Posts from September 2025 (28)

September 30, 2025

United Rugby Championship Predictions for Week 2

Team Ratings for Week 2

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Leinster 11.75 13.41 -1.70
Bulls 8.31 8.86 -0.60
Glasgow 6.64 6.18 0.50
Stormers 5.83 4.17 1.70
Munster 4.52 3.65 0.90
Edinburgh 2.07 2.67 -0.60
Sharks 0.83 1.29 -0.50
Connacht -1.05 -1.39 0.30
Scarlets -1.41 -0.54 -0.90
Ospreys -1.60 -2.15 0.50
Lions -1.69 -1.19 -0.50
Cardiff Rugby -2.23 -2.74 0.50
Benetton -2.66 -2.32 -0.30
Ulster -3.06 -3.24 0.20
Zebre -10.42 -11.02 0.60
Dragons -15.83 -15.66 -0.20

 

Performance So Far

So far there have been 8 matches played, 5 of which were correctly predicted, a success rate of 62.5%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Stormers vs. Leinster Sept 27 35 – 0 -2.20 FALSE
2 Glasgow vs. Sharks Sept 27 35 – 19 11.90 TRUE
3 Ulster vs. Dragons Sept 27 42 – 21 19.40 TRUE
4 Bulls vs. Ospreys Sept 28 53 – 40 18.00 TRUE
5 Zebre vs. Edinburgh Sept 28 31 – 28 -6.70 FALSE
6 Scarlets vs. Munster Sept 28 21 – 34 2.80 FALSE
7 Cardiff Rugby vs. Lions Sept 28 33 – 20 5.50 TRUE
8 Connacht vs. Benetton Sept 28 26 – 15 7.90 TRUE

 

Predictions for Week 2

Here are the predictions for Week 2. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Stormers vs. Ospreys Oct 04 Stormers 14.40
2 Dragons vs. Sharks Oct 04 Sharks -9.70
3 Edinburgh vs. Ulster Oct 04 Edinburgh 12.10
4 Connacht vs. Scarlets Oct 05 Connacht 7.40
5 Benetton vs. Glasgow Oct 05 Glasgow -2.30
6 Bulls vs. Leinster Oct 05 Bulls 3.60
7 Munster vs. Cardiff Rugby Oct 05 Munster 13.80
8 Zebre vs. Lions Oct 06 Lions -1.70

 

Top 14 Predictions for Round 5

Team Ratings for Round 5

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Stade Toulousain 11.61 11.56 0.00
Bordeaux Begles 4.07 4.78 -0.70
Toulon 3.62 3.49 0.10
Section Paloise 3.03 2.21 0.80
Racing 92 2.52 1.88 0.60
Stade Rochelais 2.34 1.22 1.10
Clermont 1.38 1.88 -0.50
Bayonne 0.78 1.48 -0.70
Castres Olympique 0.42 0.59 -0.20
Montpellier 0.39 -0.21 0.60
Lyon -0.40 -0.45 0.00
Stade Francais -1.19 -2.17 1.00
USA Perpignan -4.52 -3.37 -1.10
Montauban -11.15 -10.00 -1.20

 

Performance So Far

So far there have been 28 matches played, 20 of which were correctly predicted, a success rate of 71.4%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Stade Francais vs. Bordeaux Begles Sept 28 28 – 7 -0.10 FALSE
2 Montauban vs. Montpellier Sept 28 22 – 22 -5.70 FALSE
3 Racing 92 vs. Clermont Sept 28 43 – 31 7.10 TRUE
4 Section Paloise vs. Lyon Sept 28 40 – 15 8.80 TRUE
5 Stade Rochelais vs. USA Perpignan Sept 28 31 – 8 12.60 TRUE
6 Stade Toulousain vs. Castres Olympique Sept 28 59 – 12 15.80 TRUE
7 Bayonne vs. Toulon Sept 29 35 – 32 3.70 TRUE

 

Predictions for Round 5

Here are the predictions for Round 5. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Bayonne vs. Stade Toulousain Oct 05 Stade Toulousain -4.30
2 Bordeaux Begles vs. Lyon Oct 05 Bordeaux Begles 11.00
3 Castres Olympique vs. Racing 92 Oct 05 Castres Olympique 4.40
4 Clermont vs. Montauban Oct 05 Clermont 19.00
5 Montpellier vs. Stade Rochelais Oct 05 Montpellier 4.60
6 Toulon vs. Section Paloise Oct 05 Toulon 7.10
7 USA Perpignan vs. Stade Francais Oct 05 USA Perpignan 3.20

 

Rugby Premiership Predictions for Round 2

Team Ratings for Round 2

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Bath 11.07 10.30 0.80
Sale Sharks 7.31 6.70 0.60
Saracens 5.59 5.03 0.60
Bristol 4.66 3.66 1.00
Leicester Tigers 4.56 5.55 -1.00
Gloucester 3.52 4.13 -0.60
Northampton Saints -2.27 -1.47 -0.80
Exeter Chiefs -3.78 -4.58 0.80
Harlequins -3.79 -3.02 -0.80
Newcastle Falcons -19.00 -18.45 -0.60

 

Performance So Far

So far there have been 5 matches played, 4 of which were correctly predicted, a success rate of 80%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Sale Sharks vs. Gloucester Sept 26 27 – 10 9.60 TRUE
2 Harlequins vs. Bath Sept 27 31 – 47 -6.30 TRUE
3 Newcastle Falcons vs. Saracens Sept 27 17 – 39 -16.50 TRUE
4 Northampton Saints vs. Exeter Chiefs Sept 29 33 – 33 10.10 FALSE
5 Bristol vs. Leicester Tigers Sept 29 42 – 24 5.10 TRUE

 

Predictions for Round 2

Here are the predictions for Round 2. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Bath vs. Sale Sharks Oct 04 Bath 10.80
2 Exeter Chiefs vs. Newcastle Falcons Oct 05 Exeter Chiefs 22.20
3 Leicester Tigers vs. Harlequins Oct 05 Leicester Tigers 15.30
4 Saracens vs. Bristol Oct 05 Saracens 7.90
5 Gloucester vs. Northampton Saints Oct 06 Gloucester 12.80

 

Bunnings NPC Predictions for the Quarter-Finals

Team Ratings for the Quarter-Finals

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Bay of Plenty 10.25 6.48 3.80
Taranaki 9.84 5.30 4.50
Canterbury 7.76 4.02 3.70
Hawke’s Bay 4.52 0.68 3.80
Wellington 3.04 6.60 -3.60
Otago 2.94 -1.15 4.10
Counties Manukau 2.78 -0.26 3.00
Tasman 2.44 3.49 -1.00
Auckland -0.65 -0.04 -0.60
Waikato -1.40 5.46 -6.90
North Harbour -3.41 1.50 -4.90
Northland -6.17 -6.54 0.40
Southland -11.60 -5.90 -5.70
Manawatu -14.16 -13.45 -0.70

 

Performance So Far

So far there have been 63 matches played, 41 of which were correctly predicted, a success rate of 65.1%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Hawke’s Bay vs. Auckland Sept 25 45 – 28 6.60 TRUE
2 Southland vs. Tasman Sept 26 38 – 55 -9.20 TRUE
3 Otago vs. North Harbour Sept 27 41 – 26 7.60 TRUE
4 Taranaki vs. Wellington Sept 27 39 – 20 8.20 TRUE
5 Bay of Plenty vs. Waikato Sept 28 41 – 5 11.60 TRUE
6 Counties Manukau vs. Manawatu Sept 28 48 – 24 18.70 TRUE
7 Northland vs. Canterbury Sept 28 19 – 19 -12.80 FALSE

 

Predictions for the Quarter-Finals

Here are the predictions for the Quarter-Finals. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 North Harbour vs. Southland Oct 03 North Harbour 11.20
2 Auckland vs. Otago Oct 04 Otago -0.60
3 Wellington vs. Bay of Plenty Oct 04 Bay of Plenty -4.20
4 Waikato vs. Northland Oct 04 Waikato 7.80
5 Manawatu vs. Hawke’s Bay Oct 04 Hawke’s Bay -15.70
6 Tasman vs. Counties Manukau Oct 05 Tasman 2.70
7 Canterbury vs. Taranaki Oct 05 Canterbury 0.90

 

NRL Predictions for the Grand Final

Team Ratings for the Grand Final

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Storm 8.36 9.29 -0.90
Roosters 8.04 7.44 0.60
Panthers 7.83 8.50 -0.70
Sharks 6.41 5.10 1.30
Broncos 4.54 -1.82 6.40
Bulldogs 2.21 0.07 2.10
Dolphins 1.52 -1.96 3.50
Sea Eagles 1.02 2.97 -2.00
Raiders 0.92 -3.61 4.50
Warriors -1.33 -1.68 0.30
Cowboys -1.69 4.11 -5.80
Eels -1.79 -3.02 1.20
Rabbitohs -5.19 -4.35 -0.80
Dragons -5.45 -4.55 -0.90
Titans -7.67 -5.50 -2.20
Wests Tigers -7.73 -10.97 3.20
Knights -10.01 -0.05 -10.00

 

Performance So Far

So far there have been 212 matches played, 134 of which were correctly predicted, a success rate of 63.2%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Storm vs. Sharks Sept 26 22 – 14 4.40 TRUE
2 Broncos vs. Panthers Sept 28 16 – 14 -0.70 FALSE

 

Predictions for the Grand Final

Here are the predictions for the Grand Final. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Storm vs. Broncos Oct 05 Storm 3.80

 

September 28, 2025

Briefly

  • From the Guardian: Exclusive: Study gives 85.7% probability Badminton House version of The Lute Player is by 17th-century master. As I said about a previous rating from the same company, there’s no way this probability is meaningful to three significant digits (except potentially to the computer). The company’s head, Dr Carina Popovici, told the Guardian: “Everything over 80% is very high.” which is, um, reasonable.  Importantly, we’re not told any of the “compared to what” information. Is this 85.7% considering that it was previously described as fake and doesn’t have good provenance, or it is 85.7% if the painting was selected from a training set of half real and half fakes.  Or what?
  • From The Xylom via Flowing Data, a map of H1B visa holders at US universities, including what fraction of the research budget it would take to keep hiring at the same rate under the new rules.  I’m not sure the research budget is the right comparison — yes, a lot of H1B’s are postdoctoral researcher, but I was in a regular academic job when I had an H1B.
  • Voting has just closed in Bird of the Year, the only online bogus clicky poll endorsed by StatsChat.  Bird of the Year takes a lot more care than most online bogus polls to clamp down on virtual ballot-box stuffing. Its results are more trustworthy than the typical online clicky poll.  You should definitely be more confident that it’s identified the truely most popular bird in Aotearoa than you are that the average unweighted opt-in survey is telling you the truth.
September 23, 2025

Panadol scare

R.F. Kennedy Jr managed to predict almost perfectly the day on which his research initiative would “find”  “the” “cause” of autism.  Of course, it’s easier when you don’t have to actually do any new research.

What do we actually know about paracetamol and autism or ADHD?

About a decade ago, there was a surprise finding of a fairly weak but not negligible correlation between paracetamol use during pregnancy and ADHD symptoms in the infant.  A New Zealand study repeated this analysis and found the same answer, at which point it became a bit more interesting.  There have been other replications since then.  The correlation is reasonably well established. The problem is deciding what we can say about causation.

Clearly no-one has done a randomised trial where some pregnant people take paracetamol and others don’t, because that would be unethical and also no-one would volunteer to be in the trial.  In the absence of randomisation, the question is how comparable the paracetamol and non-paracetamol infants would be otherwise. ADHD and autism diagnosis varies in frequency by all sorts of social factors, and there’s good evidence for a genetic basis in at least some cases of autism, so comparability is not automatic.  Also, one thing we do know about all the pregnant people who took paracetamol is that they had a reason to take paracetamol (probably pain or fever).  In contrast to alcohol or tobacco,  no-one’s taking paracetamol just for fun.

So, at that point things were all a bit unclear. On the one hand, maybe you want to avoid paracetamol during pregnancy if you didn’t need it, on the other hand, you probably already were.

Last year, a very large study in Sweden reported its results. They also found a weak correlation between paracetamol use and ADHD and autism symptoms in the whole population. However, they went further than this.  They did a study restricted to comparisons between siblings.  Oversimplifying massively, you could imagine taking all the families with two children where paracetamol was used in pregnancy for just one child and not the other. You could then count up the number of families where the paracetamol-exposed infant had ADHD or autism and not the unexposed child, and vice versa.  The point is that any other factor that differs between families will be the same for the two kids in the comparison and so can’t cause a  correlation. This c0uld be a genetic factor, or some ethnic or social class difference, or access to health care, or many other things.  (My description was oversimplified in the sense that they didn’t just use families with two kids, but also those with more than two, and they adjusted for variables that they know about and are different within a family. )

Importantly, this isn’t just a case of preferring a newer study or a bigger study.  The fact that the Swedish study saw the broadly the same whole-population correlations as other research studies argues that there isn’t something different about Sweden or about their data collection. The fact that they didn’t see the same correlation when doing within-family comparisons argues that the correlation is caused by something that varies between families, not something about individual pregnancies such as paracetamol use.

Estimating rare proportions

There is a statistic circulating on social media claiming that the average person in the USA thinks 21% of the population is transgender.  Obviously this isn’t true (both obviously it isn’t 21% and obviously that isn’t what the average person believes). It’s similar in some ways to the claim that some Americans think Iran is in the middle of the Atlantic Ocean, which I’ve dealt with before, except that estimating small proportions is an extensively studied problem in psychology, so a lot is known about the biases. In fact, if you look at the original source for the claim, demonstrating this phenomenon was the actual point of the story.

As Danielle Navarro explains, all small proportions are overestimated and all large proportions underestimated when people aren’t certain of the true value. This is an extremely consistent phenomenon, to the extent that we can actually say Americans are better informed about the proportion of transgender people than they are about other comparably extreme proportions.

[Update: Andrew Gelman writes about a slightly different, but related phenomenon, in the context of people reporting having been present for mass shootings.  It’s slightly different because people are reporting their own experience, which they presumptively do know, rather than their estimates of some proportion they have no way of knowing. We’d expect the bias to be smaller in this setting, but to still be present — it’s like the estimate of the frequency of virgin birth from the National Longitudinal Study of Youth]

United Rugby Championship Predictions for Week 1

Team Ratings for Week 1

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Leinster 13.41 13.41 0.00
Bulls 8.86 8.86 -0.00
Glasgow 6.18 6.18 -0.00
Stormers 4.17 4.17 0.00
Munster 3.65 3.65 -0.00
Edinburgh 2.67 2.67 -0.00
Sharks 1.29 1.29 0.00
Scarlets -0.54 -0.54 -0.00
Lions -1.19 -1.19 0.00
Connacht -1.39 -1.39 -0.00
Ospreys -2.15 -2.15 -0.00
Benetton -2.32 -2.32 -0.00
Cardiff Rugby -2.74 -2.74 -0.00
Ulster -3.24 -3.24 -0.00
Zebre -11.02 -11.02 -0.00
Dragons -15.66 -15.66 -0.00

 

Predictions for Week 1

Here are the predictions for Week 1. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Stormers vs. Leinster Sept 27 Leinster -2.20
2 Glasgow vs. Sharks Sept 27 Glasgow 11.90
3 Ulster vs. Dragons Sept 27 Ulster 19.40
4 Bulls vs. Ospreys Sept 28 Bulls 18.00
5 Zebre vs. Edinburgh Sept 28 Edinburgh -6.70
6 Scarlets vs. Munster Sept 28 Scarlets 2.80
7 Cardiff Rugby vs. Lions Sept 28 Cardiff Rugby 5.50
8 Connacht vs. Benetton Sept 28 Connacht 7.90

 

Top 14 Predictions for Round 4

Team Ratings for Round 4

The basic method is described on my Department home page.
Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Current Rating Rating at Season Start Difference
Stade Toulousain 10.67 11.56 -0.90
Bordeaux Begles 4.76 4.78 -0.00
Toulon 3.58 3.49 0.10
Section Paloise 2.47 2.21 0.30
Racing 92 2.23 1.88 0.30
Stade Rochelais 1.95 1.22 0.70
Clermont 1.67 1.88 -0.20
Castres Olympique 1.36 0.59 0.80
Bayonne 0.82 1.48 -0.70
Montpellier 0.74 -0.21 1.00
Lyon 0.16 -0.45 0.60
Stade Francais -1.88 -2.17 0.30
USA Perpignan -4.13 -3.37 -0.80
Montauban -11.49 -10.00 -1.50

 

Performance So Far

So far there have been 21 matches played, 15 of which were correctly predicted, a success rate of 71.4%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Clermont vs. Section Paloise Sept 21 50 – 27 4.50 TRUE
2 Bordeaux Begles vs. Montauban Sept 21 71 – 24 21.10 TRUE
3 Castres Olympique vs. Bayonne Sept 21 48 – 17 5.40 TRUE
4 Lyon vs. Stade Francais Sept 21 42 – 37 9.00 TRUE
5 USA Perpignan vs. Racing 92 Sept 21 15 – 28 1.10 FALSE
6 Montpellier vs. Stade Toulousain Sept 21 44 – 14 -5.50 FALSE

 

Predictions for Round 4

Here are the predictions for Round 4. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

Game Date Winner Prediction
1 Stade Francais vs. Bordeaux Begles Sept 28 Bordeaux Begles -0.10
2 Montauban vs. Montpellier Sept 28 Montpellier -5.70
3 Racing 92 vs. Clermont Sept 28 Racing 92 7.10
4 Section Paloise vs. Lyon Sept 28 Section Paloise 8.80
5 Stade Rochelais vs. USA Perpignan Sept 28 Stade Rochelais 12.60
6 Stade Toulousain vs. Castres Olympique Sept 28 Stade Toulousain 15.80
7 Bayonne vs. Toulon Sept 29 Bayonne 3.70