Holiday Road Toll

January 2, 2012 – 10:02 pm

Every long weekend we hear how many people died, as though it means something, but there’s never any analysis beyond whether it’s more or less than last year’s number. It doesn’t help me know what’s going on: are we better drivers or worse? What’s the point of measuring if you don’t analyse? After all, I just kissed goodbye to my wife as she set out for a 100km trip to Auckland to see a friend. Should I have encouraged her to stay at home?

Comparison to last year’s number is largely useless without knowing what the variation is. Is a 50% increase within the bounds of normal, or does it represent a nation of speeding drunks, blearily passing out behind the wheel and mowing over toddlers as we tow our boats back from the bach?

If you want to make sense of the holiday road toll (as I write, we’ve had 17 dead) then you must look at it in context. You can see the numbers on the Transport web site (thanks for steering me there), and with a little munging you can pull out holiday deaths:

As you can see, we’re in a declining trend of road deaths on the holiday. The variation from year to year is substantial. Look at the 1970-1975 range: 26, 34, 37, 16, 29, 24. That’s a 21 death range! Or just look at the last five years: 22, 9, 18, 25, 13, 12. From that you can see that this year’s is not exceptional, even though it is nearly half as much again as last year’s fatalities.

Think of it like rolling two dice. Seven is the most likely number you’ll get, 2 and 12 the least common (there are many ways to make seven, only one way to make each of 2 and 12). Even though you might roll a 12, that doesn’t mean the dice are suddenly tilting high and now you’ll get lots of 9s and 10s. The next roll still has the same probabilities of coming up low, middling, or high as it did last time.

Similarly, a high death-rate one year doesn’t mean there’ll be high death-rate next year. And a low death-rate one year doesn’t mean there’ll be a low death-rate next year. The probabilities are roughly what they were last year, except for this overall slow decline in the average from 20 to 15 in the last decade.

If we rolled lots of dice, we’d see that overall we get few 2s or 12s but many 7s as we expected. Similarly, over the last ten years we see a few below 10 or above 20, but most in-between. This year’s number is higher than normal, but not as much cause for alarm as (say) 30 deaths might be.

The probabilities of dice come from their construction: you could change the probabilities by changing the shape, making one side heavier, painting different numbers on. Similarly, the holiday road toll probabilities are affected by many things. Off the top of my head, I can think of: population (doubled since 1950!), weather, road quality, timing of weekends (which might change whether people make their holiday roadtrips during the period being counted), quality of cars on the road (turning crashes into fatalities), and of course the police presence on the roads. I’m sure there are more. These aren’t constant across the holiday period or across the country.

The biggest influence is undoubtedly population: it has more than doubled since 1950. 24 deaths in 1975 is the equivalent rate as 35 deaths today. Here’s the graph, taking population into account:

But I can’t collect or correct for all of the possible variables in holiday numbers. For a better idea, we should look at annual road toll trends. We see there that this year has been one of the best on record and it’s part of a continuing downward trend in deaths. While each individual road death is a tragedy, this year’s Christmas numbers are not a sign that the roads are necessarily a more dangerous place overall.

That’s a relief to me, though not as much as when the Mrs returns home safe and sound. Statistics can only provide so much comfort …

(wondering what happened in the late 60s and early 70s to have such massive changes in deaths? New Zealand History has some milestones that might be relevant: Speed limits were raised in the late 60s, sending the death rates up, and the drunk-driving policing helped bring them down, starting with blood alcohol tests which were introduced just before 1970.)

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