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David writes in a request:

I was wondering if it would be possible for you retroactively to run simulations for the Confederations Cup before the last games were played in Group B. I realize how unlikely the U.S. advancing was, I’m just curious how many times it would have happened in your simulations. Was this a 1 in 100 thing? Or even more unlikely.

Thanks for writing in David. If I was selling Voros t-shirts, I’d send one out to you.

Anyway that’s a good question with implications involving two of my favorite subjects: statistics and philosophy. Anyway first the nuts and bolts. I re-ran the latest National Team rankings to include all result through June 20th. That way it would account for the stink from the US’s first two games and the surprise quality of Egypt’s first two. We dropped a few places down to 22nd, Egypt rose a few up to 42nd. Then I ran 10,000 simulations of the final two games in the group. The results:

Team/Finish    1st   2nd   3rd   4th
Brazil        9358   598    44     0
Italy          603  4921  4405    71
Egypt           39  4310  4755   896
USA              0   171   796  9033

It’s interesting that, by this anyway, Brazil’s chances of not qualifying were less than the US chances for making it.

The more interesting thing is the discussion of what that 1.71% means, both specifically toward the World Cup qualifying sims, and more generally what it means to us as people when something likely to happen 1.71% of the time, actually does happen.

From the standpoint of the World Cup qualifying sims I do, that 1.71% stands as convenient point of discussion when talking about which teams are longshots and how likely it is they will make it. Considering how little of a chance most people thought the US had and the reaction it got when it actually happened (with many using the word “miracle” in the description), that pretty much establishes how monumental a comeback a 1.71% team making it would be, or how epic a collapse a 98.29% team missing it would be.

Truthfully whenever such an event occurs, good statistical practice involves re-examining everything you _now_ know about the variables and seeing if you would still peg the chances the same. That will usually result in the number going up a bit depending on how solid your info is, but still taking into account that 1.71% does happen from time to time. I’m not really going to do that because it isn’t likely to go up very much (a little above 2% maybe). The US was there mostly because of the Grand Canyon sized hole they dug themselves and nothing to do with faulty ratings. The US was certainly capable of beating Egypt and Brazil was certainly capable of beating Italy, but the goal differentials needing to be overcome were a tough ask for anybody.

And so the bigger question is, what does it mean when we see the number “1.71%” in the context of the chances of something happening? Often its meaning depends on how often we get to try it. Once? Well it’s a long shot to be sure. 100 times? Well there’s a good chance it will happen at some point. Scott Podsednik has homered in almost exactly 1% of his career Major League plate appearances. But on the other hand he hit one on Saturday and also hit one a couple years ago to win a World Series game. Give “1.71%” enough bites at the apple, and it’ll get its share.

If it does happen in one try, does it mean the “1.71%” number was wrong? That depends too; sometimes it is and sometimes (and I think this is the case here) it was right and lightning just struck. But trust me you don’t want to be sitting in a bar bragging on how you just bet on “98.29%” and “1.71%” comes in. It’s the quickest way in the world to be absolutely right about something and look like a complete idiot anyway.

When it comes to examining that number, ultimately the thing to examine is process. How did you get there? What different ways could you have gotten to a number and will a re-examination reveal an error or a mistake that needs correcting? Could you have adjusted for ‘x’ when you didn’t. Did you adjust for ‘x’ when you shouldn’t have? Have you tested your methods? Have conditions changed since you tested them? Are there things you wanted to include but didn’t due a difficult implementation, and would these things have changed that number?

Or was today the day “1.71%” got its due? It does, in a way, make the probability field quite a sad one to be as heavily involved in as I am. For the chemist, water isn’t two parts hydrogen, one part oxygen most of the time. It always is. You just know going in that after all the hard work, all the considerations and calculations, all the study and corrections and the data analysis, you know that after all of it, there’s a chance you’ll be wrong anyway. Uncertainty is a bitch, but if probability is your field, you’re married to her with no hope of divorce. Your wired Aces get cracked, the dealer hits a 5 on 16 and the US makes up six goals worth of goal differential on Italy in one game. And your friends just laugh as Scott Podsednik drives one over the right field wall. C’est la vie.