Analysing the Six Nations - Week 2

We’ve had another rollercoaster weekend in the Six Nations, so it’s time to follow-on from my predictions from last week and have a look first of all at how my statistical model faired, and also at what we might expect in the next weekend’s worth of fixtures.

How did my predictions do?

So, the predictions for the weekend just past were:

So we were expecting Irish, Scottish, and French victories. Now, if you’ve not caught up yet, you might want to look away briefly.

In the end Ireland beat Italy 20-13, Scotland beat England 31-20, and France beat Wales 12-54. So overall, it did pretty well, correctly predicting the winner of all three matches. For a second week it’s somewhat overestimated the actual scorelines (though it was pretty close for Scotland). Though perhaps it could be argued the other way for the France game, where the model was always a little over-confident that Wales would manage to keep the score close.

So the model is now six for six.

What about next week?

First, a warning. I need to retrain the model after this weekend’s results, and the setup for doing this isn’t working as automatically as I would like, so I may need to update these later in the week. That said, the current predictions for the next round of matches are:

I have my suspicions that this week is where the model will break; a Wales win doesn’t seem right to me, but it would certainly continue to muddy the waters over Townsend’s continued tenure. Of the three games this weekend the France v Italy game is the most likely to have a significant effect on the final state of the competition (in statistical terms, it has the highest mutual information with the final state of the tournament), and that’s probably no great surprise, since an upset there would prevent France achieving the Grand Slam, while also pulling Italy further up the table.

Whiler we’re on specific predictions, we can look ahead to the final two weeks:

Of those matches anything involving France is likely to have the most impact on the tournament, followed by the first game of Super Saturday, where a Scottish win would bring maximal chaos to the final standings.

Speaking of final standings…

Predicted final standings

Compared to last week, Scotland have been pulled back up the table to third, while France looks to already have solidified a first place finish in the model.

All to play for, and with the surprising suggestion that Scotland and England might be fighting it out for second. I’ll believe it when I see it.

Indeed, France finishing first is now predicted with 83% probability (beating Scotland has the largest single effect on this, pushing the probability up to 98%; make of that what you will). England have an 8% chance of topping the table (beating France is, unsurprisingly, their best route to the top). Scotland are an outside contender, with a 4.5% chance of taking overall victory (beating Ireland being the most critical game, though surpassing France clearly requires a near-perfect performance for the remainder of the tournament), and Ireland have a 2% chance (though beating England would put their chances ahead of Scotland). Italy would need to beat France to have any chance of coming first, but there is a slim (2%) chance of this happening. However, in 1000 simulated matches the model predicts a 0.0% probability for Wales reaching the top of the table.

Let’s close for the moment with the overall predicted probabilities for each team’s final position in the table. It’s worth noting that this table and the previous one appear to be in contradiction; the last table is the most likely final table, which is not quite the same as the overall most likely outcome for each team (so those of us with split Scotland-Ireland loyalties can confidently remain stressed).