Big savings in insurance?

A few weeks ago I received a bit of junk mail from RIAS that’s led me to the most amusing use of statistics I’ve ever seen.

I wouldn’t normally read this kind of mail, especially as I’m neither over 50, nor in the market for some new insurance, but the letter began along the lines of ‘I know that getting letters like this is annoying’. I threw it away, thinking ‘damn right’, but then got it back out of the bin in disbelief that they’d start like this… the pitch worked.

Anyway, to the numbers. When an insurance company says ‘You could save up to £182’ or whatever, it’s worth examining the small print, because the important word here is ‘could’. In their favour, this is of course a one-way bet: if you ring up and they give you a higher quote, you’ll stick with what you’ve got. When the Halifax say in a current ad, ‘you could save £99’, this is the average savings of a ‘random sample of 715 customers… by switching’. Obviously this doesn’t include those who don’t switch who might be saving a hundred quid by staying put. But at least it’s an average saving, that makes sense to the general public.

For others, it’s a different figure altogether, and one that made me choke on my cornflakes. Hastings and RIAS give figures that ‘10% of customers achieved’ were ‘achieved in 10% of quotes’. This means 90% of people (i.e. most of them) didn’t get this saving, and we don’t even know if these figures only include people who switched. Yes, they do say ‘look, this what you could get up to’, but as a headline figure it makes you think that’s your approximate gain. We’ve no idea of the distribution: maybe 10% save £150 and the other 90% save nothing.
I guess this is what those recruitment ads do when they say ‘earnings up to £70k’ when in reality very few get anywhere near that. Maybe I’ll start to measure things like this. I could offer to do ‘up to 2 hours of housework each weekday’, knowing I’ll do next to nothing except a couple of hours every fortnight.