And more importantly – what is Scotland’s most likely fate?
As a scientist, I am often asked: how does the Six Nations look this year, and can you tell me the result? Will there be another Irish grand slam? Will Scotland win…or even get the wooden spoon? Will Italy finally emerge from the doldrums?
As with modern politics, nobody can say what will actually happen once the dust settles. But unlike politics, these questions can be looked at from the viewpoint of statistical likelihood to at least give us an idea.
In a manner reminiscent of those 1980s football manager games which were largely just spreadsheets with nice interfaces, I have digitally simulated the Six Nations to estimate the results: running this a million times or so gives an indication of what is statistically probable and what is not.
The simulator works by estimating results of games based on the world ranking points difference – the likelihood of the result given by an s-shaped curve, with 50/50 for a ranking difference of 0, and essentially 100/0 for differences above 10. To these raw scores, a home advantage of 3 points is added, and a random “swing” is added to simulate variations in performance. Finally, the ranking points are updated according to the result during the tournament as they would be by World Rugby.
The Six Nations can be simulated by running the series of 15 matches, and making a virtual table, based on wins, losses and points differential. Try bonus points are not so easy, being largely related to the “character” of the match, so are not included. I have run the simulator a million times based on this model for 2017, 2018 and 2019.
For 2017 the simulator correctly predicted the results of 13 of the matches. The two upsets were Scotland vs Ireland (42% likelihood) and Ireland vs England (29%). The overall table was predicted correctly, with Scotland predicted to be the most likely in fourth or fifth (France, Scotland and Wales were fairly interchangeable in 5th , 4th and 3rd ).
For 2018, 12 matches were correctly predicted, but again England’s downfall was not, with unlikely losses to Scotland (22%), France (2%) and then Ireland (8%) not predicted. Aside from England, the overall table positions were in correct order – with Scotland’s most likely predicted spot being fourth.
And so to 2019.
The most likely prediction for an overall winner is Ireland with 63% chance of winning, as they are predicted to win all their games. Wales are the next most likely winner at 32%. The final game of Ireland against Wales is shaping to be the tournament decider according to the data.
Scotland’s outlook is not so good, with just two wins predicted against Italy (99% chance of winning) and France (61%), but also a reasonable chance of overturning Wales (29%). The Ireland (10%) and England (8%) games look highly likely to be losses.
Compared to 2017, the home games vs Wales and Ireland are seen as less likely to turn out in our favour, but we are predicted to do better in France and in England, the latter still very unlikely however.
|H Win (%)||A Win (%)||Draw (%)||Likely Winner|
|SCO v ITA (H)||99.19||0.75||0.06||Scotland|
|SCO v IRE (H)||9.75||89.71||0.53||Ireland|
|FRA v SCO (A)||38.01||60.85||1.14||Scotland|
|SCO v WAL (H)||29.03||69.99||0.99||Wales|
|ENG v SCO (A)||91.38||8.19||0.43||England|
All of this results in Scotland finishing in a most likely position of fourth (58%) or fifth (22%), but possibly third (12%). We won the tournament in just 1.2% of a million simulations, but in better news the wooden spoon is, at least, less likely at 0.5%. The most likely table order is Ireland, Wales, England, Scotland, France and Italy.
2019 Six Nations % likelihood of finishing position by country
It looks like we have a challenge ahead of us.
As in previous years it looks tight in the 3rd to 5th spots, and bonus points will be crucial in deciding the middle of the order, so plenty of tries please Gregor!
Editors note: this is not a sponsored gambling post so please don’t use the information in this article to gamble irresponsibly! All data is subject to author’s own interpretation.