Wednesday, 7 January 2015

Proof I'm average

I was talking to Sunshine Mountain Operations Manager the other day, and he mentioned that Sunshine has an injury rate of 2.2 per 1,000 skier visits, which is basically industry average. When I heard this, I did some checking and found the "2.2 per thousand" rate is indeed pretty normal. "Injury rate" in the industry is the frequency that ski patrol attends an accident that requires care delivered by patrol on the hill.

Now, my brother the statistician is going to probably give me a hard time for this generalization, but if you flip that around, that rate is one injury per 454 skiers per day, or one injury per 454 days of risk exposure. Which got me to thinking...

I'm an anal-retentive engineer and have tracked every day I have skied since 1996 (19 years of data). That year, I got a recording altimeter watch, and I've just been logging my info ever since. Now, I first started skiing in 1978 (on borrowed equipment from a friend of mine, through a University ski club that let me learn dirt cheap). So I'm missing 18 years of data, or half of my ski years. But I am certain that:

  • I only got ~10 days a year from in my university years from 78-81, virtually all of which were in lessons;
  • I probably only got 5 days a year from 81-84 (before I moved to Edmonton);
  • I hardly skied at all from 84-89 -- perhaps 2 days per year -- due to living in Edmonton (too far from the mountains to ski much), work and getting married;
  • I didn't ski at all from Nov 90 to Nov 92, since I was living in Victoria;
  • I was so broke from 92-95 that I was lucky to get 2 days in per year.
So I add that up and probably only add 60-70 days to what I have skied since keeping records. And looking at my records, I have been injured exactly twice.
  • On logged day 178 (Day 250?) I crashed on ice at Big White and broke a rib in my back. No lost time, no ski patrol, but an accident nonetheless.
  • On logged day 540 (Day 610?) I broke my leg.
If you ignore my broken rib (a non-injury accident according to Sunshine's stats), my injury rate is 1 in 610 ski days, or 1.64 per thousand days of exposure. If you include it, it's 2 injuries in the same time, or 3.28 per thousand days of exposure.

If you look at the time between those accidents (362 ski days), that's 2.7 injuries per thousand days of exposure.

I'm feeling like an average kinda guy right around now. 


Ali Ryder said...

An average guy who skis WAY more than average.

Unknown said...

Not anywhere near enough data to claim average-ness. You need to keep skiing!

If you are average (2.2 events per 1000) then you have a 35% probability of experiencing one injury in 610 attempts to injure yourself. This is your most likely score. But you still have a 26% chance of 0 events, a 23% chance of 2 events and an 11% chance of 3 events. If you had 4 (or more injuries) you would have proof on non-average-ness (at statement made with 95% confidence). But 0-3 injuries does not prove anything. Nice try ...

RyderDA said...

So you're saying I need to injure myself again to prove I'm not average? I'd prefer not to do that. I'd kinda like to not injure myself again. So as long as I don't injure myself again, I can claim pseudo-averageness.

Astrid said...

Derek, no matter how hard you try ... you will never be average

Alan Ryder said...

Again, nice try. This is like the actuary who flies with a bomb because the chances of two bombs being on the same plane are 1 in a million.

You are about 0.3 standard deviations better than the population (your second injury does not count!). So you are close to the mean. You can therefore claim pseudo-average-ness.

RyderDA said...

Astrid, can I at least strive for mediocrity?