainbow. She turned away with Applejack and the two friends cantered out of the room.

“That didn’t go quite as I expected,” said Applejack once they were outside of the castle.

“Sure didn’t,” said Rainbow. “How can Twilight and Starlight take it so seriously? It’s supposed to be a game.”

“Well we need to find another unicorn. Maybe we’d do better holdin' trials—so we can actually see how they play.”

“That’s the way to go. We can get Pinkie and Fluttershy to help us play a few rounds. Somehow we need to find a unicorn who can actually play buckball instead of just thinking about playing it.”

“Yeah. Ideally, we want a unicorn who won’t think about anything. Ever.”

Author's Notes:

Further details: Sport for Statistics Fans

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