Probabilities of uncertain outcomes (say 50/50 odds) are often visualized like this:
But this can be misleading, it implies a 'connectedness' that is incorrect.
Specifically, I think the above representation makes us feel subconsciously we can aim at a specific outcome. If we imagine these visualizations as dart boards, a more accurate representation is disjointed, as if a collection of many potential outcomes:
And we can imagine larger and larger sets:
There is nothing to aim at in these. If you were asked to throw a dart at them, your throw would be a random outcome: you cannot impact it.
I like how I've heard Nate Silver describe such odds as "5 out of 10", and not "50%". These visuals try to represent that.
But even the above representations can imply fixed patterns and clumps that are actually inconsequential. So we ought to jitter the sets as well:
But in an outcome like whether team A or B will win a game, there is a single end result, not a distribution. And so the following may be more appropriate:
Here it's like we are watching the stream of outcomes that make up the set one at a time. This communicates the relative quantity of each possibility and the totality of each individual outcome.
Overall, the basic idea is to remove any sense of pattern or clumping where there is none, and to also communicate the absoluteness of the outcome.
Now we compare some different probabilities, here 20/80, 40/60, 60/40 and 80/20:
The difference between 40/60 and 60/40 is clear, but the exactness of that difference is blurry.
My basic point is that we should think harder about visual representations of uncertain/probabilistic outcomes that:
- better reflect the disjointed, uncorrelated nature of the outcome sets
- and the absoluteness of each specific outcome.
Doing so better reflects the true nature of our random world.