Today’s post is over at Edgehogs.
I wanted to see how extreme bookies would go in making NFL picks, as judged by the probabilities of home-team wins as derived from moneylines (see this post for how to convert moneylines to probabilities).
The top 10 most extreme games had derived probabilities anywhere from 93 to 96%. Those who know about NFL intricacies can tell me why the New England Patriots have had more than their fair share of appearances in this list (but if you know, leave that comment on the Edghog’s site).
Do these probabilities appear high to you? A 95% chance for a thing to occur seems like a mighty good bet. But it means a 1 in 20 chance of being wrong, which doesn’t sound so rare anymore (especially to classical statisticians, where this level has mystical properties).
Anyway, although today’s investigation may be classified as “statistics lite”, there is something to be learned from it of deep importance. Why don’t bookies ever use the sure thing? I.e., post a probability that a team has a 100% (or 0%) chance of winning?
Well, bookies don’t issue probabilities, but moneylines. To get to a 99% chance of a win requires issuing the equivalent of a +10,000/-10,000 line. That means that you’d have to risk $10,000 just to win $100. It’s difficult to imagine anybody willing to make this bet, therefore it’s unlikely any bookie would float it.
Similarly, a 99.99999% chance, which I remind us is still less than 100%, requires the equivalent of a +1 billion/-1 billion line. You’d have to wager a billion dollars to win 100. Not many takers here! But you can see where this is going. To arrive at 100% requires a +infinity/-infinity line. Only the federal government has that kind of money.
And this all makes sense. All statements of knowledge about some event, including probability statements, are conditional on explicitly stated premises. If you have as one of your premises, or this fact is derivable from them, that your event is contingent then the probability for this event must be less than 100% (and greater than 0%). It can never—as in never— reach these limits, except—bad pun alert—in the limit, that is to say, in the long run.
Now let’s recall Keynes’s truth that in the long run we shall all be dead. This is not just witty, but important. Because we never—as in never—reach the limit we are always dealing with non-extreme probabilities for contingent events. Yet we sometimes act as if probabilities are extreme. This only proves that decisions or actions are not the same as probabilities, even though the two concepts are often confused.
This is going too far, however, and giving too much for a post on NFL bets. We’ll come back to the whole thing on another day.