For rugby followers the lengthy wait is sort of over, like Christmas the Six Nations comes every year to carry our spirits within the chilly winter months. For those who’re not very acquainted with rugby, the Six Nations is an annual event the place the highest nationwide sides in Europe (England, France, Eire, Italy, Scotland, Wales) every play 5 fixtures alternating who performs at house or away annually. All groups compete to win, however essentially the most coveted prize is a ‘Grandslam’ — the place a group wins all 5 of their fixtures. Given how aggressive the event is a Grandslam within reason uncommon, and because the event was expanded to 6 sides in 2000 there have solely been 13 Grandslams of a potential 25.
This yr, within the 2025 event, Eire come into the competitors competing for a 3rd consecutive collection win with stiff competitors from France, who’s home league (The Prime 14) has been electrical this yr within the European Champions Cup.
With that in thoughts, and provided that roughly half of tournaments have led to a Grandslam, how doubtless is a Grandslam in 2025? On this brief article we’ll discover how we are able to use earlier fixture outcomes and different info to make a greatest guess at how doubtless a Grandslam is. We’ll be specializing in linear fashions, and we’ll discover this from each the Frequentist and Bayesian Perspective. The fashions are constructed utilizing SciKit-Be taught and the Bayesian modelling library Bambi (which is constructed on prime of the wonderful PyMC framework).
Learn on to grasp how and why I estimate the chance of a Six Nations Grandslam to be round 30–40% in 2025.
Within the age of AI individuals are more and more used to mapping inputs to outputs with extremely correct predictions. Whether or not that is utilizing LLMs to generate pure language responses, Pc Imaginative and prescient fashions to tag photos and even Auto ML to foretell tabular datasets it’s more and more taken with no consideration that these fashions simply work.
Regardless of this, the connection between inputs and outputs naturally entails a stage of uncertainty — and when you find yourself working with small or noisy datasets, such as you typically see in sports activities, you will need to connect an estimate of uncertainty to your predictions. For instance, the opening fixture of the 2025 Six Nations France host Wales at house — we could predict that France will win, however how assured are we about this?
The dataset used for this evaluation is sourced from publicly accessible assets, equivalent to Wikipedia. The problem with predicting 2025 fixture outcomes is that the out-of-sample predictions are primarily based on panel knowledge, and group type usually fluctuates throughout the years as squads and managers change.
In our publicly sourced knowledge we collect stats from 2020–2024 together with:
- The age profile of squads
- The expertise of squads (i.e. variety of worldwide caps)
- The variety of distinct membership sides that make up a nationwide squad
- Earlier desk place
- Earlier fixture end result
- Whether or not there’s a change of coach because the earlier event
The info preparation right here is finished utilizing Pandas. Determine 1 exhibits how we merge the info on a fixture stage foundation, incorporating details about the squad for annually of the event. Taking a look at this we are able to see that in 2025:
- Eire have the oldest squad with a proportionally excessive variety of caps on common. This tells us that the squad is very established and, since Irish rugby is provincial, the squad is made up of solely 4 sides. Given the age profile of the facet and that they’ve a brand new coach for this event there could also be uncertainty over whether or not they might be at or close to the ‘peak’ as a squad
- France have one of many youngest squads on common and, on common, the bottom variety of caps. Regardless of this they’ve been performing exceptionally effectively, and got here second within the 2024 event suggesting their squad is on the rise
- England have the second youngest squad, however proportionally extra caps on common suggesting they’re attempting to steadiness youth with expertise within the 2025 event
- Scotland have the second oldest and probably the most capped squads within the event. They’ve a longtime facet and, arguably, underperformed in 2024 the place they got here in fourth place. Their facet could also be nearing its peak earlier than they undergo a interval of rebuilding
- Italy are in an analogous place to Scotland by way of common variety of caps, however with a barely youthful age profile. There was a variety of modifications in administration through the years however come into the competitors this yr with a longtime squad and the identical coach. They may shock folks this yr
- Wales are in a interval of rebuilding and have a younger and inexperienced squad and underperformed within the 2024 event the place they got here in final place
Since we’re utilizing linear strategies to foretell outcomes, I created a binary flag for whether or not or not the house facet gained the fixture, and for every fixture we’ll predict the chances of the house facet successful (i.e. sure/no). The likelihood of not successful at house is, implicitly, the identical as predicting that the away facet win.
Earlier than constructing a predictive mannequin, you will need to do some exploratory evaluation. Determine 2 exhibits the correlation plot for the options.
As you may anticipate, the place you completed final yr is very correlated to successful this yr. Likewise, your squad profile is very correlated with successful. Having a change of coach is correlated, however not as strongly — although this can be as a result of there are proportionally fewer cases the place this occurs between tournaments.
An vital consideration right here is whether or not there may be correlation amongst the inputs (options) of the mannequin, since autocorrelation can negatively affect mannequin reliability. We are able to see right here that there’s a robust correlation to the age and variety of caps, that is intuitive since older gamers will (on common) have extra caps. To accommodate this we substitute these inputs with a composite characteristic which represents the proportion of caps to age. We additionally take away a couple of of the much less correlated inputs from the mannequin, since typically much less is extra when becoming a mannequin to keep away from overfitting.
As soon as we have now recognized the options of our mannequin we are able to put together the info for coaching. Since this can be a panel knowledge downside we break up the info as beneath.
Mannequin Validation: We begin by validating the mannequin and getting an estimate of out-of-sample accuracy. To do that we back-test on earlier tournaments
- Prepare dataset — fixture outcomes 2020–2023
- Check dataset — fixture leads to 2024 event
Mannequin Predictions: We are able to create our predictive mannequin for 2025 for out-of-sample predictions as
- Prepare dataset — fixture outcomes from 2020–2024
- Prediction dataset — upcoming fixtures for 2025
We put together the dataset for modelling utilizing:
- One-hot encoding for fixtures
- MinMax scaling for numeric options
It is very important apply the scaling on every dataset individually to mitigate the danger of data leakage.
We are able to create our Frequentist mannequin utilizing SciKit-Be taught’s Logistic Regression classifier. Determine 3 exhibits the Confusion Matrix for the back-testing on 2020–2024 fixtures
In Determine 3 we are able to see that the accuracy of the mannequin is round 73%. You could be questioning why there’s a complete of 30 fixtures for the 2024 predictions when there’s solely 15 fixtures every event? The rationale for that is, with the intention to enhance mannequin accuracy, we stack the info in order that we get a Dwelling and Away end result for every fixture. It’s because sides solely play one another as soon as per yr and swap house and away every event. We, as people, perceive that France v Wales is identical as Wales v France, however the mannequin can’t straight perceive this. To do that we swap house and away, after which swap the binary flag for house win, preserving the integrity of the info.
For instance:
- 2024 Wales v France → HomeWin = 0 [original]
- 2024 France v Wales → HomeWin = 1 [inverted]
Utilizing our out-of-sample predictions for 2025 we get the beneath win possibilities for the upcoming 2025 event.
In Desk 1 we see that:
- Eire are anticipated to do effectively primarily based on earlier type and an opportunity to get a ‘three-peat’ (third consecutive title)
- France are anticipated to do very effectively, significantly at house
- England have a fairly robust likelihood, however in all chance will end mid-table
- Scotland are anticipated to have the slight edge within the Calcutta cup once more this yr, however will probably be tight
- Italy and Wales will likely be anticipated to compete to keep away from the picket spoon, with Italy anticipated to be slight favourites
As soon as we’ve estimated the chances for the fixtures, we are able to use Monte Carlo strategies to simulate the event and estimate the chance of a Six Nations Grandslam. Monte Carlo strategies use random sampling to estimate possibilities and quantify uncertainty.
To do that we run 10,000 event simulations making a random selection seeded with our win possibilities. To do that we use Numpy’s random selection methodology for our set of house and away fixtures with the corresponding win possibilities. Determine 4 exhibits us a violin plot for the simulated variety of wins per event per facet
It’s value noting that these factors are jittered to enhance the aesthetics of the plot, however general, we are able to see from Determine 4 that:
- France and Eire are clear favourites to win, although primarily based on previous type Eire may be anticipated to be extra prone to win a Grandslam
- It’s vital to notice that previous type doesn’t all the time predict present type, for instance Eire have a brand new head coach, the oldest group and are a rebuild section following the retirement of their key playmaker, Jonny Sexton
- England and Scotland may trigger some upsets, however are prone to be battling it out for the upper-mid desk place. Based mostly on current type Scotland usually tend to get 3 wins and England 2 wins, however there may be extra uncertainty on how England may do within the competitors
- Wales and Italy are prone to be scrapping it out for the underside of the desk, with each groups pretty prone to choose up at the very least one win within the event, although this can be the Italy-Wales fixture, which Italy are potential favourites for given house benefit in 2025
General, this mannequin seems in-line with what many pundits have mentioned about their expectations for the event. One limitation of this method is that we’re making the belief that the win possibilities of the fixtures are usually distributed across the level estimates from the Logistic Regression mannequin. This can be a robust assumption.
One other assumption of the mannequin is that the end result of a win in a single fixture doesn’t have an effect on the win possibilities in different fixtures, i.e. that fixtures are impartial. Personally, I don’t assume that is completely unreasonable since that is skilled sport, and sides are coached to have a successful mindset in every fixture — and sometimes sides are inconsistent between fixtures. For instance, Scotland carried out very effectively towards England in 2024 however went on to lose subsequent fixtures and England went on to beat Eire who finally gained the event.
We are able to keep away from making robust assumptions on the distribution of win possibilities throughout the event by as an alternative sampling these straight. To do that we are able to use Markov Chain Monte Carlo (MCMC) strategies — which offer a Bayesian method to estimating the distribution of mannequin parameters by way of random sampling. Primarily, the fashions work by updating their prior beliefs on the distribution of mannequin parameters because the sampler observes actual knowledge. As soon as the mannequin converges across the ‘true’ distributions it samples straight from the posterior distribution of the mannequin parameters. Within the case of a Logistic Regression mannequin, we mannequin the goal variable as a Bernoulli distribution.
There are potential drawbacks to utilizing Bayesian Logistic Regression fashions, for instance they are often delicate to the priors that the mannequin assumes, the prediction possibilities is probably not effectively calibrated (relying on the prior assumptions) and, within the case of a hierarchical mannequin, there could also be ‘shrinkage’. Shrinkage happens the place hierarchy ranges are pulled the imply of the guardian stage — in sports activities modelling the affect of that is that groups which can be on the prime and backside of the desk could have their estimates pulled up or down in direction of the imply of the desk.
Determine 5 exhibits the violin plot for the estimated distribution of wins taken straight from the predictive posterior distribution. The distributions look a little bit extra unfold out than from our Logistic Regression, probably indicating the upper unfold of uncertainty in our mannequin. Wanting on the plot there could also be some shrinkage as each Wales and Italy are anticipated to do higher than within the Logistic Regression mannequin, and Eire seem to have much less likelihood of a Grandslam.
We are able to use our samples to straight estimate the likelihood of a Grandslam by merely taking the variety of Grandslams over the variety of tournaments, that is proven in Determine 6.
We are able to then evaluate our mannequin outcomes to revealed odds. I discovered some odds revealed by a wager maker on January 1st that gave the next odds:
- No Winner 5/6 [this implies Any Winner odds of 6/5]
- Eire 10/3
- France 9/2
- England 9/1
- Scotland 14/1
- Wales 500/1
- Italy 2000/1
We are able to convert the revealed odds to approximate possibilities utilizing the beneath formulation:
There are two issues to think about right here:
- Firstly, betting corporations publish implied odds fairly than true odds since they think about a revenue margin for the percentages they publish (i.e. the home all the time wins)
- Secondly, odds change as new info turns into accessible. Our evaluation is comparatively easy and doesn’t think about accidents or different components. That is vital since there have been notable accidents and withdrawals forward of the beginning of the event so the percentages could have modified. Because of this I’m evaluating the percentages we’ve estimated to ones revealed in the beginning of the yr the place current accidents gained’t have an effect on the revealed odds.
So how do our fashions evaluate to revealed odds? Our Frequentist mannequin was surprisingly shut, and our Bayesian mannequin implied there was much less certainty on the chance of a Six Nations Grandslam. In Desk 2 you possibly can see a comparability of the transformed odds and our estimated possibilities
General, our estimates don’t look unreasonable regardless of the comparatively small and sparse dataset we have been utilizing.
Our evaluation discovered that:
- Within the 2025 Six Nations France prone to find yourself punching above their weight given the comparatively youthful facet they’ve obtained
- Eire look the most certainly to get a Grandslam, however that is primarily based on previous efficiency. With a brand new coach, ageing squad and altering of playmakers the outlook is much less sure
- England’s True Odds are prone to be worse than their Implied Odds and primarily based on previous efficiency ought to intention for a robust mid-table place. They’ve one of many youngest squads however with extra caps than different robust sides relative to their age profile. They’ve the potential to be disruptive within the event
- Scotland have a greater likelihood of a Grandslam than England and are prone to be additionally competing for a robust mid-table place. They’ve the second oldest and most skilled group after Eire and could also be at or close to their peak as a squad. Might or not it’s now or by no means for this squad?
- Wales and Italy are unlikely to be excessive performers within the 2025 Six Nations, and Italy will likely be vying to complete above Wales for the second yr working
- There’s a fairly robust likelihood of a Grandslam by any group, round a 30–40% likelihood
- This may very well be a really aggressive event general with many sides having a very good likelihood of successful
On this article we’ve seen how we are able to leverage Frequentist and Bayesian strategies to quantify uncertainty across the doubtless winners of the Six Nations in 2025. While our fashions have been comparatively easy and constrained to utilizing a small dataset our possibilities weren’t too dissimilar from revealed odds, although these have since modified as occasions have developed (accidents, call-ups, and so forth.).
Thanks for studying this text, I hope its been fascinating. For those who’re curious about studying extra in regards to the evaluation yow will discover the total code on my GitHub account.
