Stats Chat

Yesterday I noted RNZ had just quoted an Auckland Transport claim about the cost of driving that was implausible on the face of it, and didn’t seem to have done any checking or provided any explanation.  Today, the same story is in the Herald, with the same  lack of explanation.

Here’s the RNZ quote; the Herald one is almost identical

Auckland Transport said before the Iran conflict began late last month, the cost of public transport was roughly the same as the cost of driving a vehicle with single occupancy in Auckland.

It’s now costing people nearly double to drive their own cars.

“The cost of petrol has risen at least 50 cents per litre since then, with a 15-kilometre single person commute now costing roughly 80 cents per kilometre, which is equal to about $12 for the total trip.”

So where does this come from? In comments to yesterday’s post, David Welch pointed me to the IRD page on the cost of driving.  The “Tier 1” cost in 2024-5 was $1.17/km for petrol cars. That’s higher than 80c/km, and it’s also not the right comparison — it’s an average cost per km. That is, it includes a per-km share of the fixed costs of having a car. Auckland Transport are (or should be) talking about just the extra per-km cost of using the car to commute. Taking a bus won’t make your car loan go away.

The IRD view on the cost of running a car is their “Tier 2” number, which is only 37c/km.   That, interestingly, is close to half the 80c/km that Auckland Transport is claiming. Since they say that this is double what last year’s cost was, their estimate of last year’s cost is interestingly close to the IRD Tier 2 value and might come from the same methods?

I found an estimate of national average petrol prices as $2.66/L  from December last year.  That would be an increase of 44c/L compared to the one Auckland station I checked yesterday.  If, instead, we take Auckland Transport’s “at least 50c/L”, the increase in running costs would be 5c/km for a vehicle that gets 10 km/L, and less than that for a more typical single-commuter vehicle, so again we can’t get the AT figure.

Even without trying to work out and replicate their calculations, however, we can say one simple thing.  Petrol prices have not yet nearly doubled, so they can’t have caused driving costs, however defined, to have nearly doubled.

On the other hand, the conclusion that people should consider switching to public transport is true: we want to save the potentially scarce supply of oil for people and industries who don’t have any alternatives.

Update: Greater Auckland have also reprinted the claim from AT, again without comment.

• RNZ passes on a claim by Auckland Transport  that Cost of driving 15km in Auckland nearly double that of public transport. Specifically, they say we have “a 15-kilometre single person commute now costing roughly 80 cents per kilometre, which is equal to about $12 for the total trip.” That seems a lot?  I won’t claim to be an expert on driving costs, but the nearest petrol station for which I can see data (Mobil on K Rd)  is charging $3.099/litre.  To get 80c/km you would need to use a bit over a 1/4 litre per km (more precisely, 0.258l/km). This is 25.8 L/100km (for our US readers, about 9 mpg).
• The US celebrated Pi Day this week, and there was a niche popular video describing how to estimate π by coin tossing.  Toss a coin until there are more heads than tails. The expected value of the proportion at this point (which is obviously more than 1/2 and at most 1) is π/4, so by repeating this procedure lots and lots of times and averaging the results you can estimate π/4, and thus π.  This is not a good way to compute π, but it’s surprising that it works at all (sadly, the explanation for why it works is not very illuminating)
• From newsroom, “Mazda NZ’s Driving Good promotion promises the company will donate five trees to environmental charity Trees That Count and that “over each vehicle’s five-year warranty term, these five trees will not only mitigate any environmental impact from CO2 emissions, but they will significantly contribute to the ecosystems in which they are planted”.” Whether this is true turns out to be sensitive to your interpretation of “mitigate”.  There is a sense in which planting any trees provides some mitigation of the environmental impact from CO2 emissions, but you might think Mazda was saying something more like “will absorb as much CO2 as the car emits”. If that’s what you think, you agree with Lawyers for Climate Action, who say it would take 41,000 trees to absorb a comparable amount of CO2.
• StatsNZ said “food prices were up 2.5 percent in January 2026 compared with December 2025. The correct increase was 2.1 percent.”  They’ve fixed it, and it didn’t impact the CPI.

Team Ratings for Week 6

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.

Performance So Far

So far there have been 25 matches played, 15 of which were correctly predicted, a success rate of 60%.
Here are the predictions for last week’s games.

Predictions for Week 6

Here are the predictions for Week 6. 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.

Team Ratings for Week 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.

Performance So Far

So far there have been 96 matches played, 62 of which were correctly predicted, a success rate of 64.6%.
Here are the predictions for last week’s games.

Predictions for Week 13

Here are the predictions for Week 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.

Team Ratings for Round 3

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.

Performance So Far

So far there have been 16 matches played, 9 of which were correctly predicted, a success rate of 56.2%.
Here are the predictions for last week’s games.

Predictions for Round 3

Here are the predictions for Round 3. 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.

Team Ratings for Week 3

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.

Performance So Far

So far there have been 14 matches played, 9 of which were correctly predicted, a success rate of 64.3%.
Here are the predictions for last week’s games.

Predictions for Week 3

Here are the predictions for Week 3. 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.

The National Party is saying in ads “Stats show people under the age of 25 on Jobseeker Support will spend an average of 20 years on a benefit over their lifetimes.” That’s a surprising claim.  Most surprising numerical claims in political advertising are true (though often misleading) and so we should expect this one to be true. It’s not so much that it might be misleading — I don’t think anyone will actually believe the natural interpretation of it — but it’s the sort of statement that (without context) is corrosive to the public confidence in statistics.

The natural interpretation is that people who go on Jobseeker Support while looking for a job under age 25 will spend an average of 20 years on unemployment benefits and similar. I don’t see how that could really be true. Lots of young people apply for Jobseeker Support while looking for jobs.

Let’s consider possibilities.  One explanation would be that “on a benefit” is being interpreted to include, say, child support or pensions. In that case the claim might be true but uninteresting, and you might worry about attempts to change the statistics.  Another possibility is that “Jobseeker Support” is a term with hidden complexities. A third is that there’s something happening with the calculation itself that is different from our expectations.

We need to find out what the actual “stats show”. This is trickier than it should be.  Advertisers are required to have some support for certain sorts of claims, but they don’t have to make it easy to check. There’s nothing on the ads that I saw. There’s a story on Stuff that has expanded versions of the claims being made.  In fact, there’s a substantially stronger claim

MSD analysis shows beneficiaries aged under 25 are projected to spend at least 20 of their working years on welfare 

It doesn’t explain the implausible numbers, but it does at least provide links.

One of the links is to a page at MSD that gives some of the numbers

This table is useful. It makes two things clear. First, there are hidden complexities in the “Jobseeker Support” label — it also includes people unable to work for health or disability reasons. Second, and more surprising, this doesn’t help with the explanation.  The “work ready” and “health condition and disability” subgroups have pretty much the same estimated years on benefit.  The time is longer for young people, but that’s for the obvious reason that they have more time before age 65 available.  The page also gives a list of what they count as “on a benefit”, confirming that they aren’t cheating by including things like retirement or child support.

Another link is to the underlying report (PDF).  From this report, Table 3.1 is informative (click to embiggen)

One important piece of information is the middle one of the brown-tagged rows: “Benefit history within last year”.  This, together with the use of a modelling date of 30 September, and a table adding up to plausibly the NZ adult population, makes me think the denominator for the average time on a benefit is determined just by who is on a benefit on 30 September each year.  If Chris finishes study in December, takes a month off, and starts looking for work in January, finding a job in June, they won’t be counted as “on a benefit under 25”.  Using “on benefit at a particular date” as means your denominator will miss out on most people who have a short period of unemployment.  In statistics, this is called “length-biased sampling”. We don’t mean “biased” in a negative way, necessarily, but sampling at a single date means you get more people with long eligibility periods and fewer people with short eligibility periods.

This, I think, is the context that makes the number more plausible. It’s not measuring people who start on a benefit when under 25, it’s measuring people who, at a particular point in time, are currently on a benefit. On top of that, the particular point in time is chosen to miss the short-term unemployment decrease each year as people leave full-time education.   We can see that the length-biased sampling matters, because the group “Benefit history within last year” have about half the expected future time on benefits, and “Benefit history within 1-5 years” about another half lower.

With this in mind, the expected time on benefits in the future still probably does count as worryingly high.  There’s no particular partisan side to concern about benefit traps — they are well recognised as a potential problem by progressives as well as conservatives.  The policy questions are more about whether you should spend more money helping people get into jobs vs making it harder and more unpleasant to stay on benefit, and about what the appropriate income level of benefits should be.

I don’t feel the either the Ministry or the National Party have published these numbers in a way that makes the context easy to understand. I don’t think journalists have done a great job in explaining the numbers, either. In some ways the ads are the least worrying manifestation of these numbers, since no-one really expects a political ad to be fair and informative, but it would be nice if we could.

From an admittedly bogus poll of my followers on Mastodon

The correct answer is “none of the above”. The most appropriate common name is probably “avocado”

It looks like most respondents didn’t know what Persea americana is, but assumed the question was about some actual controversy such as the appropriate name for Actinidia deliciosa cultivars  — ‘kiwifruit’, but often called ‘kiwi’ in the US. This is frivolous, but it’s similar in many ways to putatively serious survey questions such as “bombing Agrabah” or asking about Harambe as a presidential candidate in 2016.

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.

Performance So Far

So far there have been 5 matches played, 2 of which were correctly predicted, a success rate of 40%.
Here are the predictions for last week’s games.

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.

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.

Performance So Far

So far there have been 20 matches played, 11 of which were correctly predicted, a success rate of 55%.
Here are the predictions for last week’s games.

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.