On a Jiu Jitsu Elo System - Actual Grappling Effectiveness
In Jiu Jitsu we have a belt system—white, blue, purple, brown, black. This determines "rank", but it doesn't always accurately predict the outcome of rolls between different belt levels. It's not uncommon for people of a lower belt to submit higher belts, and there's a lot of reasons for this; weight, age, strength, and even actual technical ability. Your belt level doesn't necessarily reflect your current skill. People often take years off of jiu jitsu and come back later, and their skills are eroded. Their belt no longer reflects their actual grappling effectiveness (AGE), but we don't take that belt away from them—a belt is earned forever.
I'll define actual grappling effectiveness as your ability to control and submit people of different sizes and skill levels.
Even at the black belt level there are effectiveness gaps as large as the gap between white belt and brown belt. Professional black belts are much better than your non-professional hobbyist instructor, and they'd tap your everyday black belt 10/10 times. And that's okay! In jiu jitsu we say that belts are a personal journey, and that's why there's such a spread. We accept that belts do not necessarily reflect actual grappling effectiveness.
I'd like to pose an idea for a new ranking system.
In Chess, they have "elo" (ee-low).
From the elo wiki:
A player's Elo rating is a number that may change depending on the outcome of rated games played. After every game, the winning player takes points from the losing one. The difference between the ratings of the winner and loser determines the total number of points gained or lost after a game. If the higher-rated player wins, only a few rating points (or even a fraction of a rating point) will be taken from the lower-rated player; however, if the lower-rated player scores an upset win, many rating points will be transferred. The lower-rated player will also gain a few points from the higher-rated player in the event of a draw. This means that this rating system is self-correcting. In the long run, players whose ratings are too low or too high should do better or worse, respectively, than the rating system predicts and thus gain or lose rating points until the ratings reflect their true playing strength.
So, my idea, which is just a toddler of an idea right now, is to have a jiu jitsu elo that's separate from belts. A measure of your actual grappling effectiveness Your starting elo? Your weight. Because at the beginning, that's all you really have. I'm going to use "AGE" and "elo" sort of interchangeably here, moving forward.
Here’s the system:
Starting AGE
AGE = body weight (lbs)
Expected Score - The chances of you winning.
E = 1 / (1 + 10^((opponent AGE - your AGE) / 84))
Actual Score - Did you win or lose?
Submission win = 1
Decision/points win = 0.5
Loss = 0
K Tier - Variable to affect how much rating change happens, based on whether or not your AGE score has "settled".
Matches 1-10: K = 50
Matches 11-40: K = 30
Matches 41+: K = 16
Updated AGE
New AGE = Old AGE + K × (Actual - Expected)
So, the Expected Score is a measure of how likely you are to win. With an 80 point difference, the higher rated player is expected to win 90% of the time.
Submissions reward more elo than decision/points wins.
The K-Tier is a multiplying factor that will cause newer competitors' elo to swing more than seasoned competitors, helping newbies land in their correct division and settle their AGE faster, while people with lots of matches will gain and lose rating more slowly.
This would make for a different style of competition, based around elo clusters. You wouldn't compete at your weight, or your belt level, but instead at your elo.
You're 165lb. It's your first tournament. You're in the 150-170 elo division, your AGE is 165. Your first match is against a dude who's 200lbs, but his AGE is 168. He's more experienced than you in competition, he's bigger than you, but he's lost most of his matches in his first three tournaments—that's why his elo is below his weight.
Your AGE is pretty close together. According to the expected score formula, your chances of winning are about 48%.
You submit him!
Your elo immediately rises.
165+50 x (1- .479) = 191
That's a big 26 point gain. Your opponent has over 10 matches, so they only lose 15 elo, moving down to 152.
You win the tournament. You're the next Mica Galvao.
Anyways!
I haven't done a deep dive into where the best athletes in jiu jitsu might be in terms of their AGE scores, but I'm really curious about it. I'm sure I'll have more on this in the future, and I'll probably start giving my students AGE scores and pitting them against each other in "Rated AGE Matches". I hope this doesn't spiral into me starting my own competitive league.
Some things I'm thinking about further are:
Rating decay - If you don't compete for some amount of time, your rating should decay.
K value change - If you haven't competed for some amount of time, your K value should swing back up.
I also don't want to undermine the belt system or make them less valuable. They are a reflection of personal development and skill, and I think they're a great measure of progress.