A number of years ago, when I was working in a New Hampshire mountain hut, a man walked in from the rain and saw a piece of paper thumb-tacked to the wall with the day’s weather forecast on it. It said 30 percent chance of showers. “Thirty percent chance of showers!” he roared, spraying me with his rain-soaked beard, “you sure messed up that one!”
Actually, “messed up” wasn’t quite his word choice. And the Mount Washington Observatory hadn’t messed up at all. If you get wet on a zero percent day, count that as a mess up. But if you get wet on a 30 percent day, welcome to the mountains.
The image of the soaking man yelling “thirty percent!” has stuck with me over the years because it was very funny at the time and because it nicely typifies our troubled relationship with statistics. As Mark Twain had it, “there are three kinds of lies: lies, damned lies, and statistics.”
Because weather forecasting is a statistical game, it makes sense that climate change models are sometimes viewed with skepticism. If meteorologists can’t give a hiker a “yes or no” answer to the seemingly simple question of whether or not it’s going to rain today, how can scientists come up with an accurate climate model to predict what’s going to happen 100 years in the future?
Consider a statistical case that’s easier to understand: the coin toss. If you were asked to predict whether a coin toss would come up heads or tails, you’d have a 50 percent chance of getting it right. No amount of data or theoretical modeling or super-computing power will improve your odds – your forecast is going to stink. There are too many unrelated elements in play – how high will the coin be tossed, how fast is it rotating, is there any wind blowing – that will affect the outcome.
But if you were asked to predict how many heads you would get if the coin were tossed 100,000 times, you’d know for sure that it’s going to be very close to 50,000. That’s because the random, independent elements that act on a coin toss cancel each other out over time. In the end, the true statistical nature of the coin toss is revealed: the coin will ultimately land on both sides equally. Which is to say, you can indeed average a bunch of hard-to-predict events and reach an easy-to-predict outcome.
Weather and climate are far more complicated than a coin toss, of course, and there’s nothing easy about predicting the Earth’s climate 100 years down the road. But the central point of the metaphor holds: the randomness of weather events are averaged out over time, making a climate forecast more accurate than a weather forecast.
A casino owner, to look at the statistical question from another perspective, would have little luck predicting whether or not the next quarter put into a slot machine would unleash a torrent of money but no trouble at all predicting that the house will always win in the end.
And here’s a third analogy relevant to statistics and weather: steroids in baseball. Of the thousands of home runs hit in the 1990s, which ones were the result of batters taking steroids and which ones would have been hit anyway? It’s impossible to know – there are too many independent factors in play. Was the batter rested? Was the wind blowing out? Had the pitcher just come up from Double A? You get the idea.
But the fact that no particular home run can be conclusively linked to steroids does not mean that the steroids era is in any doubt. This is true even though we’ll never know which homers would have left the yard without the juice and couldn’t have accurately forecast any one of them in advance.
Compared with baseball, climate science is a far more complicated business, and forecasts for the Earth’s climate 100 years from now still contain substantial variability. But that’s because so many factors are in play, and it’s hard to know which ones are most important. It’s not because today’s weather forecast is wrong.
I found myself thinking back to the soaked hiker in New Hampshire a few weeks back, while I was reading the weather forecast on my computer. One of my farmhands looked over my shoulder and asked me, “What’s the forecast?” To which I found myself replying, “It’s gonna rain.” A few seconds later, I realized I’d made the exact same mistake as Mr. Thirty Percent, though in the other direction. The forecast was a 70 percent chance of thunderstorms.