Embarrassed By Improbability

HoopoeMy Baltimore Orioles are about to play in the American League Divisonal Playoffs tonight, and the experts say that their opponents — the Detroit Tigers — should win the series. That’s OK with me; I never expected the Orioles to go this far, certainly not to finish first in the Easter division by twelve games over the New York Yankees. Based on everything that experts on baseball know, the Orioles’ season has been exceptionally improbable.

Since the Orioles have defied the odds this year, a great many people — some partisans of the O’s, some just ordinary sane sports fans — have wondered whether the experts reasoned incorrectly about the strength of the team. Especially since the Orioles have surpassed the experts’ estimates for three consecutive years, people suspect that there’s something about the Orioles that the experts just aren’t getting right: “the intangibles,” as sports writers often say, or “chemistry” or “clubhouse leadership.” Reasonable people look at the discrepancy between projections and results and wonder where the projections went wrong.

A onth and a half ago, Dave Cameron (no, not that one) wrote an elegant piece explaining that No, the experts haven’t been wrong at all; they’ve been exactly right, and the Orioles’ performance actually demonstrates their correctness rather than undermining their status. How can that be? It can be because improbable things happen all the time. Mildly improbable things happen daily; somewhat improbable things happen occasionally; very improbable things happen rarely; and utterly improbable things happen once in a lifetime, or an epoch, or a millennium, or what-you-will. But improbable things happen, and they happen at a rate we can measure and make sense of.

The point relative to my beloved O’s, the team that gave us the 1966 World Champions, is that although the Orioles have outperformed expectations for three years running — a very considerable sample size — their improbable streak of winning falls exactly where we would expect it to on the spectrum of “teams doing better than projected.” In cameron’s words, “the existence of an outlier does not prove that a model is broken. In fact, the existence of the right amount of outliers is actually evidence that the model works really well. The question isn’t whether we can find outliers in the data; the question is whether there are more outliers than we’d expect given a normal distribution.” And it turns out that, yes, the Orioles’ record falls neatly within the expected distribution of teams outperforming (and underperforming) projections. In fact, once you look at the distribution, other recent teams have been even luckier than the Orioles over a three-year stretch; the Angels had a five-year stretch of luck in the late aughties and early ’teens. Improbable things happen all the time.

So sport supporters should relax about trying to argue that the experts are wrong about their formulas (it’s possible, of course, but… improbable). Teams have long stretches of luck, good or bad, and that’s why sport is entertaining even when we know the projected outcomes.

All of this pertains to another field of my interest: namely, the study of the Bible. The Bible narrates a great many utterly improbable events. On the basis of their radical improbability, many very sensible people argue that these events did not take place, a sound enough conclusion when you look at the great span of human history and the great number of claims that have been made on behalf of utterly improbable alleged events. Most people, most of the time, reject out of hand most of these improbable claims, so one can hardly complain if sensible people reason that the events described in the Bible should likewise be rejected.

Like Orioles supporters, though, a great many adherents to traditions (biblical and non-) want to assert that our extraordinary events not only happened despite the odds, but indeed should be understood as the most reasonable explanation of the circumstances and allegations surrounding that alleged event. While the experts on biblical batting averages say “No one has hit for an average over .500 in major league history, so we decline to believe that Joshua slugged Canaanite pitching to the tune of a .633 average,” supporters of the Hebrew Conquerors say “Well, the Bible says Joshua hit .633, and in those days they played without leather gloves, and the pitcher’s mound was probably not very sturdy (else we’d have found archaeological evidence of pitcher’s mounds in antiquity, which we haven’t), so the best explanation for the biblical story of Joshua’s amazing batting average is that he had a career year against uneven Canaanite pitching.” Joshua’s alleged batting record must not only be true, according to this line of thought, it must be probable.

Of these two perspectives, I think the sceptics have by far the strongest case. They’re looking at the records, the circumstances, and the propensities of sport fans to exaggerate, and they’re unconvinced.

The fans tend to take two steps, both of which I think problematic. The first is that they sometimes take it as granted that in order to claim that something is true, it must be probable. Modern life certainly provides a propitious context for this step, since nobody doubts that it’s true that the Orioles won their division this year. So many claims about so many matters of probability or improbability can be tested very easily, with outcomes so near to certainty as makes no practical difference, that the “truth” bit of a claim can seem to be either given and necessary, or false and unsustainable. Orioles fans have not been satisified that experts agreed that the team finished first; they want experts to agree that the Orioles should have finished first, in a way similar to people who believe that not only did Joshua hit .633, but that it’s likely that he hit .633. (I think they are wrong to reason so.)

Similarly, supporters of unlikely events suppose that they may not be permitted to think that improbable things ever happen. Of course, everyday life should dispel this supposition. A friend whose nickname is “37” (srsly) was recently in a queue at the Department of Motor Vehicles and drew the ticket numbered 37. Now, I’m not sure how many numbers were on the roll of tickets; I would estimate the number as probably upwards of 999, since the tickets wouldn’t fit four digits, and cycling through 1 – 99 over and over might run some risk of confusion if there was a particularly long queue. So the chance that a gentleman nicknamed “37” would draw number 37 in the queue is about one in a thousand, and only if he were damned to several lifetimes of annual visits to the DMV (a fate of eschatological cruelty beyond the imagination even of the Christian apocalypticists) could one regard his drawing the number as nearing “probable.” At the same time, among improbabilities, this example is pretty small-scale (however striking and mmeorable it was to 37). In other words, it is not the case that “improbable things happen, so there’s no good reason to be sceptical about the Bible”; contrariwise, a great many things in the Bible are so improbable that we can’t reasonably complain if people don’t believe them to have happened.

Neither, on the other hand, is everyone obliged to doubt something just because it’s wildly improbable. Part of the point of the stories in the Bible, after all, is that these seemed to be extraordinary events even to those who reported them. If one is confident that certain extraordinary events happened two to five thousand years ago, well, there we are. But such believers should be straightforward about just how profoundly improbable the allegations are, and should not try to wrest the improbability dial from “nearly impossible” to “well, of course.” I accept that the maths tell against some of what I assent to having happened in Roman Judea. I don’t think I can screw up my credulity to think that every improbable thing narrated in the gospels (or the rest of the Bible) happened just as reported. I have various reasons for making distinctions among them, which cumulatively do not have the astringent rigour of simply denying all of them or (for that matter) affirming all of them. And my observation of improbability suggests that however comforting that rigour might be, my capacity to ascertain which improbabilities did happen and which didn’t, which teams will win and which won’t, is no better than the sport experts’ capacity to anticipate the Orioles’ winning season.

I know the Tigers are more likely to win three of the next five games against the Orioles, and I know that even if the Orioles defeat the Tigers, they’ll face a challenging opponent in Kansas City or Cleveland. And whoever wins the National League Championship* will be a strong opponent, too. Go, Orioles!


* I was hoping the Pirates would win, partly because I retain some affection for the team I saw so often at Forbes Field in the days of my youth, but mostly so my Orioles would have a chance at a measure of revenge for the two World Series that the Pirates won from us by 4 games to 3 margins.