In previous
articles, I have looked at the new-ish IBJJF seeding system as a way to predict
match outcomes at the IBJJF No Gi Pans. I used IBJJF medal results to
rank fighters after the 2019 World Championships. I also created a
machine learning model to help predict who will win a match up at the ADCC tournament. Today, we (yes a collab project
between myself and Dan Tsinis) are introducing
the Elo Rating System for Brazilian Jiu Jitsu as a way to rank fighters and predict the probability of fighters winning in a potential match up.
Below are the top 50 pound for pound competitors and the top 10-20 by each weight class. The ratings only include the last three years (2017-2019) and each year has a seasonal weight. This is not reflective of the best competitors of all time, but the most accurate of who competed the most in the last year. These are the current 2019 year-end standings.
Predictions for First Round Matches at IBJJF Europeans 2020
With
our Elo rating system for BJJ, we are able to calculate the probability
that a fighter will win their first round match against an opponent at
the upcoming IBJJF European Championships. Based on the point difference
between the two fighters, we have calculated the following:
Not all fighters had an Elo rating, so not all matches were predicted for the first round. Some predictions are for the first round fights and others include the second round match ups if a fighter had a bye (which accounts for fighters having multiple entries).
We believe our Elo for BJJ rating system to be accurate of the performance of fighters in 2019. For instance, Bruno Malfacine only competed at the World Championships and had two fights, losing one. The rating is weighted more heavily for the 2019 season, so hence his score being low regardless of the fact that he has won multiple world titles. In comparison, Thalison Soares has a higher rating, and thus stronger win probability in the chart above due to his recent performance since getting his black belt. Similarly with Keenan Cornelius, he didn't competed as much in 2019 as previous years, so his rating is lower than expected. Bruno and Keenan are considered outliers in the dataset for not competing often, although they may be considered the heavy favorite to win. Our rating system will be updated after the European Championship, for which these fighters may improve their performance rating in 2020. With the Elo rating system, a fighter's true score evens out over time.
Year-End 2019 Elo Ratings for BJJ
Note: In the Elo rating system, competitors that compete more are rated higher than those that only sign up for one tournament a year.
What is the Elo Rating System?
Developed by
Hungarian-American physics professor Arpad Elo, the Elo system calculates the
relative skill level of players in zero-sum games.(1) Elo was
originally developed for chess but has wide applicability today for video
gamers and pro-sports leagues such as the National Football League and Major
League Baseball. The system uses the difference in the two players’ relative
score over time to predict an outcome when they face off in competition.
How Does Elo Work?
We have seen
how a win/loss ratio works; a fighters’ win percentage is calculated by the
number of times he or she wins divided by the total number of matches they
fought. Example: 7 wins and 3 losses result in a 70%-win ratio (7/10=70%).
For the Elo
Rating System, each fighter is assigned a starting score (in our calculations,
we started with 1000). After each match, the winning fighter takes points away
from the loser. The number of points the winner is given is determined by how
big the different scores are between the two fighters.
If the
fighter with a higher score wins, only a few points are taken from the loser.
If a lower scoring fighter wins, the lower ranked fighter gains significantly
more points. The benefit of the points transfer is that the rating system is
self-correcting over time and it is used to compare two fighters.
Historical
rating systems in sports have assigned a subjective value of perceived 'greatness'
to players, often connected to a player's popularity among fans. The Elo rating
system departed from that convention towards a statistical estimation of player
abilities.
About the BJJ Heroes Dataset
The BJJ
Heroes A-Z Fighters List contains 1,075 fighters as of December, 2019. Of
those, 396 black belt male fighters have a grappling record and fight history,
from which our dataset is based upon. The fight history details an extensive
list with the opponent's name, the win or loss, the method the fight concluded
(submission, points, etc.), competition name, weight class, match round
(semifinals, super-fight, etc.), and year. For the 396 fighters, there are
24,852 total matches recorded in the dataset. Here is a quick synopsis of the
dataset:
The dataset
had 1,147 unique competitions; initially we did not distinguish this by year but
it does include all super fights and tournament iterations (ex. Polaris 1,2,3,
etc.), all seasons (winter, spring, summer, and fall opens), gi and no gi (see
the limitations section for further details). It spanned 50 years of
competitions. For our purposes, we cut down the dataset to only the last 10
years ranging from 2010-2019. It recorded 98 weight classes, compiled from all
tournaments using different weight systems (see limitations section). Also for
our calculations, we cut this down to 8 weight classes aligning to the IBJJF gi
weight classes, since the spring of 2020 is upon us and it is gi season. Most
interesting in the dataset, it recorded 376 different ways a match was
concluded.
Here are the
top 30 fighters in the dataset with the most recorded wins. Leandro Lo tops the
list as he is a prolific competitor, multi-time world champion across several
weight classes, and one of the most exciting competitors to watch. Second on
the list is Erberth Santos. In the 2018 season, he was in the running with
Leandro Lo for the top IBJJF ranked fighter in an effort to win the $10,000
prize, only to be narrowly knocked out by Lo at a local tournament in Brazil
before the World Championships.
One of the
biggest contributions to our knowledge and understanding of Jiu Jitsu is the
chart above on the top 50 most common ways matches have concluded. If you are
looking to get good at submissions, you should focus on chokes from the back
and arm bars, followed by triangles and kneebars. Most matches in the dataset
are recorded from IBJJF tournaments where the point system is dominant.
Submission-only tournaments have grown in popularity and super fight decisions
and EBI over-time (EBI/OT) are represented in the chart.
Winning by
points is the most common way to win a match. Second most common way is winning
by 2 points. Winning by points of any kind (all points finishes combined)
accounted for 45% of all match outcomes. Even more fascinating is that
referee's decision was the third most common way that matches concluded at 8%
of all the data. When segmented by the last 3 years, a referee decision was
second in line for most match finishes only by a narrow margin. Referees do
play a large role in tournament outcomes, according to the data. More emphasis
should be placed on fair referee decisions with video playback options, like
what the UAE tournaments currently have in place.
The top
tournaments by total number of matches in the dataset include the IBJJF World
Championships, followed by the Pan Championships and No Gi World Championships.
Nothing too surprising there.
The number
of Jiu Jitsu matches in the last decade has grown exponentially. In 2010, there
were 426 recorded matches in the dataset. By 2019, there were 4,397 matches
that took place at the adult black belt male level.
Elo for BJJ Rating System:
The dataset
is derived from the BJJ Heroes' Fighter List. Only a small subset was needed to
calculate the Elo for BJJ rating system, specifically we only used matches from
2019.
Once we
organized the data of fighters by the year, weight, and outcome we were able to
generate ratings. This methodology was applied to all of the IBJJF weight
classes, creating separate scores for each category. For instance, if a fighter
fought in two categories (their weight and absolute) they would get two separate
ratings for each respective weight category.
Fighter Rating Formula:
Rn = Ro + K × (W - We)
Rn is the new
rating, Ro is the old (pre-match) rating.
K is a
weighted value at.
We is the
expected result (win expectancy).
After the
fighters obtained a rating, we were able to obtain the probability of a match
outcome as provided by this equation:
We = 1 / (10(-dr/400) + 1)
dr equals the
difference in ratings.(2)
Although Elo
is agnostic to many attributes in head to head matches, this leaves room for
future exploration of other approaches which will consider other match details.
Thanks for reading! Feel free to
send us questions or comments and we'll try to get back to you in a timely
manner.
Special
Thanks to Andre Borges and BJJ Heroes. This site is one-of-a kind
for the Jiu Jitsu community and its contribution to the industry cannot be
overlooked. Without it, the BJJ community would not have the extensive
background information, fighter lineage, major tournament achievements,
statistics on submissions, a fighter's grappling record, and fight history. If
you have not checked out the site, please show some support. Cheers! www.BJJHeroes.com
Methodology: Elo for
BJJ Rating System was created by Dan Tsinis and Amanda Riggs. The data was
collected in December 2019 with permissions from BJJ Heroes, a site developed
and maintained Andre Borges. The fighter histories are maintained for black
belt male fighters after major Jiu Jitsu competitions, for which the Elo for
BJJ Rating System was developed. Our model was based on a similar model
developed for collegiate wrestling(3), the World Football Elo
Ratings, as well as others. All calculations and
opinions in this article are our own.
On
tournaments, there were 1,147 unique tournament names in the dataset. Some
duplicates existed and this section would need to be cleaned further. However, the
names of events did not affect the Elo calculations.
Tournament
weights were included and the top tournaments were weighted higher to indicate
a greater difficulty for a win. The K value for regular tournaments was
10. The following received additional weights:
- World Championships - 70
- ADCC - 70
- Pan American - 40
- Brasileiro - 40
- No Gi Worlds - 40
- World Pro - 40
- South American - 20
- American Nationals - 20
On weight
classes, there were originally 98 weight classes in the dataset from many
tournaments using different weight systems. For the pound for pound comparison,
the weight classes were not a factor in calculation our Elo rating system.
However, we cleaned this up to include 10 weight classes that spanned across
IBJJF, UAE, and ADCC, and most other tournament weights fell with those ranges. Here are the
custom weight ranges we used:
- Rooster - 53-59 kg
- Light Feather - 60-65 kg
- Feather - 66-70 kg
- Light - 71-77 kg
- Middle - 78-83 kg
- Medium Heavy - 84-89 kg
- Heavy - 90-94 kg
- Super Heavy -95-100
- Ultra Heavy - 101-120
- Absolute Division
On seasons, we added a weight for the season by the year. The 2019 competition year received a score of x 1, 2018 x .75, and 2017 x .25. The weighting system gives matches in the last year the highest weight and thus the overall ratings are indicative of the most recent year for 2019.
Limitations: Major Jiu
Jitsu tournaments do not release statistics on matches or match outcomes. The
dataset is maintained by hand overtime. We cleaned and wrangled the dataset to
the best of our ability. Please excuse any errors or omissions.
Citations: