Posts from February 2017 (23)

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.

Performance So Far

So far there have been 9 matches played, 7 of which were correctly predicted, a success rate of 77.8%.
Here are the predictions for last week’s games.

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.

Team Ratings for Round 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.

Predictions for Round 1

Here are the predictions for Round 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.

Each week, we would like to invite readers of Stats Chat to submit nominations for our Stat of the Week competition and be in with the chance to win an iTunes voucher.

Here’s how it works:

• Anyone may add a comment on this post to nominate their Stat of the Week candidate before midday Friday March 3 2017.
• Statistics can be bad, exemplary or fascinating.
• The statistic must be in the NZ media during the period of February 25 – March 3 2017 inclusive.
• Quote the statistic, when and where it was published and tell us why it should be our Stat of the Week.

Next Monday at midday we’ll announce the winner of this week’s Stat of the Week competition, and start a new one.

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If you’d like to comment on or debate any of this week’s Stat of the Week nominations, please do so below!

Nick Smith, the Environment Minister, on Stuff

This bit is very nerdy. We are saying at 540 E.coli the risk is one in 20 (of getting sick).  But that one in 20 is at the 95 per cent confidence level. So there is an extra level of cautiousness. Even if you put 20 people in water and it has a 540 E.coli level it’s not saying on average one person gets sick out of 20. It’s saying one in 20 of 20 groups will have one in 20 get sick.

No, it’s not saying that.

Let’s step back a bit.  First, why is such a baroque description of the risk, less than 1/20 95% of the time, even being used?

As Dr Smith does convey in the interview, the problem is that risk varies. There are two sources of uncertainty if you go swimming in the Hutt River. First, the bacteria count varies over time — with rain, temperature, and whatevever else — so you don’t know what it will be at precisely the time you stick your head under.  Second, if you end up swallowing some  Campylobacter you still only have a chance of getting infected.

Summarising these two types of uncertainty in a single number is hard. One sensible approach is to pick a risk, such as 1/20.  If we want to say that the chance of getting infected is less than 1/20, we need to handle both the variation in shittiness of the water, and the basically random risk of infection for a given level of contamination.

Suppose we imagine a slightly implausible extreme sports facility that sends 100 backpackers on one-day swimming parties each day.  On 95% of days (347 days per year), they’d expect fewer than 5 to get infected. On 5% of days (18 days per year) they’d expect more than 5 to get infected, but it couldn’t possibly be more than 100.  So the total number of infections across the year is less than 5*347+100*18, or 10% of swimmers. That sounds bad, but it’s an extremely conservative upper bound.  In fact, when the risk is less than 5% it’s often much less, and when it’s greater than 5% it’s usually nowhere near 100%.  To say more, though, you’d need to know more about how the risk varies over time.

There are statistical models for all of this, and since everyone seems to be using the same models we can just stipulate that they’re reasonable.  The detailed report is here (PDF), and Jonathan Marshall, who’s a statistician who knows about this sort of thing, has scripts to reproduce some calculations here.

Using those models, a `yellow’ river, with risk less than 1/20 95% of the time actually has risk less than 1/1000 about half the time, but occasionally has risks well over 10%.  Our imaginary extreme sports facility will have about 3 infections per 100 customers, averaged over the year. About half these infections will happen on the worst 5% of days.

So, the 1/20 of 1/20 level doesn’t by itself guarantee anything better than 10% infection risk for people swimming on randomly chosen days, but combined with knowledge of the actual bacteria distribution in NZ rivers, seems to work out at about a 3%  risk averaged over all days.  Also, if you can detect and avoid the worst few days each year, your risk will be reduced quite a lot.

Team Ratings for Round 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.

Predictions for Round 1

Here are the predictions for Round 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.

Q: It’s nice to see a balanced nutrition story in the Herald today, isn’t it?

A: Um.

Q: They talk about benefits and drawbacks of a vegan diet.

A: Um.

Q: It’s impressive that just one serving of butter a day can double your risk of diabetes, isn’t it?

A: <sigh>

Q: Isn’t that what the research paper says?

A: It’s a bit hard to find, since they don’t link and don’t give any researcher names.

Q: Did you find it in the end?

A: Yes. And that’s not really what it found.

Q: Is this the weird yoghurt thing?

A: Yes, that’s part of it.  They found a higher risk in people who ate more butter or more cheese, a lower risk in people who ate more whole-fat yoghurt, and “No significant associations between red meat, processed meat, eggs, or whole-fat milk and diabetes were observed.”

Q: That doesn’t sound like a systematic effect of meat. Or animal products.

A: And there wasn’t any association at the start of the study, only later on.

Q: So it’s eating butter in a research study that’s dangerous?

A: Could be.

Q: Ok, what about the bit where men need meat for their sons to have children?

A: No men in the study

Q: Mice?

A: No, smaller.

Q: Zebrafish?

A: Smaller.

Q: Um. Fruit flies?

A: Yes.

Q: Do fruit flies even eat meat?

A: No, there wasn’t any meat in the study either. The flies got higher or lower amounts of yeast in their diet.

Q: But don’t vegans eat yeast?

A: I’m not sure that’s the biggest problem with extrapolating this to Men Need Meat.

Each week, we would like to invite readers of Stats Chat to submit nominations for our Stat of the Week competition and be in with the chance to win an iTunes voucher.

Here’s how it works:

• Anyone may add a comment on this post to nominate their Stat of the Week candidate before midday Friday February 24 2017.
• Statistics can be bad, exemplary or fascinating.
• The statistic must be in the NZ media during the period of February 18 – 24 2017 inclusive.
• Quote the statistic, when and where it was published and tell us why it should be our Stat of the Week.

Next Monday at midday we’ll announce the winner of this week’s Stat of the Week competition, and start a new one.

(more…)

If you’d like to comment on or debate any of this week’s Stat of the Week nominations, please do so below!

I was on Radio LIVE Drive earlier this evening, talking about lotto (way to be stereotyped). The underlying story is on Stuff

A Nelson Lotto player who won more than $100,000 playing the same numbers 12 times on the same ticket says he often picks the same numbers multiple times.

“So that when my numbers do come up, I can win a greater share of the prize.”

The player won 12 second division prizes on a single ticket bought from from Nelson’s Whitcoulls on Saturday, winning $9481 on each line, totalling $113,772.  

There’s nothing wrong with this as an inexpensive entertainment strategy. As a strategy for getting better returns from Lotto it can’t possibly work, so the question is whether it doesn’t have any effect or whether it makes the expected return worse.

In this case, it’s fairly easy to see the expected return is worse. If you play 12 lines of Lotto every week, with 12 different sets of numbers, you’ll average one week with a Division 2 win every thousand years.  If you use the same set of numbers 12 times each week, you’ll average one week with 12 Division 2 wins every twelve thousand years. You might think this factor of 12 in the odds is cancelled out by the higher winnings, but that’s only partly  true.

This week there were 25 winning Division 2 tickets, which each got an equal share of the $237,000 Division 2 prize pool. The gentleman in question held 12 of those 25 winning tickets, and so got about half the pool.  If he’d bought that set of numbers and 11 others he would have held 1 of 14 winning tickets and won, not 1/12 as much, but about 1/7th as much.   By increasing the number of winning tickets, he reduced the prize for each of his tickets, and so his strategy has slightly lower expected return than picking 12 different sets of numbers.

On the other hand, these calculations are a bit beside the point. If you play Lotto for the expected return you’re doing it wrong.