Rugby Club Ranks

New Site, New Me.

2026-03-25T00:00:00+00:00

This project has been simmering for some time. About a year ago I started a complete refactor to move to a more abstracted framework, and while it took a while it was successful. I now have my rugby predictions running on a server at a reliable cadence, I have automated posting of most of that content, and I have achieved some accuracies that I’m happy with.

Now I get to decide what I do with it next. I set out to be able to predict any match in URBA or the PWR as well as I could Le Crunch or the Bledisloe Cup, so intentionally limited my inputs to this model to just the two teams involved and the final score. I wanted to add to the coverage of the sport, not just on those matches that were already being covered.

I’ve acomplished that with my club model, then developed a player-based model that only requires teamsheets to be added but allows for player and club rankings. Now I have predictions being made for every professional match that I can find data for, and can dig into the best ways to share out my data and visualize what I’ve developed. That’s what this new site is for.

But right now, finding the BEST visulizations feels more like banging my head against the wall than a fun coding project. I’ve got some ideas for things like in-match win probabilities, player history pages, or match interest ratings, but those are on hold for a while while I take a bit of a break. If you’ve got something you’d like to see from my rugby data, toss me the idea.

And Now Some Non-Rugby Things

Here’s the pivot bit. In doing all this, I’ve also made a pretty flexible framework for multiplayer competitions, which can be applied to some other sports. This feels more fun/engaging to me right now - I have some experimental applications to other sports I watch, and they’ve got a bit of a different tack. While I intentially limited my input features for rugby, I have some more data-intensive applications in mind. My hope is that playing in those spaces may lead to some learnings I can apply back to the rugby stuff, and vice versa. Ideally I can find a fun wrinkle for each application. More to come on those later.

This is entirely separate from my actual paying job, however, so don’t expect any firm roadmaps. If you’re invested in this continuing or expanding, let me know. If you’re instead looking for some predictive help for your problems, reach out here for some consulting. I ramble a lot less in that work.

How Strong Are New Teams?

2024-02-27T11:00:00+00:00

MLR is starting up again, which means its another round of changing teams. This year we have lost three teams and gained three, keeping the total at 12. Rugby ATL was sold, and new ownership has moved the team to Los Angeles. With the move comes a rebrand, which is about as bad as the last one was, but also changes up the squad enough to basically be a new team. Both New York and Toronto have folded, and been replaced by one planned expansion - the Miami Sharks - and one surprise team, Anthem, in North Carolina - a development oriented squad that is a joint effort of World Rugby and USA Rugby. This leaves us with just 9 teams we have some historical performance for, and 3 that we need to start making predictions for.

Usually, a new team is given a predefined mean rating and a very high variance, with that variance decreasing over time as the team plays some matches. Those matches won’t have much of an impact on the new teams’ opponents, because of the high variances, and we should arrive at a decent rating for the new teams within just a few matches. But we have the opportunity to come up with a more intelligent bayesian prior - essentially just a best current guess - at the new team’s ratings if we look at the squads that have been announced.

These are the rankings for the nine returning clubs:

We have the two finalists at the top, and roughly match the 2023 table with the current club rankings. So this all seems sane, and will be our comparison point going forward.

We can take the released squad lists and our player rankings to pick the “best possible” lineups for each of these clubs, and then generate some possible performances for them. That results in this plot, which has a very messy x-axis unit we can mostly ignore and just talk about order and overlap instead:

We again have the semifinalists at the top, but the Hounds are much higher than in the club model and the Jackals are not quite at the bottom. This may point to the importance of some measure of familiarity between players - teams that have been around and stable for longer perform better than you’d expect looking at just the players, and new teams perform a bit worse than you’d expect looking at the players. From just the lineups, we have three groups of teams - a close top 4, a lagging bottom four, and then the four in the middle. All the expansion teams are towards the middle - LA at 6, Miami at 8, and Anthem a bit worse at 9. But as we saw with the Jackals and Hounds, new teams may need to have slightly lower club scores.

So now we get to make guesses. We have RFC LA as the strongest of the expansion clubs, and Anthem as the weakest. Anthem looks to be about as strong as the Jackals - our lowest rated club. LA is about as strong as Houston and Utah, while Miami is more like Utah, NOLA, and DC. We can definitely start all three with very high variances, though could argue LA should have lower variance and Anthem higher variance.

That gives us a pre-season ranking like this, which seems to make more sense to me

Champions and Challenge Cups

2023-12-05T11:00:00+00:00

These are some of my favorite competitions, because it is so hard to predict what might happen. We toss together three separate leagues, add in some teams that rarely play anyone else in these competitions, and also have club managers trying to balance success here and in their own league, as the matches alternate through the spring (spring in the Northern Hemisphere, at least). Its a mess, and its fun.

Its also a great opportunity to gather some data for our predictions. We have some matches in these competitions, then some more matches in the usual component competitions, and can use all of them to update our predictions each week. We expect the club level models to be a bit off at the start of the competition, but within a few weeks we should learn a lot - seeing how leagues perform against the other teams gives us lots of new data points to adjust ratings appropriately, and we’d expect the predictions we make after one or two weeks of pool matches to be much more accurate than the ones we can make today.

We’d also expect our player models to perform a good bit better than the club models. Plenty of these players have just played with or against each other in the world cup, so we expect those ratings to be a bit better tuned. But it’s very hard to make predictions far into the future with the player model, so we’ll just be using the club model here.

Champions Cup

This year, we have four pools where teams ought to play the teams that are in their pool but not in their usual competition. Then the top four teams from each pool advance into the knockout stages, while the fifth best team in each pool will actually move into the knockouts of the Challenge Cup, getting an away match in the first knockout round. This does allow for the strange edge cases where a strong team performs poorly in their pool, then is highly favored to win the Challenge Cup. Which does happen to Leinster in one of our predictions.

	Reach Round of Sixteen	Reach Quarterfinals	Reach Semifinals	Reach Final	Win Final
Leinster	99.9 %	97.9 %	93.1 %	85.3 %	77.7 %
Munster	98.5 %	77.4 %	52.0 %	27.3 %	8.7 %
Stade Toulousain	98.1 %	72.7 %	48.1 %	21.5 %	3.2 %
Bulls	87.7 %	61.8 %	29.1 %	12.3 %	2.5 %
Saracens	93.8 %	66.2 %	32.2 %	11.2 %	2.1 %
La Rochelle	68.3 %	36.0 %	12.3 %	3.9 %	1.4 %
Glasgow Warriors	91.7 %	54.6 %	26.4 %	9.2 %	1.1 %
Stormers	77.4 %	42.7 %	15.8 %	5.5 %	1.0 %
Exeter Chiefs	85.9 %	42.0 %	19.0 %	6.7 %	0.7 %
Harlequins	84.7 %	37.9 %	15.4 %	3.5 %	0.5 %
Leicester Tigers	57.7 %	20.8 %	5.4 %	1.5 %	0.5 %
Ulster	56.8 %	22.6 %	7.8 %	2.3 %	0.3 %
Toulon	67.7 %	25.4 %	9.6 %	3.3 %	0.1 %
Racing 92	88.0 %	40.5 %	13.8 %	3.2 %	0.1 %
Sale Sharks	74.1 %	20.4 %	5.2 %	1.3 %	0.1 %
Bordeaux Begles	71.5 %	26.3 %	5.4 %	0.7 %	0.0 %
Bristol Rugby	46.1 %	9.4 %	1.6 %	0.5 %	0.0 %
Bath Rugby	68.8 %	19.0 %	3.9 %	0.3 %	0.0 %
Connacht	46.7 %	7.6 %	1.0 %	0.3 %	0.0 %
Lyon	54.2 %	12.6 %	2.0 %	0.1 %	0.0 %
Northampton Saints	50.3 %	5.7 %	0.9 %	0.1 %	0.0 %
Stade Francais Paris	22.6 %	0.3 %	0.0 %	0.0 %	0.0 %
Bayonne	5.9 %	0.1 %	0.0 %	0.0 %	0.0 %
Cardiff Blues	3.6 %	0.1 %	0.0 %	0.0 %	0.0 %

Challenge Cup

In the challenge cup, the top four teams from each pool will also advance, then be joined by the 5th place teams from the champions cup. This gives us a ton of possible permutations, before we even consider the invitational sides. The Cheetahs have not played many matches outside of these competitions, and Black Lion have not played any of these teams yet - both have some very wide variances and our model has some predictions where they do very well, and some where they do very poorly. It’ll be fun to see how they do, especially as they don’t have another competition to balance their player management with (Yeah, the Black Lion is wrapping up the Rugby Europe Super Cup, but there’s just a match remaining there).

	Reach Round of Sixteen	Reach Quarterfinals	Reach Semifinals	Reach Final	Win Final
Lions	98.9 %	75.9 %	49.0 %	30.1 %	14.9 %
Black Lion	75.6 %	51.1 %	31.9 %	21.0 %	12.8 %
Clermont Auvergne	90.1 %	61.7 %	38.5 %	21.7 %	11.9 %
Edinburgh	87.6 %	58.0 %	35.7 %	18.8 %	9.2 %
La Rochelle	25.1 %	19.2 %	11.5 %	7.8 %	6.9 %
Castres Olympique	83.8 %	51.7 %	27.4 %	13.1 %	6.7 %
Pau	99.7 %	62.0 %	34.0 %	15.4 %	5.0 %
Benetton Treviso	95.7 %	59.9 %	31.3 %	14.9 %	4.9 %
Leicester Tigers	23.5 %	15.3 %	8.2 %	4.2 %	3.4 %
Toulon	26.7 %	16.8 %	7.7 %	4.0 %	2.7 %
Sale Sharks	19.3 %	11.9 %	6.1 %	3.2 %	2.7 %
Sharks	94.4 %	46.2 %	17.8 %	7.4 %	2.3 %
Montpellier Herault	88.8 %	46.7 %	18.9 %	6.8 %	1.9 %
Stormers	12.8 %	8.2 %	4.3 %	1.8 %	1.5 %
Exeter Chiefs	10.5 %	6.1 %	3.1 %	1.7 %	1.4 %
Cheetahs	68.1 %	18.5 %	5.8 %	2.9 %	1.2 %
Saracens	4.8 %	3.1 %	2.2 %	1.5 %	1.2 %
Oyonnax	98.5 %	46.2 %	20.0 %	7.4 %	1.1 %
Ulster	37.7 %	19.3 %	6.6 %	1.9 %	1.1 %
Bulls	8.2 %	4.9 %	2.8 %	1.8 %	1.1 %
Stade Toulousain	1.9 %	1.6 %	1.1 %	0.8 %	0.8 %
Gloucester Rugby	46.1 %	17.2 %	7.4 %	3.1 %	0.7 %
Harlequins	12.7 %	6.6 %	2.9 %	0.9 %	0.7 %
Munster	1.5 %	1.2 %	1.1 %	0.9 %	0.7 %
Racing 92	11.3 %	5.9 %	2.7 %	1.0 %	0.6 %
Glasgow Warriors	6.4 %	3.8 %	1.8 %	0.8 %	0.5 %
Northampton Saints	41.3 %	15.0 %	3.6 %	0.9 %	0.4 %
Bath Rugby	24.5 %	8.6 %	2.6 %	0.8 %	0.3 %
Connacht	21.5 %	6.7 %	2.1 %	0.6 %	0.3 %
Ospreys	60.6 %	10.1 %	2.5 %	0.5 %	0.3 %
Lyon	22.9 %	8.9 %	2.5 %	0.7 %	0.2 %
Bordeaux Begles	17.1 %	6.8 %	2.2 %	0.5 %	0.2 %
Stade Francais Paris	19.2 %	6.4 %	1.2 %	0.3 %	0.2 %
Bristol Rugby	25.5 %	7.2 %	1.8 %	0.4 %	0.1 %
Leinster	0.1 %	0.1 %	0.1 %	0.1 %	0.1 %
Perpignan	35.5 %	3.1 %	0.2 %	0.2 %	0.0 %
Scarlets	16.8 %	3.4 %	0.8 %	0.1 %	0.0 %
Bayonne	13.6 %	1.7 %	0.3 %	0.0 %	0.0 %
Newcastle Falcons	20.5 %	1.6 %	0.2 %	0.0 %	0.0 %
Cardiff Blues	11.9 %	1.3 %	0.1 %	0.0 %	0.0 %
Dragons	23.6 %	0.1 %	0.0 %	0.0 %	0.0 %
Zebre	15.7 %	0.0 %	0.0 %	0.0 %	0.0 %

Rugby World Cup - 2 Week Update

2023-09-19T11:00:00+00:00

Model Review

Now that we’re nearly two weeks into the competition, we can evaluate our predictions for the first couple weekends and see what may lie ahead. Overall, predictions have been great.

The club based model only had two incorrect picks, calling Argentina over England by 3 and Fiji over Wales by 7. Not too mad about both of those - Argentina and England look like very different teams now that the tournament has started, and Fiji was that close to the win. Not sure you’d want to have anyone other than Radradra on the edge there (he was out second highest rated player on the field, just after Nayacalevu).

The player model was as good, just missing two as well. Wales and Fiji again, of course - the player model only had Fiji by 3 pregame and 4 when accounting for how long each player was on the pitch - but it also missed Australia and Georgia, favoring Georgia by 6 prematch and 7 with playing time. So we may be overvaluing Georgia or overvaluing Australia, but we’re guessing it was a bit of both, as we had Fiji beating Australia by 12 instead of just 7 last weekend too. Keeping a close eye on the model for pool C for now.

That gives us this table - good at picking winners, not so great at spreads. But a lot of that was from underestimating margins like what New Zealand had over Namibia or South Africa had over Romania.

Model	Percent Correct Predictions	Spread Error
Club Level	87.5%	17.9
Player Level: Lineup	87.5%	20.0
Player Level: Minutes	87.5%	19.9

Changes to Future Predictions

As things stand now, here’s our predictions of the knockout stages.

	Reach Quarterfinals	Reach Semifinals	Reach Bronze Final	Win Bronze	Reach Final	Win Final
South Africa	97.9 %	70.3 %	0.8 %	0.8 %	69.5 %	45.2 %
Ireland	91.0 %	63.0 %	1.0 %	0.9 %	62.0 %	32.2 %
France	95.3 %	47.0 %	1.4 %	1.4 %	45.6 %	18.4 %
New Zealand	95.3 %	18.6 %	0.8 %	0.7 %	17.8 %	4.1 %
Fiji	66.9 %	43.1 %	41.2 %	24.7 %	1.9 %	0.1 %
Australia	74.9 %	49.9 %	48.9 %	28.5 %	1.0 %	0.0 %
Scotland	11.0 %	1.1 %	0.2 %	0.2 %	0.9 %	0.0 %
England	93.5 %	42.2 %	41.6 %	18.2 %	0.6 %	0.0 %
Samoa	78.2 %	30.8 %	30.3 %	11.8 %	0.5 %	0.0 %
Wales	51.7 %	23.9 %	23.7 %	9.1 %	0.2 %	0.0 %
Argentina	28.2 %	8.4 %	8.4 %	3.3 %	0.0 %	0.0 %
Georgia	6.4 %	1.7 %	1.7 %	0.4 %	0.0 %	0.0 %
Italy	9.4 %	0.0 %	0.0 %	0.0 %	0.0 %	0.0 %
Japan	0.1 %	0.0 %	0.0 %	0.0 %	0.0 %	0.0 %
Portugal	0.1 %	0.0 %	0.0 %	0.0 %	0.0 %	0.0 %
Tonga	0.1 %	0.0 %	0.0 %	0.0 %	0.0 %	0.0 %

And more interestingly, here’s the change (in percentage points) to the predictions since the tournament started.

	ReachQuarterfinals	ReachSemifinals	ReachFinal	WinFinal	ReachBronzeFinal	WinBronze
South Africa	+9.5	+11	+13.3	+9.8	-2.3	-2.2
Ireland	+7.6	+9.4	+12.6	+3.9	-3.3	-3.2
France	+2.3	+10.3	+13.6	+3.7	-3.3	-3
England	+66.1	+37.1	+0.5	+0	+36.6	+17.1
Wales	+40.4	+20.3	+0.2	+0	+20.1	+8.5
Australia	+17.9	+19.7	+0.2	+0	+19.6	+20.3
Italy	+1.6	-0.1	+0	+0	-0.1	+0
Japan	-1.7	-0.1	+0	+0	-0.1	+0
Portugal	-2.8	-0.4	+0	+0	-0.4	+0
Georgia	-27.8	-10.2	-0.2	+0	-10	-1.6
Argentina	-61.8	-31.2	-1.3	+0	-29.8	-9.7
Samoa	-2.7	1.2	-0.7	-0.1	1.9	3.9
Scotland	-17.2	-4.6	-3.4	-0.7	-1.2	-0.8
Fiji	-27.8	-36.6	-11.3	-2.8	-25.3	-27.1
New Zealand	-3.9	-26	-23.5	-13.8	-2.4	-2.1

South Africa has benefitted most - they’ve beaten Scotland, and while New Zealand’s loss to France makes their win in Twickenham less impressive, they still benefit when another team looks like less of a contender than was once assumed. Ireland and France also saw their winning chances increase but still have plenty to prove before the final, while Australia, Wales, and England have started to make a case for themselves and seem poised to escape the pools. Georgia and Argentina suffer most from these teams’ wins so far

Fiji and New Zealand are the worst off. We had them likely to succeed this year, but just one loss can make the path much more difficult. Fiji’s loss to Wales greatly decreases the chance to get out of the pool as it may go to tiebreakers. Which we didn’t think were enough of a priority to include properly in these projections, so pool C remains tricky. But we still have Fiji as nearly favorites for the bronze, just behind Australia who have a better chance to advance as they haven’t yet played Wales, and could win. New Zealand should still get out of the pool, but may struggle more than we thought they would in the Quarterfinal against what will likely be either South Africa or Ireland. And Scotland’s loss to South Africa has unfortunately likely relegated them to third in the pool unless they can pull off a great upset against Ireland

World Cup Squad Strengths

2023-09-05T11:00:00+00:00

The previous post detailed my predictions using the club based model, where each team is treated as a single entity. This completely ignores the changes in lineups from game to game or injuries that may change a team’s makeup, so has some inherent disadvantages. Especially where we have had some high profile injuries and surprise changes to world cup squads. Here, I compare the predictions made with the club model to the predictions I can make with a player based model.

Obviously no official sides for matches have been announced yet, but I can make a best guess at what a team’s best side would be, then compare those best sides against each other. These predictions may quickly fall apart if there are any more major injuries, but its not like we can - or would want to - predict those anyways.

Team Rankings

On the left we have rankings from the club model, and on the right are rankings from the player model. The top five teams are unchanged, and remain the strong favorites. But the player model rates Fiji, Argentina, and Australia worse than the club model, and ranks Japan, England, Samoa and Wales higher. I may add some future, deeper analysis on why this is and what the repercussions may be, but for now - it looks like the results from pools A and B should be unchanged, and pools C and D may be even more competitive.

Rugby World Cup Predictions

2023-09-01T11:00:00+00:00

Just a week out from the opening match, I’m recording the current predictions being made by my club level model. These predictions are updated a few times a week here as matches are played and new information becomes available, but they shouldn’t change much before kickoff, and recording them here allows for evaluation once matches are played. (Note - the page refereced above doesn’t exist anymore. Shows I was right.)

So lets have at it. First, here’s the predicted tables for each pool. The top two teams from each pool would advance to the knockouts, and the top three teams from each pool will qualify for the next world cup, avoiding the lengthy qualifying process. Each pool’s table shows the average number of wins across all of the many predictions made, and the average point differential - a measure of how much a team has outscored their opponents in head to head matches. Last and perhaps most importantly is the percentage of predictions in which the team was among the top two in the pool and advance to the Quarterfinals.

Pool A

Club	Average Wins	Average Point Differential	Chance to Reach QFs
New Zealand	3.7579	79.8393	99.2%
France	3.1273	61.5069	93%
Italy	2.0392	7.2973	7.8%
Namibia	0.7164	-69.1397	0.0%
Uruguay	0.3592	-79.5039	0%

Unfortunately for Italy, this one seems pretty settled. France and New Zealand should both advance, but I’m not sure there’s any real benefit from winning this pool instead of being the runner up. Both advance, and would play whoever comes out of the strong pool B. Italy should wind up at third, and qualify for the next tournament, but the nearly 8% chance to advance is not bad given the competition.

Pool B

Club	Average Wins	Average Point Differential	Chance to Reach QFs
Ireland	3.2826	59.4172	83.4%
South Africa	3.2773	61.78	88.4 %
Scotland	2.4094	29.8988	28.2%
Tonga	0.8953	-48.763	0.0%
Romania	0.1354	-102.333	0%

My models are all very bullish on South Africa after they beat New Zealand in Twickenham. Which is fair, but may be a bit overexaggerated. They’re likely to advance, with Ireland close behind and Scotland with a smaller chance due to the unfortunate draw. Since this pool plays pool A in the Quarterfinals, it again may not matter much who wins and who gets second. Both will play difficult teams - one likely gets the All Blacks and the other likely gets France on home turf. And only two of these four teams can make it to the finals. Scotland has a decent chance at advancing as well - just one upset and then beating Tonga and Romania would do it. They’ve certainly showed they’re capable.

Pool C

Club	Average Wins	Average Point Differential	Chance to Reach QFs
Fiji	3.5219	38.4123	94.7 %
Australia	2.4442	7.6306	57.0 %
Georgia	1.9794	-0.9265	34.2 %
Wales	1.4208	-12.7164	11.3 %
Portugal	0.6337	-32.4	2.9 %

Another team I’m bullish on here - Fiji. Wales and Australia haven’t looked like they’ll be the toughest competition, but a world cup can be a different beast. This if the first pool with some real competition for who may advance. Everyone has at least some chance - and watch out for Georgia beating Wales for that third spot and qualifying for the next world cup in Australia. And maybe even making it to the knockouts. There’s a lot of unknowns here, so could be a fun pool to watch.

Pool D

Club	Average Wins	Average Point Differential	Chance to Reach QFs
Argentina	3.3028	44.3683	90.0 %
Samoa	3.1587	35.8415	80.9 %
England	2.1944	14.4155	27.4 %
Japan	1.193	-22.4929	1.8 %
Chile	0.1511	-72.1325	0 %

As bad as they’ve looked recently, England is still a pretty good team. They should at least qualify for the next world cup, and they have about as much of a chance to escape their pool as Scotland… but this isn’t quite the pool of death that pool B is. Argentina is set to have a strong start, and Samoa is poised well to take advantage of any slip-ups, as their last pool match will be against the English.

Knockouts

And here’s the predictions for the knockout stages. Note that these predictions do incorporate any results that would happen to allow these teams to advance - for example, if Samoa were to reach a Quarterfinal, they likely would have had to defeat England and/or Argentina, and the future predictions would integrate this new, higher level of performance. This is extremely visible in the breakdowns of possible quarterfinal matchups. If Ireland were to meet New Zealand in the quarterfinals, one team would have to win their pool and the other team would have to be the runner up in the other pool. If Ireland wins the pool and the All Blacks are a runner up, Ireland has a nearly 71% chance to win (Ireland would likely have had to beat both South Africa and Scotland, while New Zealand likely lost to France). But if Ireland are the runners up and New Zealand topped their pool, the Irish have only a 42% chance to win that same matchup.

	Reach Quarterfinals	Reach Semifinals	Reach Final	Win Final	Reach Bronze Final	Win Bronze
South Africa	88.4 %	59.3 %	56.2 %	35.4 %	3.1 %	3.0 %
Ireland	83.4 %	53.6 %	49.4 %	28.3 %	4.3 %	4.1 %
New Zealand	99.2 %	44.6 %	41.3 %	17.9 %	3.2 %	2.8 %
France	93.0 %	36.7 %	32.0 %	14.7 %	4.7 %	4.4 %
Fiji	94.7 %	79.7 %	13.2 %	2.9 %	66.5 %	51.8 %
Scotland	28.2 %	5.7 %	4.3 %	0.7 %	1.4 %	1.0 %
Samoa	80.9 %	29.6 %	1.2 %	0.1 %	28.4 %	7.9 %
Argentina	90.0 %	39.6 %	1.3 %	0.0 %	38.2 %	13.0 %
Australia	57.0 %	30.2 %	0.8 %	0.0 %	29.3 %	8.2 %
Georgia	34.2 %	11.9 %	0.2 %	0.0 %	11.7 %	2.0 %
England	27.4 %	5.1 %	0.1 %	0.0 %	5.0 %	1.1 %
Wales	11.3 %	3.6 %	0.0 %	0.0 %	3.6 %	0.6 %
Italy	7.8 %	0.1 %	0.0 %	0.0 %	0.1 %	0.0 %
Portugal	2.9 %	0.4 %	0.0 %	0.0 %	0.4 %	0.0 %
Japan	1.8 %	0.1 %	0.0 %	0.0 %	0.1 %	0.0 %

Potential Quarterfinals

Note that for quarterfinals 1 and 3, there are some matchups that are predicted to occur less than 0.05% of the time and have been excluded.

Note that the last column here, win percentage, refers to the win percentage of the team in the leftmost column for the given matchup. For example, if Fiji and Argentina were to meet in the first quarterfinal, Fiji will have won pool C and Argentina will have been the runner-up in pool D, and in this case Fiji was predicted to win 84.2% of the time.

Quarterfinal 1

Pool C Winner	Pool D Runner Up	Likelihood of Matchup	Pool C Win Percentage
Fiji	Argentina	31.03 %	84.2 %
Fiji	Samoa	30.13 %	86.6 %
Fiji	England	16.57 %	91.5 %
Australia	Samoa	4.65 %	68 %
Australia	Argentina	4.42 %	58.1 %
Georgia	Argentina	3.04 %	39.1 %
Georgia	Samoa	2.78 %	50 %
Australia	England	2.54 %	78.3 %
Georgia	England	1.52 %	63.2 %
Fiji	Japan	1.34 %	100 %
Wales	Argentina	0.57 %	36.8 %
Wales	Samoa	0.51 %	37.3 %
Wales	England	0.28 %	71.4 %
Portugal	Argentina	0.14 %	28.6 %
Portugal	Samoa	0.14 %	50 %
Georgia	Japan	0.12 %	83.3 %
Australia	Japan	0.11 %	81.8 %
Portugal	England	0.06 %	16.7 %
Wales	Japan	0.05 %	80 %

Quarterfinal 2

Pool A Winner	Pool B Runner Up	Likelihood of Matchup	Pool A Win Percentage
Ireland	France	35.34 %	66.1 %
South Africa	France	32.07 %	70.7 %
Ireland	New Zealand	9.73 %	70.7 %
South Africa	New Zealand	9.39 %	74.2 %
Scotland	France	4.93 %	25.4 %
South Africa	Italy	2.99 %	99.3 %
Scotland	New Zealand	1.25 %	26.4 %
Scotland	Italy	0.45 %	91.1 %

Quarterfinal 3

Pool D Winner	Pool C Runner Up	Likelihood of Matchup	Pool D Win Percentage
Australia	Argentina	23.09 %	44 %
Australia	Samoa	19.08 %	52.5 %
Georgia	Argentina	13.29 %	25.2 %
Georgia	Samoa	11.8 %	34.9 %
Fiji	Argentina	7.89 %	68.4 %
Fiji	Samoa	6.75 %	70.4 %
Wales	Argentina	5.29 %	24.2 %
Wales	Samoa	3.87 %	34.9 %
Australia	England	3.04 %	68.4 %
Georgia	England	1.54 %	49.4 %
Portugal	Argentina	1.19 %	4.2 %
Portugal	Samoa	1.15 %	13.9 %
Fiji	England	0.94 %	83 %
Wales	England	0.66 %	43.9 %
Portugal	England	0.21 %	19 %
Australia	Japan	0.09 %	88.9 %
Georgia	Japan	0.06 %	50 %

Quarterfinal 4

Pool A Winner	Pool B Runner Up	Likelihood of Matchup	Pool A Win Percentage
New Zealand	South Africa	34.76 %	38 %
New Zealand	Ireland	27.23 %	41.6 %
New Zealand	Scotland	16.82 %	82 %
France	South Africa	8.9 %	45.3 %
France	Ireland	7.07 %	50.8 %
France	Scotland	4.65 %	86.9 %
Italy	Scotland	0.12 %	16.7 %

Potential Semifinals

This is where the imbalance in pools comes to light - whatever teams come out of pools A and B are favored in the Semifinals. Note that there are some matchups that are predicted to occur less than 0.05% of the time and have been excluded.

Similar to above, the win percentage in the rightmost column is the chance of the team in the leftmost column winning the potential matchup.

Semifinal 1

QF 2 Winner	QF 1 Runner Up	Likelihood of Matchup	QF 2 Win Percentage
Ireland	Fiji	23.72 %	85.5 %
South Africa	Fiji	22.36 %	89 %
France	Fiji	16.96 %	76.5 %
New Zealand	Fiji	4.22 %	69 %
South Africa	Argentina	3.05 %	99.7 %
Ireland	Argentina	2.91 %	98.3 %
Ireland	Australia	2.7 %	98.1 %
Ireland	Samoa	2.44 %	98.8 %
South Africa	Samoa	2.37 %	99.2 %
France	Argentina	2.36 %	96.2 %
South Africa	Australia	2.36 %	97.5 %
France	Australia	2.11 %	94.3 %
France	Samoa	1.91 %	97.4 %
Scotland	Fiji	1.41 %	53.9 %
South Africa	Georgia	1.39 %	99.3 %
Ireland	Georgia	1.07 %	100 %
Ireland	England	0.93 %	100 %
France	Georgia	0.89 %	94.4 %
South Africa	England	0.83 %	100 %
France	England	0.67 %	98.5 %
New Zealand	Argentina	0.56 %	98.2 %
New Zealand	Samoa	0.49 %	98 %
New Zealand	Australia	0.48 %	95.8 %
Ireland	Wales	0.27 %	100 %
New Zealand	Georgia	0.22 %	100 %
South Africa	Wales	0.2 %	100 %
Scotland	Argentina	0.18 %	83.3 %
New Zealand	England	0.17 %	94.1 %
Scotland	Australia	0.16 %	81.2 %
Scotland	Samoa	0.1 %	100 %
France	Wales	0.1 %	100 %
South Africa	Portugal	0.06 %	100 %
Scotland	Georgia	0.06 %	83.3 %

Semifinal 2

QF 4 Winner	QF 3 Runner Up	Likelihood of Matchup	QF 4 Win Percentage
New Zealand	Argentina	11.68 %	95.8 %
New Zealand	Samoa	8.72 %	95.3 %
New Zealand	Australia	8.36 %	97.1 %
South Africa	Argentina	8.12 %	98.4 %
Ireland	Argentina	6.1 %	97.7 %
South Africa	Australia	6.09 %	98.5 %
South Africa	Samoa	5.79 %	96.9 %
Ireland	Samoa	4.39 %	95.2 %
New Zealand	Fiji	4.36 %	85.6 %
Ireland	Australia	4.35 %	98.2 %
France	Argentina	3.53 %	96.9 %
New Zealand	Georgia	3.15 %	98.4 %
South Africa	Fiji	2.8 %	95.4 %
France	Australia	2.71 %	97.8 %
France	Samoa	2.54 %	95.7 %
Ireland	Fiji	2.15 %	89.8 %
South Africa	Georgia	2.12 %	99.5 %
Ireland	Georgia	1.53 %	98 %
France	Fiji	1.25 %	88 %
France	Georgia	1.13 %	99.1 %
Scotland	Argentina	1.05 %	76.2 %
New Zealand	Wales	1.03 %	100 %
South Africa	Wales	0.96 %	100 %
New Zealand	England	0.94 %	97.9 %
Scotland	Australia	0.84 %	89.3 %
Scotland	Samoa	0.81 %	85.2 %
South Africa	England	0.7 %	100 %
Ireland	Wales	0.55 %	100 %
Ireland	England	0.42 %	97.6 %
Scotland	Fiji	0.4 %	55 %
Scotland	Georgia	0.33 %	84.8 %
France	Wales	0.29 %	100 %
France	England	0.2 %	100 %
Scotland	England	0.18 %	94.4 %
Scotland	Wales	0.12 %	91.7 %
New Zealand	Portugal	0.12 %	100 %
South Africa	Portugal	0.07 %	100 %
Ireland	Portugal	0.05 %	100 %

Potential Finals

There’s a lot to happen between now and late October. And these predictions may be way off. But, my most likely final, happening in about 16% of simulations, is South Africa v Ireland, with South Africa winning 52% of those matchups. There’s a 48% chance that the final is some combination of France, New Zealand, Ireland, and South Africa, and a 25% chance that it’s a repeat of a pool match.

Just like the tables above, the win percentage in the rightmost column is the chance of the team in the leftmost column winning the potential matchup.

Final

Team 1	Team 2	Likelihood of Matchup	Team 1 Win Percentage
South Africa	Ireland	15.9 %	52.93 %
South Africa	New Zealand	7.99 %	68.58 %
France	New Zealand	7.13 %	49.92 %
Ireland	New Zealand	6.64 %	65.48 %
France	South Africa	5.98 %	35.73 %
France	Ireland	4.47 %	38.29 %
New Zealand	Fiji	2.74 %	75.94 %
South Africa	Fiji	2.46 %	83.54 %
Ireland	Fiji	1.46 %	82.99 %
France	Fiji	0.97 %	81.88 %
South Africa	Scotland	0.97 %	95.03 %
Ireland	Scotland	0.79 %	88.46 %
France	Scotland	0.39 %	75.38 %
South Africa	Argentina	0.28 %	100 %
New Zealand	Scotland	0.26 %	58.14 %
Ireland	Argentina	0.22 %	100 %
South Africa	Samoa	0.19 %	100 %
Ireland	Samoa	0.18 %	93.33 %
France	Argentina	0.16 %	88.46 %
Fiji	Scotland	0.16 %	59.26 %
France	Samoa	0.15 %	95.83 %
South Africa	Australia	0.15 %	95.83 %
Ireland	Australia	0.15 %	100 %
Fiji	Samoa	0.1 %	76.47 %
New Zealand	Australia	0.1 %	93.75 %
France	Australia	0.09 %	100 %
New Zealand	Argentina	0.08 %	92.86 %
South Africa	Georgia	0.06 %	100 %
New Zealand	Samoa	0.05 %	100 %

Bronze Final

This one is just hard to predict, there’s a ton of possible matchups. But Fiji has the highest chance of ending up in this match, and would be the favorite against anyone outside those top 4 from pools A and B. They may be the biggest beneficiaries of the early pool draws - they’re a good side peaking at the right time, with a straightforward path to the semifinals.

Team 1	Team 2	Likelihood of Matchup	Team 1 Win Percentage
Fiji	Argentina	11.14 %	75.77 %
Fiji	Australia	9.89 %	79.4 %
Fiji	Samoa	7.49 %	79.68 %
Argentina	Samoa	3.79 %	58.36 %
Fiji	Georgia	3.64 %	88.33 %
Australia	Argentina	1.83 %	53.08 %
Australia	Samoa	1.25 %	59.91 %
Fiji	Wales	1.17 %	88.07 %
Fiji	England	1.13 %	84.76 %
Argentina	Georgia	0.75 %	69.78 %
Ireland	Argentina	0.64 %	100 %
France	Argentina	0.64 %	92.44 %
France	Samoa	0.62 %	94.78 %
France	Australia	0.58 %	91.59 %
Ireland	Australia	0.56 %	99.04 %
Argentina	England	0.55 %	77.45 %
New Zealand	Fiji	0.45 %	78.31 %
Samoa	Georgia	0.44 %	54.32 %
Australia	Georgia	0.42 %	66.67 %
South Africa	Argentina	0.42 %	100 %
Ireland	Samoa	0.42 %	96.15 %
New Zealand	Argentina	0.41 %	93.42 %
South Africa	Australia	0.38 %	100 %
South Africa	Samoa	0.38 %	97.18 %
Samoa	England	0.34 %	69.84 %
New Zealand	Australia	0.33 %	91.8 %
Australia	England	0.28 %	73.58 %
France	Georgia	0.27 %	96 %
Ireland	Georgia	0.27 %	100 %
New Zealand	Samoa	0.26 %	93.88 %
Fiji	Scotland	0.2 %	54.05 %
Ireland	Fiji	0.19 %	82.86 %
Argentina	Wales	0.18 %	72.73 %
South Africa	Fiji	0.17 %	96.77 %
Scotland	Argentina	0.16 %	75.86 %
Scotland	Australia	0.15 %	89.29 %
Wales	Samoa	0.15 %	57.14 %
New Zealand	Georgia	0.15 %	100 %
France	Fiji	0.14 %	92.31 %
South Africa	Georgia	0.13 %	100 %
England	Georgia	0.13 %	64 %
Scotland	Samoa	0.12 %	72.73 %
Fiji	Portugal	0.11 %	95.24 %
France	Wales	0.11 %	100 %
France	England	0.09 %	100 %
Ireland	Wales	0.08 %	100 %
Australia	Wales	0.07 %	53.85 %
Ireland	England	0.07 %	100 %
New Zealand	Wales	0.05 %	100 %
South Africa	Wales	0.05 %	100 %
Scotland	Georgia	0.05 %	100 %

Six Nations Round 5 Projections

2023-03-16T11:00:00+00:00

Model Review

Match	Result	Lineup Prediction	Minutes Prediction	Club Prediction
Wales V Ireland on 2023/02/04	-24	-19.3	-21.1	-10.1
England V Scotland on 2023/02/04	-6	-9.5	-6.7	6.3
Italy V France on 2023/02/05	-5	-15.7	-14.8	-10.7
Ireland V France on 2023/02/11	13	27.3	31.6	7.5
Scotland V Wales on 2023/02/11	28	25.1	27.4	9.5
England V Italy on 2023/02/12	17	17.8	18.9	14.9
Italy V Ireland on 2023/02/25	-14	-12.3	-12.5	-13.7
Wales V England on 2023/02/25	-10	-8.7	-9.1	-2.4
France V Scotland on 2023/02/26	11	2.9	4.6	11.1
Italy V Wales on 2023/03/11	-12	11.2	13.4	4
England V France on 2023/03/11	-43	-7.3	-5.8	0.4
Scotland V Ireland on 2023/03/12	-15	-8.2	-9.2	-4.5
Average Error	-	9.5	9.3	11.3
Correct Winner	-	91.7%	91.7%	75.0%

This last week was not a good one for the model - Italy v Wales was a complete miss, and France’s dismantling of England was a much bigger win than any projection had. In total, we have had 3 incorrect winners from the club model, and just one (Wales beating Italy) from the player level model. The average error is about 11 for the club model and just below 10 for the player model, with a lot of that coming from the 43 point France win. Without that game (which is unfair to completely drop but may be useful to focus on the less extreme matches sometimes) the club model has an average error of 8.4 and the player model has an average error of 6.9.

All numbers are using the most recent models, and always predict a match using only data available before that match kicks off. Except for the Player Minutes model, of course, as we need the match to be played to see how long any player is on the field.

Week Five Projections

After the matches last week, the models don’t think there’ll be anything close this weekend. Which is unfortunate for a final round. The biggest bit of drama is whether or not Ireland could pull off the grand slam with all of their injuries - something that the club model does not take into account. But then the player model gives Ireland an even better chance to win. Looking for silver linings in the other two matches, it does give each team a chance to line up against relatively strong competition six months before the world cup. We could see some new ideas, and are seeing some new names and faces on the teamsheets across the competition.

Scotland v Italy

Club Model: Scotland by 16.3

Lineup Model: Scotland by 7.5

Simulation Prediction: Scotland by 14.84

Outcomes	Occurrence in Simulation
Scotland Victory	99%
Italy Victory	0.6%
Tie	0.4%
Scotland Losing Bonus Point	0.6%
Italy Losing Bonus Point	11.5%
Scotland 4 Try Bonus Point (BETA)	71.5%
Italy 4 Try Bonus Point (BETA)	6.7%

France v Wales

Club Model: France by 18.2

Lineup Model: France by 29

Simulation Prediction: France by 16.98

Outcomes	Occurrence in Simulation
France Victory	99.1%
Wales Victory	0.4%
Tie	0.5%
France Losing Bonus Point	0.4%
Wales Losing Bonus Point	7.1%
France 4 Try Bonus Point (BETA)	65.1%
Wales 4 Try Bonus Point (BETA)	1.8%

Ireland v England

Club Model: Ireland by 17.4

Lineup Model: Ireland by 25.9

Simulation Prediction: Ireland by 16.4

Outcomes	Occurrence in Simulation
Ireland Victory	99.4%
England Victory	0.6%
Tie	0%
Ireland Losing Bonus Point	0.6%
England Losing Bonus Point	7%
Ireland 4 Try Bonus Point (BETA)	65.4%
England 4 Try Bonus Point (BETA)	6.9%

Simulation for the Final Week

Team	Average Wins	Average Point Differential	Average Competition Points (NOW WITH Future 4 Try Bonuses)
Ireland	4 + 0.99 = 4.99	66 + 16.4 = 82.4	19 + 4.64 = 23.64
France	3 + 0.99 = 3.99	46 + 16.98 = 62.98	15 + 4.63 = 19.63
Scotland	2 + 0.99 = 2.99	8 + 14.84 = 22.84	10 + 4.69 = 14.69
England	2 + 0.01 = 2.01	-22 + -16.4 = -38.4	10 + 0.16 = 10.16
Wales	1 + 0.01 = 1.01	-50 + -16.98 = -66.98	5 + 0.12 = 5.12
Italy	0 + 0.01 = 0.01	-48 + -16.4 = -64.4	1 + 0.21 = 1.21

At the beginning of this tournament, I had projected this table after week 4: | Team | Average Wins | Average Point Differential | Average Competition Points (Without 4 Try Bonus) | | —- | ———— | ————————– | ———————————————— | | Ireland | 3.86 | 50.96 | 15.56 | | England | 3.28 | 36.75 | 13.68 | | France | 2.47 | 21.34 | 10.72 | | Wales | 1.59 | -6.35 | 7.64 | | Scotland | 0.74 | -31.92 | 3.84 | | Italy | 0.06 | -70.79 | 0.62 |

I was a bit off on England and Wales and definitely off on Scotland. Perhaps I need to add some harsher consideration of new coaching teams, which would have penalized England and Wales a bit leading into week 1.

However, I don’t think the Scotland error is one that the club model could have caught in this current setup. Perhaps, after after the teamsheets were announced and the player model picked Scotland by 7 (13 points different than the club model) performing a deeper analysis of the simulations where Scotland beat England could have been useful. Maybe this will be in my competition retrospective in a week or two.

Six Nations Round 4 Projections

2023-03-10T11:00:00+00:00

Model Review

Match	Result	Lineup Prediction	Minutes Prediction	Club Prediction
Wales V Ireland on 2023/02/04	-24	-19.8	-21.5	-10.1
England V Scotland on 2023/02/04	-6	-9.1	-6.4	6.3
Italy V France on 2023/02/05	-5	-15.7	-14.8	-10.7
Ireland V France on 2023/02/11	13	28.2	32.3	7.5
Scotland V Wales on 2023/02/11	28	25	27.1	9.5
England V Italy on 2023/02/12	17	17.8	18.9	14.9
Italy V Ireland on 2023/02/25	-14	-12.5	-12.6	-13.7
Wales V England on 2023/02/25	-10	-8.3	-8.6	-2.4
France V Scotland on 2023/02/26	11	3.2	5.1	11.1
Average Error	-	5.3	4.8	7.3
Correct Winner	-	100.0%	100.0%	88.9%

So far so good. All the models were 3 of 3 in week 3, with the player level predictions being a bit better than the club predictions again. Except for France v Scotland, which did have two red cards and was 25-21 France until the 80th minute, so the player model was still pretty good.

Week Four Projections

Italy v Wales

Club Model: Italy by 4

Lineup Model: Italy by 10.7

The player predictions feel too bullish for Italy and too bearish for Wales at the same time. The Welsh team is good, but is struggling to mesh and their ratings have reflected that. But once things gel, they may be right back to competing (hopefully in time for the world cup). Italy has been solid, but has also suffered some injuries and is playing some players out of position. So far they’ve been excellent at home, so I fully expect them to win this match. But I do think it’ll be closer to by 6 points or so.

Simulation Prediction: Italy by 3.11

Outcomes	Occurrence in Simulation
Italy Victory	66%
Wales Victory	29.5%
Tie	4.5%
Italy Losing Bonus Point	22.5%
Wales Losing Bonus Point	39.1%
Italy 4 Try Bonus Point (BETA)	5.8%
Wales 4 Try Bonus Point (BETA)	0.7%

England v France

Club Model: England by 0.3

Lineup Model: France by 6.4

This one looks close, and its only the second time that the player and club models have disagreed: last time the player model had Scotland by 9 and was much more accurate than the club prediction of England by 6. This may be a case of Borthwick’s selections being different than Eddie Jones’, but no matter the case I’d trust the player model more for this one.

Simulation Prediction: France by 0.89

Outcomes	Occurrence in Simulation
France Victory	52.5%
England Victory	41.6%
Tie	5.9%
France Losing Bonus Point	29.9%
England Losing Bonus Point	34.7%
France 4 Try Bonus Point (BETA)	3.3%
England 4 Try Bonus Point (BETA)	5.5%

Scotland v Ireland

Club Model: Ireland by 4.3

Lineup Model: Recent lineups suggest Ireland by 3

Teamsheets haven’t been announced yet. May update this tomorrow.

Simulation Prediction: Ireland by 5.5

Outcomes	Occurrence in Simulation
Ireland Victory	77.3%
Scotland Victory	17.6%
Tie	5.1%
Ireland Losing Bonus Point	15.1%
Scotland Losing Bonus Point	39.2%
Ireland 4 Try Bonus Point (BETA)	16.1%
Scotland 4 Try Bonus Point (BETA)	2.8%

EDIT (3/11) Lineup model is saying Ireland by 8.5, which makes sense as it’s been liking Ireland. Rightly. So maybe a strong Ireland win without a Scotland bonus point, which would pretty much determine the final outcomes.

Simulation for the Next Two Weeks

Team	Average Wins	Average Point Differential	Average Competition Points (NOW WITH Future 4 Try Bonuses)
Ireland	3 + 1.76 = 4.76	51 + 18.2 = 69.2	15 + 7.8 = 22.8
France	2 + 1.54 = 3.54	3 + 17.2 = 20.2	10 + 7.1 = 17.1
Scotland	2 + 1.17 = 3.17	23 + 8.1 = 31.1	10 + 5.6 = 15.6
England	2 + 0.48 = 2.48	21 + -13.6 = 7.4	10 + 2.6 = 12.6
Italy	0 + 0.71 = 0.71	-36 + -10.5 = -46.5	1 + 3.3 = 4.3
Wales	0 + 0.33 = 0.33	-62 + -19.4 = -81.4	0 + 1.8 = 1.8

Simulations now include an estimate of 4 try bonus points, but it’s a conservative estimate that is rarely given except to teams that are pretty strong favorites and/or tend to score four or more tries each match. That addition, and last week’s results, seem to have put Ireland firmly in charge, with France, Scotland, and England chasing second place. This weekend should decide most of the final table.

Model for Try Bonus Points

2023-03-09T23:00:00+00:00

The Problem: Try Bonus Points

Most rugby competitions are scored using competition points rather than just wins and losses to try and make matches more interesting. The usual system awards 4 points for a win, 2 for a draw, 0 for losing, and then two ways to get a bonus point: 1 point is awarded for losing by seven or fewer points, and one is awarded for scoring at least four tries. This last one was a bit more challenging for my predictions. I’ve been predicting just margins of victories, not final point totals, and definitely not how those points are scored. So the losing bonus point was simple, whereas the try bonus point needed an entirely separate system. Which I now have in a basic binary predictor model.

The Solution

Since we do have a record of scoring for a bunch of played games, we have an idea of where try bonus points have been scored in the past. So I can predict when they’ll be scored in the future. This first pass solution considers the ratings and names of both clubs, the location, the competition, and the projected outcome to then predict if each of the teams score four tries or more. It’s reasonably accurate, but I have erred on the side of caution - its a bit less likely to award the bonus points than they’re seen in actual matches. We’ll see how much this affects the competition projections over time. Overall we have an accuracy of about 75%, but a precision of 80% and recall of just 55% for the positive case (awarding the bonus point). This should make the bonus points less likely to swing projections too much, but they’ll be in their own column for a while to make things more transparent.

And yes, I know France and SANZAAR have their own slightly different systems. But this should cover most competitions.

We’ll see them in the Six Nations Prediction tomorrow.

Six Nations Round 3 Projections

2023-02-23T23:00:00+00:00

Week Three Projections

With the week off, model review was done in the last post. They’ve been pretty spot on so far.

Club ratings have been updated from last week’s outcomes, so we re-ran simulations and have new projections.

Italy v Ireland

Club Model: Ireland by 14.6

Lineup Model: Ireland by 9.6

This should be straightforward. Ireland are heavy favorites. But it is in Rome, and Italy has been surprising this year.

Simulations now have Ireland winning by 16 points, on average.

Outcomes	Occurrence in Simulation
Ireland Victory	87.5%
Ireland Victory, Losing Bonus Point	10.9%
Italy Victory, Losing Bonus Point	1.3%
Tie	0.3%

Wales v England

Club Model: England by 3.3

Lineup Model: England by 10.9

There’s a lot of issues in the Welsh rugby union right now, and even though England are solidly favored in this match it could really go either way. I think we’re more likely to see some extreme results, given emotional states and new coaching teams.

Simulations now have England winning by 3.8 points, on average.

Outcomes	Occurrence in Simulation
England Victory, Losing Bonus Point	40.8%
England Victory	27.8%
Wales Victory, Losing Bonus Point	21.8%
Tie	5.4%
Wales Victory	4.2%

France v Scotland

Teamsheets haven’t been announced yet. May update this tomorrow.

Simulations now have France winning by 6.2 points, on average.

Outcomes	Occurrence in Simulation
France Victory	42.8%
France Victory, Losing Bonus Point	37.4%
Scotland Victory, Losing Bonus Point	13.4%
Tie	4.3%
Scotland Victory	2.1%

Simulation for the Next Three Weeks

Team	Average Wins	Average Point Differential	Average Competition Points (Without Future 4 Try Bonuses)
Ireland	2 + 2.79 = 4.79	37 + 35.33 = 72.33	10 + 11.32 = 21.32
France	1 + 2.42 = 3.42	-8 + 23.61 = 15.61	5 + 10.11 = 16.11
Scotland	2 + 1.34 = 3.34	34 + 2.61 = 36.61	10 + 2.61 = 12.61
England	1 + 1.12 = 2.12	11 + -12.14 = -1.14	6 + 5.21 = 11.21
Italy	0 + 0.68 = 0.68	-22 + -27.7 = -49.7	1 + 3.22 = 4.22
Wales	0 + 0.65 = 0.65	-52 + -21.7 = -73.7	0 + 3.52 = 3.52

Another 10,000 simulations of the next four weeks, combined with the actual results from the first weekend, gives us the above table. Not a lot of change from last week, but perhaps there’s more of a fight for second place. We’ll see how the Scotland-France lineups look: a lot now rides on that match