EdgeworthArena
Live dataSign in
live Five sports · fitted on real results · documented, licensed, playable

Winning is a maths problem.

Every match, race and rally reduced to the equations that decide it. Fitted on fifty thousand real matches across thirteen leagues, checked against the closing line every week, written up so you can licence the models, taught so you can build them yourself, and turned into games you can lose to.

14,505
Real matches
5
Leagues, live
40
Fitted models
19
Documented specs
This week · model priceloading
Thirteen doors

Where do you want to start?

Play against the models, price a match, trade one on paper, read the specification of every model in the library, learn to build them in the Academy, or sit back and watch the films.

Play

Six games where the model is the opponent. Manage a real match, take ten penalties against a keeper who learns, pace an 800 m.

Enter the arena →

Predict

Pick two teams. Every market, fair prices, the confidence band and the words that explain it.

Price a match →

Live

This week's fixtures, the tables, the tennis draws and the NBA slate, each with the model's number beside the market's.

See the week →

Lab

Sixteen live models with sliders. Move a parameter and watch the optimal strategy move with it.

Open the lab →

Films

Twenty-two short films, six of them in 3D, and three flight explorers with wind and altitude on the sliders.

Watch →

Factors

Weather at the ground, altitude, the crowd, the journey, gear and fuelling. Each one graded by its evidence, each one a toggle on the price.

Stack them →
P(x,y)=τ·e−λ

Quant Library

Nineteen models written up properly: what goes in, what it does, what comes out, what it was measured at, and where it stops being trustworthy. Free to read, licensed to use.

Read the specs →
Gear

What the kit is worth

Shoes, spikes, rackets, strings, suits and balls, brand by brand, measured by the papers, modelled by the physics, priced as a chance of winning.

Compare the kit →

Trade

The model's price beside the market's on every fixture, Kelly-sized paper tickets, and a walk-forward that says plainly whether any of it beats not betting.

Open the desk →

Academy

Six courses that teach the maths on this site, with figures drawn from the live models, worked examples and a certificate that verifies.

Start learning →

Library

Five books, the validation report, model cards and league data sheets as PDFs, certifications, and the model licences.

Browse →
P(x,y)=τ·e−λ

The equations

Forty equations, each with a picture that moves. Fitted, physics, literature or solved: the grade is on the card.

Watch them →

Pricing

Free for fans. The engine by the call for licensed operators, with the same maths at every tier.

See the tiers →
Maths is the weapon

The equations that decide it

Nothing here is a hunch. Each model is written down, fitted on results, and scored against the closing line. These are the six that do the most work.

FootballDixon–Coles

Goals are Poisson arrivals

P(x, y) = τρ · e−λλx/x! · e−μμy/y!
λ = attackhome × defenceaway × home advantage, decayed by time; τ fixes the low-score dependence.

Fitted on every result since 2014, blended with shots on target because shots are a less noisy signal than goals.

FootballFitted this week

The chase is real

Second-half scoring by half-time score, after controlling for how good both sides are. A side one goal down scores faster; a side ahead barely slows. The Manager game runs on this.

FootballDecision process

When to press, when to park

V(t, d) = maxa Σ P(goal | a, d) · V(t+1, d′)
Solved backwards from the final whistle for every minute and goal difference. The answer is a policy, not an opinion.

Chase variance when you are behind, kill it when ahead, time the switch by the clock. Try to beat it in the Manager game.

TennisMarkov chain

A 2% edge becomes 25%

P(game) = p4(1 + 4q + 10q2) + 20p3q3 · p2/(1 − 2pq)
Point → game → set → match, nested. Ratings from this season's ATP and WTA results give p for real players.

Morris importance says which points matter. Spend your big serves there. Break Point tests whether you do.

AthleticsOptimal control

Pace is a store, not a feeling

dv/dt = f − v/τ,  dE/dt = σ − f·v
Keller's runner: propulsive force limited, energy store draining. The optimum for 800 m is full force, then hold.

Split Second lets you set your own splits against the optimal ghost and watch the store drain.

BasketballBallistics

The rim is bigger from above

m dv/dt = mg − ½ρCdA|v|v + ½ρClA|v|²(ω̂×v̂)
Drag, gravity and the Magnus force integrated step by step. The most forgiving free throw leaves at about 52°.

The same integrator bends the free kick round the wall and dips the kick serve inside the line. See it in 3D on Films.

Honest numbers

Checked against the market

A model that never meets the closing line is a story. Ours is scored on every match it did not see, and the report says where it wins and where it does not.

Walk-forward test
27.3k
priced legs across thirteen leagues, every one before the result was known. Every league's score →
Beyond goals alone
+8.6%
of the gap to the market closed by adding shots on target
Execution beats selection
taking the best price rather than the average halves the cost of being in the market, and matters more than any staking rule. The seven rules →
Where we lose
0.594
mean Brier score across thirteen leagues, still behind the closing line's 0.578 in every one. On the desk, not betting beat all seven systematic rules. It says so on the page.
Five sports

One method, five arenas

FB

Football

Dixon–Coles with time decay and shots, contextual effects, referee tendencies, state-space form, style clusters, game-state effects, the strategy solver, pitch control, penalties as a game, free-kick flight.

TN

Tennis

Nested Markov chain, Morris point importance, live ratings from this season's tour results, serve flight with topspin.

BK

Basketball

Expected points per shot location, possession value, endgame decision trees, Pythagorean expectation, the forgiving arc.

AT

Athletics & Olympics

Keller optimal pacing, Banister fitness–fatigue and the taper, medal-table allocation by marginal return.

SW

Swimming

Critical power with cubic drag, even-pace optimality, the underwater breakout distance.