April 2, 2026

Briefly

  • For the day between March 31 and April 2nd, Andrew Gelman takes on an app that claims to find patterns in lotto numbers and make you money.
  • RNZ reports the plans for tolls on the Road of Northland Significance, a charge of $4.50 each way from Warkworth to Te Hana (you will see some quotes of $14.20, which includes current tolls on the already-existing road to Puhoi). They don’t report what fraction of the cost the tolls will cover. Greater Auckland looked at the NZTA consultation papers about the tolling and say 35 years of tolling will raise $391m. That would be nearly 10% of the (phase 1) cost if you didn’t include interest; it’s a much smaller fraction when you do. And this is phase 1 — there are two more phases in the planned road to Whangārei.  Whether the road is worth the cost isn’t my specialty, but it’s a lot of cost.
  • Len Cook (former Government Statistician) is in the Otago Daily Times disapproving of the planned removal of the census enumerations. We’ve covered this topic before.  The changes to the Data and Statistics Act are up for public comment, as are the necessary changes to the Electoral Act.   The electoral changes are not intrinsically controversial but are needed because electoral redistricting is currently triggered by the census. The electoral changes are important because they need a 75% supermajority in Parliament.
  • RNZ reports on an NZTA report on public consultation about road changes in Wellington. First, the usual whinge: please link to this sort of report, so we can read it if your summary gets us interested!  Second, and the StatsChat motivation, the NZTA report displays pretty graphics of the public feedback, which are systematically wrong! For example, on the question “will a second Terrace Tunnel make things worse or better for you?” the lower bar is from the report and the upper bar is correct based on the percentages.  The right end of the bar is “better”, and is exaggerated

    Or the next question, about Te Aro improvements (original above, correct version below). Again, the “better” end is exaggerated

    I don’t think this is likely to be deliberate, but it’s a bad look

Oily rag

The Ministry of Transport have put up a fuel monitoring dashboard. It shows estimates of demand, supply, and price.

At the moment, the reduction in demand is less than 10%, a level of demand that’s probably not sustainable in the medium when global supply is down at least 25%. On the other hand, we are still at level 1 of the alert system, and even level 2 doesn’t ask for any real reductions in demand.

What this display doesn’t show is any sort of “time to running out”.  That’s probably sensible, because it’s not even well-defined, let alone predictable. If you define “running out” as some petrol stations being out of supplies then it’s already happened. If you define it as “no fuel in the country”, it probably won’t happen. And if you define it as level 3 or level 4 restrictions on supply then it’s a choice by the government based on unknown criteria, and so is hard to forecast statistically.

 

March 31, 2026

United Rugby Championship Predictions for Week 15

Team Ratings for Week 15

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
Glasgow 8.61 6.18 2.40
Leinster 8.25 13.41 -5.20
Bulls 7.78 8.86 -1.10
Stormers 6.32 4.17 2.20
Lions 1.89 -1.19 3.10
Ulster 1.87 -3.24 5.10
Munster 0.85 3.65 -2.80
Sharks 0.22 1.29 -1.10
Connacht -0.25 -1.39 1.10
Edinburgh -2.03 2.67 -4.70
Scarlets -2.10 -0.54 -1.60
Cardiff Rugby -2.39 -2.74 0.30
Ospreys -2.62 -2.15 -0.50
Benetton -4.56 -2.32 -2.20
Dragons -8.89 -15.66 6.80
Zebre -12.93 -11.02 -1.90

 

Performance So Far

So far there have been 112 matches played, 77 of which were correctly predicted, a success rate of 68.8%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Sharks vs. Cardiff Rugby Mar 28 21 – 15 10.60 TRUE
2 Glasgow vs. Benetton Mar 28 31 – 10 19.90 TRUE
3 Leinster vs. Scarlets Mar 28 36 – 19 17.40 TRUE
4 Bulls vs. Munster Mar 29 34 – 31 15.40 TRUE
5 Connacht vs. Ospreys Mar 29 21 – 14 10.00 TRUE
6 Lions vs. Dragons Mar 29 42 – 26 18.30 TRUE
7 Stormers vs. Edinburgh Mar 29 33 – 14 14.30 TRUE
8 Zebre vs. Ulster Mar 29 12 – 28 -6.60 TRUE

 

Predictions for Week 15

Here are the predictions for Week 15. 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 Dragons vs. Bulls Apr 18 Bulls -9.70
2 Edinburgh vs. Zebre Apr 18 Edinburgh 17.90
3 Ulster vs. Leinster Apr 18 Leinster -4.40
4 Stormers vs. Connacht Apr 18 Stormers 13.60
5 Lions vs. Glasgow Apr 19 Lions 0.30
6 Scarlets vs. Cardiff Rugby Apr 19 Scarlets 2.30
7 Benetton vs. Munster Apr 19 Benetton 1.60
8 Ospreys vs. Sharks Apr 19 Ospreys 4.20

 

Top 14 Predictions for Round 21

Team Ratings for Round 21

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 13.99 11.56 2.40
Bordeaux Begles 6.26 4.78 1.50
Montpellier 5.13 -0.21 5.30
Stade Francais 3.92 -2.17 6.10
Section Paloise 3.16 2.21 1.00
Stade Rochelais 2.71 1.22 1.50
Clermont 2.45 1.88 0.60
Racing 92 1.07 1.88 -0.80
Lyon 0.60 -0.45 1.00
Toulon -0.65 3.49 -4.10
Castres Olympique -0.70 0.59 -1.30
Bayonne -1.26 1.48 -2.70
USA Perpignan -4.89 -3.37 -1.50
Montauban -18.89 -10.00 -8.90

 

Performance So Far

So far there have been 140 matches played, 108 of which were correctly predicted, a success rate of 77.1%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Bayonne vs. Stade Rochelais Mar 29 26 – 15 1.80 TRUE
2 Castres Olympique vs. Montauban Mar 29 49 – 17 23.70 TRUE
3 Lyon vs. Bordeaux Begles Mar 29 17 – 21 1.50 FALSE
4 Section Paloise vs. Racing 92 Mar 29 27 – 17 8.40 TRUE
5 Stade Toulousain vs. Montpellier Mar 29 45 – 29 15.30 TRUE
6 USA Perpignan vs. Toulon Mar 29 36 – 20 1.20 TRUE
7 Stade Francais vs. Clermont Mar 30 64 – 20 5.80 TRUE

 

Predictions for Round 21

Here are the predictions for Round 21. 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. Section Paloise Apr 19 Bayonne 2.10
2 Castres Olympique vs. Stade Toulousain Apr 19 Stade Toulousain -8.20
3 Clermont vs. Lyon Apr 19 Clermont 8.40
4 Montauban vs. Toulon Apr 19 Toulon -11.70
5 Montpellier vs. USA Perpignan Apr 19 Montpellier 16.50
6 Racing 92 vs. Stade Francais Apr 19 Racing 92 3.60
7 Stade Rochelais vs. Bordeaux Begles Apr 19 Stade Rochelais 2.90

 

Super Rugby Predictions for Week 8

Team Ratings for Week 8

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
Chiefs 11.18 12.36 -1.20
Hurricanes 11.16 8.29 2.90
Blues 9.86 8.91 1.00
Crusaders 7.74 8.41 -0.70
Brumbies 5.86 5.59 0.30
Reds 1.16 1.74 -0.60
Highlanders -3.03 -3.06 0.00
Waratahs -4.66 -5.84 1.20
Western Force -5.70 -6.29 0.60
Fijian Drua -7.95 -7.64 -0.30
Moana Pasifika -11.03 -7.88 -3.20

 

Performance So Far

So far there have been 35 matches played, 23 of which were correctly predicted, a success rate of 65.7%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Moana Pasifika vs. Highlanders Mar 27 19 – 39 -1.60 TRUE
2 Brumbies vs. Waratahs Mar 27 28 – 30 17.00 FALSE
3 Hurricanes vs. Reds Mar 28 52 – 14 11.60 TRUE
4 Blues vs. Fijian Drua Mar 28 40 – 15 20.90 TRUE
5 Western Force vs. Chiefs Mar 28 14 – 24 -13.80 TRUE

 

Predictions for Week 8

Here are the predictions for Week 8. 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 Crusaders vs. Fijian Drua Apr 03 Crusaders 19.20
2 Chiefs vs. Waratahs Apr 04 Chiefs 19.30
3 Reds vs. Western Force Apr 04 Reds 11.90

 

Rugby Premiership Predictions for Round 13

Team Ratings for Round 13

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 12.73 10.30 2.40
Leicester Tigers 8.25 5.55 2.70
Northampton Saints 5.59 -1.47 7.10
Saracens 4.85 5.03 -0.20
Exeter Chiefs 4.74 -4.58 9.30
Bristol 2.50 3.66 -1.20
Sale Sharks 2.36 6.70 -4.30
Gloucester -4.56 4.13 -8.70
Harlequins -8.80 -3.02 -5.80
Newcastle Red Bulls -19.80 -18.45 -1.40

 

Performance So Far

So far there have been 60 matches played, 44 of which were correctly predicted, a success rate of 73.3%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Gloucester vs. Leicester Tigers Mar 29 17 – 36 -3.40 TRUE
2 Bristol vs. Harlequins Mar 29 14 – 18 22.10 FALSE
3 Newcastle Red Bulls vs. Exeter Chiefs Mar 29 14 – 38 -16.30 TRUE
4 Sale Sharks vs. Bath Mar 29 26 – 31 -3.00 TRUE
5 Saracens vs. Northampton Saints Mar 29 17 – 21 8.10 FALSE

 

Predictions for Round 13

Here are the predictions for Round 13. 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 Bristol vs. Gloucester Apr 18 Bristol 14.10
2 Bath vs. Harlequins Apr 19 Bath 28.50
3 Exeter Chiefs vs. Northampton Saints Apr 19 Exeter Chiefs 6.20
4 Leicester Tigers vs. Newcastle Red Bulls Apr 19 Leicester Tigers 35.10
5 Sale Sharks vs. Saracens Apr 20 Sale Sharks 4.50

 

NRL 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
Panthers 14.91 8.77 6.10
Storm 8.25 6.96 1.30
Sharks 5.91 7.25 -1.30
Broncos 5.65 7.06 -1.40
Roosters 5.49 9.50 -4.00
Warriors 2.05 -1.18 3.20
Dolphins 1.35 1.85 -0.50
Bulldogs 0.28 2.13 -1.80
Raiders -1.56 1.62 -3.20
Eels -2.24 -0.37 -1.90
Wests Tigers -3.10 -7.26 4.20
Rabbitohs -3.11 -5.05 1.90
Sea Eagles -3.56 0.21 -3.80
Cowboys -4.12 -2.69 -1.40
Dragons -7.70 -6.72 -1.00
Titans -8.78 -8.02 -0.80
Knights -9.73 -14.06 4.30

 

Performance So Far

So far there have been 32 matches played, 19 of which were correctly predicted, a success rate of 59.4%.
Here are the predictions for last week’s games.

Game Date Score Prediction Correct
1 Sea Eagles vs. Roosters Mar 26 16 – 33 -3.00 TRUE
2 Warriors vs. Wests Tigers Mar 27 14 – 32 13.30 FALSE
3 Broncos vs. Dolphins Mar 27 26 – 12 6.70 TRUE
4 Bulldogs vs. Knights Mar 28 16 – 24 17.50 FALSE
5 Panthers vs. Eels Mar 28 48 – 20 15.20 TRUE
6 Cowboys vs. Storm Mar 28 28 – 24 -10.50 FALSE
7 Raiders vs. Sharks Mar 29 22 – 34 -1.90 TRUE
8 Titans vs. Dragons Mar 29 22 – 14 1.50 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 Dolphins vs. Sea Eagles Apr 02 Dolphins 8.90
2 Rabbitohs vs. Bulldogs Apr 03 Rabbitohs 0.60
3 Panthers vs. Storm Apr 03 Panthers 10.70
4 Dragons vs. Cowboys Apr 04 Dragons 0.40
5 Titans vs. Broncos Apr 04 Broncos -10.40
6 Sharks vs. Warriors Apr 05 Sharks 7.90
7 Knights vs. Raiders Apr 05 Raiders -4.20
8 Eels vs. Wests Tigers Apr 06 Eels 4.90

 

AFL Predictions for Week 5

Team Ratings for Week 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
Western Bulldogs 31.57 26.06 5.50
Brisbane Lions 22.36 26.20 -3.80
Hawthorn Hawks 21.12 22.83 -1.70
Geelong Cats 20.28 26.75 -6.50
Adelaide Crows 17.34 15.32 2.00
Gold Coast Suns 16.95 10.24 6.70
Fremantle Dockers 10.94 6.56 4.40
Collingwood 10.89 11.76 -0.90
Sydney Swans 8.70 0.56 8.10
GWS Giants 4.07 9.54 -5.50
Melbourne Demons 0.91 1.64 -0.70
St Kilda Saints -6.47 -7.63 1.20
Carlton Blues -10.81 -4.77 -6.00
Port Adelaide Power -17.39 -14.65 -2.70
North Melbourne -20.54 -21.71 1.20
Richmond Tigers -31.57 -29.44 -2.10
Essendon Bombers -32.19 -27.89 -4.30
West Coast Eagles -34.16 -39.36 5.20

 

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 Geelong Cats vs. Adelaide Crows Mar 26 68 – 60 15.20 TRUE
2 Collingwood vs. GWS Giants Mar 27 87 – 54 15.00 TRUE
3 St Kilda Saints vs. Brisbane Lions Mar 28 80 – 113 -15.00 TRUE
4 Fremantle Dockers vs. Richmond Tigers Mar 28 103 – 43 52.10 TRUE
5 Essendon Bombers vs. North Melbourne Mar 28 69 – 81 -11.60 TRUE
6 Port Adelaide Power vs. West Coast Eagles Mar 29 90 – 92 33.10 FALSE
7 Carlton Blues vs. Melbourne Demons Mar 29 77 – 100 -9.20 TRUE

 

Predictions for Week 5

Here are the predictions for Week 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 Brisbane Lions vs. Collingwood Apr 02 Brisbane Lions 22.50
2 North Melbourne vs. Carlton Blues Apr 03 Carlton Blues -9.70
3 Adelaide Crows vs. Fremantle Dockers Apr 03 Adelaide Crows 17.40
4 Richmond Tigers vs. Port Adelaide Power Apr 04 Port Adelaide Power -3.20
5 West Coast Eagles vs. Sydney Swans Apr 04 Sydney Swans -31.90
6 Melbourne Demons vs. Gold Coast Suns Apr 05 Gold Coast Suns -5.00
7 Western Bulldogs vs. Essendon Bombers Apr 05 Western Bulldogs 63.80
8 Hawthorn Hawks vs. Geelong Cats Apr 06 Hawthorn Hawks 11.80

 

Dangers of opt-in surveys

There have been two stories just recently in the Guardian about the dangers of opt-in surveys.  A survey from the respectable polling organisation YouGov reported a big increase in (Christian) church attendance among young people.  This was a bit of a  surprise, and didn’t seem to match up with other polling data (or with attendance counts by denominations that count attendance), but it was YouGov and it was what some people wanted to hear.

Apparently the problem was opt-in respondents.  This isn’t the completely useless opt-in clicky polls that our news sites put up from time to time; YouGov is a serious polling organisation.  However, I think it’s fair to say YouGov has tried to get accurate poll results by focusing more on statistical modelling of who responds and less on trying to get a good sample.  Again, that’s a perfectly reasonable strategy and has historically been competitive. You can’t get real random samples of people any more — not like in the 1950s — and so you get samples that are representative in some qualitative sense and reweight them to match the groups you’re trying to study.

You might think it’s strange that people would try to get into survey samples. It is strange, and that’s exactly the problem. Only a small fraction of people will try to get into surveys for the money, so those people are very unrepresentative, and while they are only a small fraction of the population that’s still a lot of people.   In the future, there’s the potential for LLM-based fake people to take surveys for the money (or just to be inconvenient), and they will be still worse.

When you start with a reasonably well-controlled sample and some people opt out, you have a subset of a reasonably well-controlled sample. It looks as though allowing too much self-selection can be qualitatively worse (though this is a one-off so far, and only provides limited evidence).

I also want to note that CNN reports a response from the Bible Society to the withdrawal of the survey report

The Bible Society said in a statement it was “deeply disappointed” by what had happened, but insisted the “wider picture” from other surveys pointed to “an increased engagement in faith among young adults compared to older generations.”

This isn’t a good reaction: the reason we found out the report was inaccurate was precisely that other evidence didn’t point the same way.

March 26, 2026

As and when it looks supportive

Via Russell Brown on Bluesky, the Herald has a report on the increases in people being charged with cannabis possession. Charges fell by about 1/3 from 2017 to 2021, in parallel with increasing evidence that arrests for possession didn’t really have social license, but then started rising and now are back at nearly 2017 levels.

So what do the police say? Well, the Herald reports

Director of the National Organised Crime Group Detective Superintendent Greg Williams says wastewater testing in the Auckland and Northland region shows cannabis consumption spiking in July 2024.

“If you look at that charging data, it actually perfectly almost reflects what looks like a significant increase in cannabis consumption.”

We can look at the charging data, and the Herald does. We can’t look at the wastewater cannabis data, though.  On the same day in the Herald there was a story on the newest results from wastewater drug analyses. The story reported estimates of meth, MDMA, and cocaine use. As expected, there’s a lot more meth than anything else, but there’s a potentially worrying increase in cocaine (it’s not so much that cocaine is worse than meth, but it’s a new supply chain).  There was no comment in the story on cannabis use.  There were related stories at One News and RNZ and Newstalk ZB.

If you go to the NZ Police webpage on wastewater drug testing you see

The drugs tested for include methamphetamine, MDMA, cocaine, fentanyl, and heroin. These reports focus on methamphetamine, MDMA and cocaine as these drugs are routinely detected by the programme.

At PHF Science (former ESR) you can find plenty of pages talking about their efforts in testing for meth, MDMA and cocaine, such as this one on the 2024 spike in meth, or this research paper with the mind-numbing details of how they do the testing, or this drug harm page where they say

To date, wastewater testing has been used to measure consumption of illicit drugs including methamphetamine, MDMA, cocaine, heroin and fentanyl. 

Neither the police nor PHF Science publish cannabis-use estimates from wastewater.  The reason they don’t publish the estimates is they aren’t very good.  According to a research report from PHF Science,

However, certain characteristics of cannabis – such as it being lipophilic, not dissolving well in water and its tendency to stick to surfaces such as wastewater pipes – have made analysis in wastewater more difficult. Additionally, due to the considerable chemical differences between cannabis and the other illicit substances being monitored it cannot be added to the same analysis workflow. At this stage there is still too much uncertainty for cannabis measurements to be reliably quantifiable. However, the monitoring data can still be used in trend analyses

They do measure cannabis at five sites around the country, and as the research report says, the data could still be used in trend analyses. But popping up with a claim about two regions from undisclosed data about one time period isn’t a credible trend analysis.

What other data are there?

I don’t find the NZ Drug Trends Survey all that convincing on a detailed level, but its questions asking people who admit to using illegal drugs about which drugs they use should also be ok for trend analyses, and their cocaine reports show a similar trend to the wastewater data. They see a decrease and then increase in daily or weekly cannabis use over the time period we’re talking about, but to a much smaller extent: 68% of respondents at the peak, then down to 57%, then up to 70% for the most recent data. That’s about a 15% decrease and corresponding in regular cannabis use among regular drug users.  Also, a big spike in population cannabis use would increase the number of regular drug users, and show up as a decrease in the proportion regularly using other drugs, which we don’t see.

The NZ Health Survey asks about drug use. The Drug Foundation has collected their data (along with other data sources) and it doesn’t show a pattern anything like the police charging data (click to embiggen, as always)

So, I’m not convinced by the bare assertion that wastewater data show the police are just picking up the same fraction of a varying drug-user population. If the police want to use trends in the cannabis wastewater data to influence public policy they should publish the complete data series, with all the attached caveats from the scientists behind the testing (who I do trust).