Football, modelled with the rigour of quantitative research.
Rondo Research was founded by Lucas da Silva, a quantitative researcher and PhD candidate in financial mathematics. He applies his modelling expertise to football: calibrated probabilities, full distributions, Monte Carlo simulation, out-of-sample validation, and limits set down in black and white.
- Education
- PhD candidate in mathematics — financial mathematics
- Background
- Insurance, quantitative analysis, then quantitative research applied to football
- Specialisms
- Probabilistic modelling, calibration, Monte Carlo simulation, model risk
From risk models
to football.
Three fields, one question: what is the probability of this event, and how do we know whether it is right? Football is not a change of profession; it is a new subject for the same methods.
- 01Insurance
Actuarial analyst
Estimating the probability and cost of uncertain events, then checking, as claims came in, that the probabilities used had held. There, a number commits a balance sheet; it has to be justified.
- 02Quantitative finance
Quantitative analyst
Risk models calibrated on data, Monte Carlo simulation, and one constant requirement: know what the model cannot see, and say so before the market makes the point for you.
- 03Rondo Research
Founder, quantitative researcher
Modelling expertise applied to another uncertain object: the football match. A goals model, simulated seasons, calibration measured and published.
Why a quantitative researcher
looks at football.
A match is not an opinion to defend: it is an uncertain event, whose distribution can be estimated, whose consequences can be simulated, and whose estimate can be checked on data that played no part in producing it. That is exactly what quantitative research is about.
A match is a probability distribution, not a prediction.
A probabilistic model does not name a winner: it estimates the distribution of what can happen. That is how we treat a match — three outcomes, a full grid of scorelines, each with its probability. No “favourite”, just quantified uncertainty.
Calibration first.
A probability is right if the “20%” events do happen one time in five. It is the first question quantitative research asks of a model, and the one we ask of ours, band by band, across thousands of matches.
A distribution, not a point.
The mean says nothing about risk: you need the whole distribution, and above all its tails. For every season, we give the full distribution of final positions, from the title to relegation, rather than a single “predicted” table.
Simulate rather than guess.
What is hard to compute by hand can be simulated. The rest of the season is replayed thousands of times by Monte Carlo simulation, from the estimated strengths: title or survival probabilities are frequencies, not intuition.
Judge the model out of sample.
A model that explains the past perfectly has proved nothing yet. The only test that counts is on matches it was not fitted on: that is the validation discipline we hold ourselves to, and the published calibration reports on it.
Model risk is documented.
Every model is wrong somewhere; the question is where. Ours learns from the game as it is played: an injury or a transfer only enters it once it shows on the pitch. We write that down, in the same place as the numbers.
What a risk committee would demand of us.
At an insurer or on a quantitative desk, a model does not go into production on reputation alone. It has to be documented, dated and validated, and its limits must be known to those who use it. We hold ourselves to the same rules, whether you are a newsroom or a reinsurer.
Traceability
Every number points back to the computation that produced it, and that computation to a documented method. Nothing is adjusted by hand between the model and you.
Dated computations
A probability only means something at a given date. Every output carries the date of its computation: a report is tied to a precise state of the model.
Validation against the facts
Calibration is measured on real matches, after the event, and published as is — including where the model is most wrong.
Written limits
What the model cannot see, what it underestimates, what it does not cover: stated in the methodology, in the coverage page, and in every report that depends on it.
One approach,
and what it produces.
What is open can be checked today, free of charge. What we deliver carries an honest status: available, on request, or still in development.
Methodology
AvailableTeam strengths, the scoreline matrix, season simulation: every step described, like the methodology note for an internal model.
Read the methodology →Calibration
AvailableForecast against observed, published openly. The back-testing every buyer of a model should demand.
See the evidence →Model outputs
AvailableProjected tables, strengths, match probabilities, across 24 competitions, each dated to its computation.
Explore the modelling →Risk & insurance
On requestEvent probabilities, full distributions, scenarios and dated reports: independent pricing of a sporting risk.
Details for insurers →Clubs, media, agents
On requestQuantified season objectives, graphics for newsrooms, destinations compared: the same model, one question per profession.
Details for clubs →API & data
On requestProbabilities, scoreline matrices, strengths and calibration in documented JSON, for your own models.
Details for data teams →Player impact model
In developmentWhat a player’s presence changes to his team’s goals. Open as a pilot, with its limits written down before the results.
Where the pilot stands →A model is not taken at its word.
It is tested against the facts.
For each probability band, the forecast set against what actually happened. For a home win, the mean gap currently stands at 2.3%, measured over 2,094 matches. We publish it as is, including where the model performs worst.
Each point is a probability band; its size is the number of cases. On the diagonal, the model keeps its word. Here, across 2,094 matches (1X2 result), the mean gap between forecast and observed is 2.3%.
Four commitments,
verifiable without us.
A modelling firm is judged by what it is willing to show. Ours fit in four lines, and each one points to a page you can check for yourself.
Published methodology
The goals model, the simulation and their assumptions are described. Methodology →
Public calibration
Forecast against observed, openly available, good or bad. The evidence →
Dated figures
Every probability carries the date of the computation that produced it. The outputs →
Stated limits
What the model covers, and what it does not, written plainly. Coverage →
People who like to check.
What matters here is not a line on a CV, but the ability to doubt a number, trace where it comes from, and write up clearly what you found.
- Modelling and statistics — count models, simulation, out-of-sample validation.
- Engineering — Python for the computation pipeline, TypeScript for the website and the API.
- Writing — telling what a model says without betraying it.
We do not always have open positions. Apply anyway: we read everything and we reply, even when the answer is no. No cover letter — tell us instead what you have built, and what went wrong with it.
A modelling problem to put to us?
A risk to price, a season objective to quantify, a data feed to connect: get in touch. We come back to you with the figures that matter to you, dated, and with their limits.