TL;DR: My friends and I have a stupid hobby that’s getting out of control and I need your help spiraling it further. Please help me create a fair power rankings system (using the attached spreadsheet for reference) for the Beerio Kart tournaments we host.
Dear members of the Statistics community,
I call humbly upon the statisticians, mathematicians, programming aficionados, excel experts, sports analysts, and power rankings enthusiasts of this great community to assist me with a vital task — creating a fair and representative power ranking formula for the International Beerio Kart Championships of the World.
A little background: my buddies and I were trapped at home Thanksgiving of ’21 for a fourteen day COVID quarantine. We were saddened by a missed opportunity to see our families, but with competitive spirit running through our veins and a surplus of leftover PBR from a party we threw (which was undoubtedly what gave us COVID), we found solace in roughly two weeks straight of fierce competition in the best drinking/video game pair to ever exist: Beerio Kart. For the uninitiated: Beerio Kart is Mario Kart, however, you need to finish your beer before the end of each race, and you can’t drink and drive (i.e. chug and control your character simultaneously). Our version of the game has many extra rules and sub-rules, however, that’s the basic premise of the game.
After two weeks of this, we needed an outlet to determine who was truly the best of us, and thusly the International Beerio Kart Championships of the World were born. It started with a modest eight competitors, but interest has increased steadily over the past three years and in recent events we’ve had as many as 58 competitors fighting to compete in a 32 person bracket (surplus competitors play in Play-in Prix’s for entry into the main bracket). We’ve now had 75 people play in official brackets and obtain power rankings, and close to 100 participate in the events overall. For a little context into how the tournaments are run, four competitors participate in each Grand Prix, and the top two competitors advance from each round until the championship. In the preliminary rounds, players must drink a beer on races two and four of each Grand Prix, and in the finals all four races are drinking rounds, thusly the final four competitors must drink a minimum of 10 beers to win the tournament.
As tournaments got larger and more intricate (and people started complaining that they were seeded unfairly), we realized we needed an objective ranking system to seed players so that the Prix’s leading up to the championship were fair and quantitative. This background brings me to the hallowed undertaking I beseech your help with: please help me figure out how to do this.
We’ve tried a few formulas, but we are but amateur statisticians and none have felt like they effectively capture a player’s skill level.
First we tried the following formula: ibkc power ranking = 0.33t/60n + 0.33z/60 + 0.33y/60, where:
60 = the maximum number of possible points scored in any given grand prix t = total points accrued over all past tournaments attended n = total number of grand prix’ held in all official tournaments z = average points scored per prix, per tournament, in all tournaments attended y = average points scored per prix, per tournament, in all tournaments attended this calendar year
It was a good start, but it unfairly biased players who had played in more tournaments, and wasn’t an accurate reflection of current skill level. It would be like baseball power rankings putting the Yankees are at the top because they’re an ancient ball club and have won 27 World Series’, even though the last time they won was 2009, or the Astros low down on the power rankings because they didn’t win their first Series until 2017, even though they’ve won twice in the past 5 years.
We then created a formula based on Pythagorean expectation, where a players skill level is calculated by averaging their (points accrued in a prix)/(points accrued in a prix + total number of possible points in a prix). Each round of a tournament was weighted heavier than the last, and tournaments with four rounds carry more weight than tournaments with three rounds. The player’s Pythagorean expectation was then averaged over all tournaments they’ve participated in, averaged over the last four tournaments held, and averaged over the last two tournaments held. Their power score was then calculated by averaging these three numbers together with the intention that more recent tournaments would be weighted heavier than older ones. This is the formula that the attached spreadsheet uses.
This new formula was better than the first but has an inverse problem — it weighs recent tournaments too heavily and doesn’t account for any rank decay from missing tournaments. For example, you can see that BAT has won 6 of 8 tournaments, but after a huge upset in the semi’s, BAT did not make the finals of the last tournament, and was booted from first place overall to third. All the while, Squirt4Boyz advanced from second place overall to first, even though Squirt4Boyz didn’t even participate in the last tournament.
There’s all sorts of hidden columns and rows and whatnot in this spreadsheet so please dm me with any questions you might have, but please, I beg of you fine and glorious proprietors of the world’s most stressful game, help me create a ranking system that makes sense. Ultimately we need a system that reflects how many points a player is expected to score, considers that player’s tournament wins, podium finishes and finals appearances, accounts for rank decay, and like in global tennis or golf rankings, has some bias for recent events.
Thank you, friends.
Your servant,
The International Beerio Kart Championships of the World League Commissioner
submitted by /u/zakarm22
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