bjj-graph

An exploration of graphing the positions and techniques in Brazilian jiu-jitsu.

Models

v1

This is a randomly generated subgraph, starting at Mount and randomly choosing valid techniques and positions until a submission occurs. The full graph is much too large to display here!

My first stab at this (2021-2024) reflected my simplistic understanding of jiu-jitsu as a beginner. The initial idea was that when you are in a position (node), there are a set of techniques (edges) that you can use to take you into a new position.

For example, when you are on the bottom of the Mount position, you can perform a Trap and Roll technique to take you to the top of Open Guard.

v2

TODO: Implement this new approach and include a graph here

As my practice and understanding of jiu-jitsu developed, I realized that the model should be more nuanced. When you execute a Trap and Roll, your opponent can counter with Super Hooks, and the outcome is that you're still in the bottom of the Mount position.

I had left out techniques like Super Hooks from the v1 model, because it didn't seem like there was a natural place for them. The v2 model solves this problem by modeling both positions and techniques as nodes. A node represents a temporary state, and my higher-level understanding of jiu-jitsu now tells me that when you are either holding a position or executing a technique, those are both states that can be explored, with various outcomes depending on what your opponent is doing.

Graph visualization

This project uses the ubergraph library to construct the graph and graphviz (which is built into ubergraph) to generate visualizations.

bin/viz-graph is a CLI entrypoint that wraps ubergraph.core/viz-graph to graph the BJJ positions and techniques. the options are passed into viz-graph, and the :layout :dot option is included by default.

Example usage:

# Display graph in a dedicated window
bin/viz-graph

# Save graph as SVG file (e.g. /tmp/bjj-graph-2024-01-11.svg) and open it in
# Firefox
filename="/tmp/bjj-graph-$(date '+%Y-%m-%d').svg"
bin/viz-graph "{:save {:format :svg, :filename \"$filename\"}}"
firefox "$filename"

# Refer to `(doc ubergraph.core/viz-graph)` for more options
clojure -e \
  "(require '[clojure.repl :as repl] '[ubergraph.core :as uber])
   (repl/doc uber/viz-graph)"

Random sequence generation

As a result of modeling jiu-jitsu as a graph, we can randomly generate valid sequences of techniques and positional changes.

`bin/random-sequence`

bin/random-sequence starts at a random position and keeps generating steps (either a technique or a transition to a new position that is easily accessible from the current one) until a submission occurs:

$ bin/random-sequence
Over-Under Clinch
Pummel
Body Fold Takedown
Twisting Arm Control
Take the Back
Frame Escape
Double Underhook Guard Pass
Reverse Cross-Chest
Mount Transition (High Step)
Americana Armlock (Standard)

`bin/random-subgraph`

The graphs above were generated via this script.

bin/random-subgraph takes a starting position and an optional length and generates steps in the same way as random-sequence, but rather than printing the steps in text form, it visualizes the subgraph that the randomly generated steps comprise.

# Start from a random position and keep generating steps until a submission
# happens. Display the graph.
bin/random-subgraph

# Start from Guard and generate a sequence of length ~5. (The actual length may
# be less than 5, in cases where we go down a path where the only definide
# options are submissions.) Display the graph.
bin/random-subgraph '{:start-position "Guard", :length 5}'

# Start from Mount and keep generating steps until a submission happens. Save
# the graph as a PNG file and then open it in Firefox.
filename="/tmp/random-subgraph.png"
bin/random-subgraph \
  "{:start-position \"Mount\",
    :viz-graph-opts {:save {:format :png, :filename \"$filename\"}}}"
firefox "$filename"

License

Distributed under the Eclipse Public License version 2.0.

daveyarwood/bjj-graph