For each thing that happens there is a field of potential things which could happen. Those potential events fill out a distribution where some events are more likely than others. A daughter’s height for instance, could be between four and eight feet but it’s very very likely that her height will be between her mother’s and father’s heights.
Thinking about these distributions of potential outcomes can be helpful because the areas which are not compact, like daughter’s height, are interesting.
Our annual NFL example (last year was Tom Brady passing yards) is Aaron Rodgers over/under 38.5 touchdowns. Here’s how we visualized it in September 2021:
The thinking then, as now, was that Rodgers would throw between twenty and fifty touchdowns but not with equal odds. The number of touchdowns would be asymmetrical. It was much more likely Rodgers threw half of 38.5 than double it.
Five games into the season offers a chance to be Bayesians and update our forecast. In addition to the preseason line of 38.5, his career average is 33.4, and his current pace is 32. Mix in the chance of injury, and he could also finish the year with the ten touchdowns he’s tossed thus far.
Let’s tack this on to the 2021 predictions:
– +10 TD, 90%
– +20 TD, 85%
– +30 TD, 50%
– +38.5 TD, 10%
I wanted to go lower on the 38.5 percentage, but one lesson from Cade Massey is to be less certain about extreme events. So in the same way that online doesn’t equate to real life and we should adjust for that, I will adjust my percentages as well.
Daughter height is top of mind because I have eleven and thirteen year old daughters. 😬