How it works

Overview

The Rugby Tournament Predictor uses a Monte Carlo simulation approach to forecast tournament outcomes. Rather than predicting a single result, it simulates the entire tournament thousands of times and reports how often each outcome occurred. This gives you probabilities rather than certainties.

The pipeline works in three steps:

1. Rate every team using historical match data and the Glicko-2 rating system
2. Simulate every match in the tournament using those ratings to generate win probabilities and scores
3. Repeat thousands of times and aggregate the results into the tables and charts you see

Glicko-2 ratings

Every team has a Glicko-2 rating, an evolution of the Elo system used in chess. Each team's rating has two components:

• Rating — the team's estimated strength. Higher is better. A new team starts at 1500.
• Rating deviation — how uncertain the system is about that rating. A team that has played few matches, or none recently, carries a larger deviation.

Ratings update after every match. A surprise upset causes a bigger shift than an expected result, and home advantage is factored in. The rankings also show a 1–99 version of the same number, which is easier to read and orders teams identically.

Club and international rugby are rated separately, from separate match records, and the two scales have no bridge between them. The site shows one at a time so it cannot imply a comparison the data does not support.

When a team is not ranked

Some teams are listed without a rank. There are two reasons, and neither is a judgement about the team.

Provisional

— Too few matches on record for the rating to be pinned down. A handful of results can put a rating almost anywhere, so ranking it against sides with hundreds of matches would overstate what is known.

Not comparable

— The team has never played any of the ranked field, directly or indirectly, so its rating sits on a scale that merely shares a number line with theirs. Inside club rugby this separates the northern and southern leagues from provincial competitions that have never met them.

This ranking and World Rugby's

The rankings page shows World Rugby's official position beside this model's. They are different systems built for different jobs — theirs is the sport's official standing, this one exists to feed a simulation — so where they disagree, the reason is usually structural rather than a difference of opinion about who is any good.

World Rugby's side of that table is from its own explanation of the rankings.

Why the two can differ

How much of a win counts

— Beyond fifteen points World Rugby stops reading the scoreboard and this model keeps reading it. A side that wins narrowly and often tends to sit higher in the official table; a side that wins by fifty tends to sit higher here.

What a match is worth

— A World Cup pool match moves an official rating twice as far as a July tour match does. Here they count the same, so a good or a bad World Cup shows up more sharply in the official table than in this one.

How far back the record goes

— Every official rating traces back through an unbroken chain of exchanges to the allocations made in 2003. This model rebuilds every rating from the matches themselves each time it runs, so a change to the record — a missing fixture recovered, a duplicate removed — is reflected all the way through rather than only from here on.

How confident the system is

— Two teams on the same rating are not equally well known here, and the same result moves a rarely-seen side much further than a settled one. The official exchange does not vary that way.

What the ranking is for

— An official standing has to place every member union. This one declines to place a team the record cannot pin down, which is why dozens of sides carry an official rank and no rank here.

Neither table is a correction of the other, and the official ranking is never an input to anything on this site — not a feature, not a prior, not a tiebreak. That is what makes the comparison worth publishing: two orderings built from the same results by different rules can disagree, and one built from the other could not. Where they agree, and near the top of the table they agree almost exactly, that is a check the model has passed rather than a coincidence.

Monte Carlo simulation

A single simulation plays out every match in the tournament using the teams' current ratings. Each match result is randomly sampled from the predicted probabilities, so the outcome varies each time. After all matches are played, standings are computed with bonus points and tiebreakers.

This process is repeated (typically 5,000 times). The final output reports how often each outcome occurred across all simulations. For example, if Ireland finished first in 3,200 out of 5,000 simulations, their Win % is 64.0%.

A fixture that has been played is “locked in”: every simulation replays its real score instead of drawing a new one, so the forecast is conditional on everything that has actually happened and narrows as the tournament goes on. Results are matched to fixtures by the two teams involved and the window the tournament is played in.

One consequence to keep in mind while reading a table: a locked fixture's probability is 100% for the result it had. That is not the model having been certain, and it is why a tournament's Results tab does not grade the forecast — scoring a prediction means predicting from what was known beforehand, which the model performance page does across every match on record.

What the model reads

A forecast is built in two layers. The rating comes first and carries most of the weight: it already contains everything a team has done, at the strength of the opposition it did it against. A gradient boosting model then sits on top of it and adjusts, reading 28 features — the rating gap, recent form weighted by the quality of the opposition, the head-to-head record between those two sides, rest days since each last played, and which way each side's form is trending. Home advantage is applied in the rating layer beneath it rather than being one of the 28.

Gradient boosting was chosen for the shape of the problem rather than for its own sake. There are 3,673 international matches on record, which is a small table of numbers by the standards of machine learning. Tree-based models handle that well: they cope with features on completely different scales, they do not assume any relationship is a straight line, and they handle a genuinely missing value without inventing one to fill the gap. A neural network wants far more examples than this sport has ever produced.

The first question is whether the machine learning earns its place at all. Trained before a cutoff and scored on 551 matches it had never seen, it moves the winner call from 72.8% to 73.5% and the margin error by about half a point, and does nothing at all for predicted totals. That is the honest size of it, and it is why the adjustment is capped: the model nudges the rating, it does not overrule it. The current figures are on model performance.

The second question is which learner should do it, and the answer turns out to be that it barely matters. Six alternatives were tried against the shipped one — plain regularised regression, and five other tree-based methods — with everything else held identical. The two strongest were then run head to head properly, over four thousand matches, each one predicted by a model trained only on the matches before it.

They finished level. On international rugby they call the same proportion of winners to five decimal places, and across both halves of the app the four measures split evenly between them. Choosing between the two best algorithms is worth less than a twentieth of what having one there at all is worth, and on internationals it is worth nothing measurable.

Once the rating has done its work and the adjustment is capped, the choice of algorithm is close to a free one — which is the same lesson as the section below, arriving from the other direction.

Why so simple a model works

The obvious objection to all of this is that the model is too thin. It knows almost nothing a knowledgeable supporter knows — not who is fit, not who is in form, not who has just changed coach — and it still calls about seven matches in ten. That is worth explaining, because the answer is the single idea the whole design rests on.

A rating is not a measurement of one thing. It is a running summary of results, and a result is the joint product of everything a team is: its depth, its coaching, its set-piece, its conditioning, the players it can call on. Anything that persistently helps a side win shows up as a persistently higher rating, without ever having been named as a variable. The rating does not know Ireland have a good lineout. It knows Ireland keep beating people, which is the thing the lineout was supposed to explain.

That makes the test for a new input much sharper than “does this matter?” Almost everything matters. The question is whether it tells you something the results have not already told you, and whether you can know it before kick-off. Most of what a supporter would reach for fails one of those, and usually the first.

Home advantage is the exception that shows the rule. It is deliberately not in the rating, because it is a property of the fixture rather than of the team — so it is applied separately, and it is worth roughly four points to an international side and six to a club. A team's rating travels with it; the ground does not.

The numbers bear the argument out. Rating alone calls 70.9% of the 3,673 international matches on record. Adding the machine-learning layer on top of it, measured properly on matches it had never seen, moves the same test from 72.8% to 73.5%. The second layer is real, and it is small, and that ordering is the point rather than a disappointment.

Accuracy is the weaker evidence, though. The stronger evidence is calibration across the fixture list: the rating engine is checked in ten groups running from the closest fixtures to the most lopsided, and on international rugby all ten land inside their margin of error. A model blind to something important would give itself away there — it would be right about even matches and wrong about mismatches, or the reverse. It is not. Club rugby does not yet pass that check, and model performance shows exactly where it fails rather than reporting the average and moving on.

There is a cost to this design and it should be stated plainly. A summary of what has happened is slow to notice a change. A new coach, a wave of injuries, a side genuinely in transition — the rating only learns about any of it from results, so it lags a real step change by several matches. That is the honest weakness here, and it is not one more features would fix, because the missing information is not in the record yet either.

Which leaves the reason simplicity is a choice rather than a shortcut. Every extra column buys some signal and pays for it in noise, and on a few thousand matches that trade is often a losing one. A model that is right about the size of its own uncertainty is worth more than a richer one that is confidently wrong.

Surely that matters?

Several things a supporter would expect to count are deliberately not read. In each case the reason is a measurement rather than an oversight, and where a thing was tested and dropped, the test is described below.

Team selection

A forecast does not move when a side names its XV. Two reasons, and the second is the more interesting one.

The practical reason is that the player data is a single recent snapshot — caps, age, club, World Cup pedigree, as they stand today. Applying that to a fixture from 2015 would credit the match to a squad that did not exist at the time, which would flatter the model against its own history.

The substantive reason is that it was tested directly. For 768 players with enough matches both in and out of the matchday squad, the difference their presence made was measured against what the team's rating expected. Not one of them stands out beyond what chance produces across that many comparisons — the working is on the squads page. That is not a claim that players do not matter. It is that a squad's strength is already inside the rating, because the rating was built from the results those players produced.

Weather

Weather has a real and measurable effect on scoring. Every international venue's historical conditions are on file, and across the 3,167 matches carrying both a reading and a score, wind costs about 1.6 points off the match total per 10 km/h while temperature adds about 2.1 points per 10 °C. Both are measured against the era the match was played in, without which the long rise in scoring is attributed to the weather instead.

It is still switched off, because the effect was fed into the model end to end and the forecasts came out worse. Scoring patterns have changed enormously since 1871, so the model weights recent matches far more heavily than old ones — which leaves a much smaller effective training sample than the raw match count suggests. Three more columns cost more in added noise than they return in signal.

There is a second reason that would bite even if the first did not: nothing can supply the weather for a match six months away, and a tournament forecast is made months ahead.

Altitude

Also absent, and the reason is that the record is too thin to settle it either way. Every international venue carries a terrain elevation, but only 150 of the 3,673 matches on record were played at 1,200 metres or above, and 67 at 1,500 — a sample small enough that an effect of the size anyone would claim for altitude cannot be told apart from chance. The club half cannot be checked at all: club venues are not geocoded, so the database holds no elevation for any of them.

Note that none of this contradicts the folklore about touring sides at Ellis Park. Whatever advantage a side has at its own altitude is already in its rating, having been earned in results at that ground. What is not established is a separate effect on top of that, and this record is not large enough to establish one.

Possession, territory and tackle counts

Match statistics are published on each team's profile and are never an input. The first reason is timing: they are products of the match rather than facts available before it. Nobody knows who will win possession until they have won it, so a statistic like that cannot help predict the result — it can only describe it afterwards.

The obvious repair is to use a team's historical averages instead, and that mostly restates the rating. A side that wins collisions is a side that wins matches, and the rating already counts the wins. Coverage is also partial: World Rugby publishes statistics for 1,823 of the fixtures on record, concentrated on the major competitions.

Long-haul travel

Distance travelled and time-zone shift were computed for 99% of the match record and offered to the model. The winner call did not move, and the margin error came out slightly worse, so neither was kept. All the model carries is a crude flag for which hemisphere each side comes from, and it barely registers.

Home advantage itself is very much used, and is one of the larger factors in any prediction. It is the long-haul part specifically that does not survive measurement.

News, rumours and official rankings

The news and video pages are for reading, and nothing on them reaches a forecast. World Rugby's own ranking is published beside this model's on the rankings page, and is deliberately not an input either — not a feature, not a tiebreak. The whole value of showing it is that the two can disagree, which they cannot do if one is built from the other.

Reading a probability

A published probability carries real error, and the model performance page is where that is measured rather than asserted. Three things worth knowing when reading it:

Accuracy

— The share of matches whose winner was called correctly, over the whole match record. That record starts in 1871, and the professional era is far higher-scoring, so an all-time margin error is not the error to expect on a modern fixture. Each figure names the range it covers.

Calibration

— Whether a stated 70% happens 70% of the time. A gap only counts as a fault if it is larger than the margin of error of the group it sits in, so that margin is shown beside it. The same check is repeated across the fixture list, because a model can be right on average and still wrong on close games or on mismatches.

Log loss and Brier score

— Two ways of scoring probabilities rather than calls. Both are better when lower, and both punish a confident wrong answer harder than a hesitant one.

The headline accuracy figure comes from a walk-forward test: every match is predicted from ratings that stop the day before it, so no forecast has ever seen its own result. It scores the rating engine alone. The holdout table below it scores the blended forecast that is actually published, on matches the model was never trained on.

Reading the standings table

The standings table shows averages across all simulations:

Win %

— Probability of winning the tournament (finishing first overall).

Avg Pts

— Average tournament points earned under that competition's bonus point system (see Scoring below).

Avg PD

— Average point differential (points scored minus points conceded).

Avg W / D / L

— Average number of wins, draws, and losses across all simulations. These are averages, so they can be fractional.

GS %

— Grand Slam probability — the chance of winning every match in the tournament. Only shown for the Six Nations.

Position distribution

Below the standings is a heatmap showing what percentage of simulations each team finished in each position. Darker cells indicate a higher likelihood. This reveals the full range of possible outcomes — a team might be most likely to finish 2nd but still has a realistic chance of finishing 1st or 4th.

Pools and knockout brackets

A World Cup is simulated the same way, with one difference: the pool stage decides who enters the bracket, and the bracket is then played out tie by tie. Every simulation produces its own set of qualifiers, so no knockout tie has fixed participants — who plays whom is an outcome rather than a fixture.

That changes how three parts of the page read:

Pool tables

— The numbered columns are how often the team finished in that place in its own pool, not in one overall table of every entrant. Pools are listed in expected finishing order.

How far each team gets

— The share of simulations in which the team reached each round. 3rd is winning the bronze final, which is a branch off the semi-finals rather than a step towards the trophy, so it does not sit between the semi-final and the final.

Bracket ties

— Each tie lists the teams that turned up in it. The first figure is how often the team occupied one of the two slots; the second, shaded darker, is how often it occupied a slot and won. The second figure can never exceed the first.

The Likely path view draws the same bracket as a conventional tree. To do that it has to fix one reading — each tie settled in favour of whichever side comes out of it most often — so it shows one likely path rather than a likely bracket. The odds against any exact draw are long.

Two details of a knockout are conventions rather than published rules. A tie that simulates as a draw is settled by sampling the two win probabilities renormalised, standing in for extra time and kicks. And where the published bracket allows more than one way to seat the four best third-placed qualifiers, the first eligible seating is taken — World Rugby has not released the table that resolves those cases. It moves individual paths, not the shape of the draw.

Match predictions

Each match card shows:

• Average score — where the simulated results are centred, not a scoreline the model expects
• Probability bar — the green segment represents the home team's win probability, the red segment the away team's. The draw probability is shown beneath when significant.
• Margin chart — how far apart the two sides finished across the runs, positive toward the home team

The home team is always shown on the left. The three answer different questions: the bar says who wins, the chart says by how much, and the score says where those two are centred.

How a score is arrived at

Each simulated match is two separate draws. One sets the total — how much scoring the fixture produces — and one sets the margin, the gap between the sides. The two are drawn independently and then split down the middle: the winner takes half the total plus half the gap, the loser the rest.

So a seven-point margin is not a scoreline. Against a low-scoring afternoon it is 17–10; against an open one, 27–20; against a shootout, 59–52. That is why the margin chart carries a note about the range of totals underneath it — one bar of it covers every one of those results.

It also means moving along that chart moves both sides. Two points of extra margin is a point onto the winner and a point off the loser, not two points onto one team.

Why the average score is a score nobody expects

The gap shown is an average over both outcomes, and it describes neither of them. Take a fixture where the home side are around 60% to win. When they win, they typically win by something like 17 points; when they lose, they typically lose by something like 12. Averaging a comfortable home win against a comfortable away one leaves a gap of about seven — a margin that describes the fixture as a whole and not either way it can go.

The scoreline that comes out of it turns up in roughly one simulated match in a thousand. That is not a flaw in the average: no scoreline does much better, because results are spread far too widely for any single one to be likely, and across the fixtures we have checked the commonest of all sits under 1%. A predicted score is a centre of gravity. It is a genuinely useful thing to know, and it is not a prediction of the result.

Read the probability bar for who wins and the margin chart for how close it will be. The score is there to give those a scale.

Not every fixture on the upcoming page carries a tournament forecast. A July tour or a domestic cup is not simulated as a competition, so those fixtures show a one-off prediction instead where both teams are covered — the same answer the match predictor gives. No history is kept for it, so it has no movement to show. That is a limit of what is recorded rather than of what could be: a one-off would move for the same reason a tournament fixture does.

What moves a forecast

One thing: the two sides' ratings, drifting as they and their opponents play other matches. The prediction reads ratings, venue and rest, and nothing else — not team selection, which is switched off, and not weather. The date it is measured from follows the newest match on record rather than today, so a quiet week moves nothing at all.

Which means nothing is learned about a fixture itself as it draws closer. There is no team news to arrive and no conditions to firm up. If neither side plays between now and kick-off, the forecast should sit still, and it does.

So a moving line is quieter than it looks. Across every snapshot on file the middle move is under a point of win probability. The large jumps that do appear are mostly the model itself changing — a retrain, a recalibration, a fixed bug — rather than evidence about the match. The largest in the whole record, eighty-five points inside half an hour, was a correction to which side was at home. Updates records what each run changed, which is what tells the two apart.

What if

The What if tab answers a conditional question: given that a match goes a particular way, what happens to everything downstream. Nothing is re-simulated for it. Each simulation's results are recorded, so assuming a result means keeping the simulations where it happened and reading the outcome off those.

That has two consequences worth knowing. The figures are exact rather than approximate — they are the same runs behind the published forecast, counted a second way — and they always agree with the headline numbers when nothing is assumed. But a combination the simulation never produced has no answer at all: pin five unlikely results together and there may be a handful of surviving runs, or none. The number of runs every figure rests on is shown above them, and the page says when that number is thin.

A scenario lives in the address bar, so a link carries the assumptions with it.

Scoring system

Most competitions here use the standard World Rugby bonus point system:

• Win: 4 points
• Draw: 2 points
• Loss: 0 points
• Losing bonus: +1 point for losing by 7 or fewer
• Try bonus: +1 point for scoring four or more tries

Bonus rules are read per competition rather than assumed. The Top 14 awards its losing bonus at five points rather than seven, and it and both European cups award the attacking bonus for scoring three more tries than the opponent rather than four in absolute.

Tries are simulated alongside the score in international rugby, from the relationship between the two in matches where both were recorded. Club match statistics are not available, so club competitions award the attacking bonus on a points threshold instead and their tables carry no tries column.

Tiebreakers are applied in this order:

1. Tournament points
2. Point differential
3. Points scored
4. Head-to-head record

Unlike the bonus rules, that order is not yet read per competition, and three registered competitions do not use it: both European cups and Super Rugby Pacific separate level sides on wins first. It only bites on an exact tie, so it moves a placing rather than a qualification in most simulated seasons — but where it does differ, the table here follows the order above rather than the competition's own.

Results

The Results tab lists the fixtures of an edition that have been played, and scores each one against the forecast it had beforehand. That forecast is recorded while the fixture is still to come and never rewritten afterwards: once a match is played every simulation replays its real score, so the probability published beside it becomes 100% for what happened, and scoring that would only ever agree with itself.

A fixture played before that record began cannot be scored and says so. A handful of matches is too small a sample to read as an accuracy rate in any case — model performance measures the same thing across every match on record.

Where the data comes from

Every source behind these numbers is listed on about and sources, along with what this app is and is not.