Monday, March 24, 2014

Beatrice, Nebraska, Church Explosion in 1950--Miracle or Coincidence?

I came across an interesting fact last night. Apparently, in Beatrice, Nebraska, in 1950, the West Side Baptist Church exploded just five minutes into the scheduled choir practice on the Wednesday evening of March 1, and yet not a single person was hurt or killed. As it happened, the furnace was the source of the explosion, but there were no injuries or deaths because not a single member of the choir showed up to practice on time that night. Every last one of them was late, and they all missed the catastrophe. Of course, immediately and ever since, this has been taken by those who believe in miracles as a clear example of divine intervention, a miracle of God. But is it, or was it just an extremely fortunate coincidence?

Of course, there's an obvious discussion to be had about the fact that the church blew up in the first place. God could have simply prevented the explosion instead of mysteriously delaying each member of the choir by a few minutes for a variety of mundane reasons while still destroying their church. That's not what I'm interested in, though. Instead, I want to investigate what the rough chances of such an event are. To do so, I've had to assume a number of approximations that I need to explain, and to be generous, I feel like I've low-balled on the majority of them. As I often do, I'll run the numbers a second time for different assumptions that I will also explain.

The assumed numbers

Churches: As it turns out, there are roughly 450,000 churches in the United States (and more around the world). Of course, many of these are new constructions, but since there are churches all over the world, and such a miracle at any of them would count by religious apologetics standards, I'll take this number as it is. I realize that this number overestimates going into the past, but as I've explained about the wider world, and since I'm underestimating so profoundly throughout the rest of this discussion, I'll stick with this number. (Note also that the same miraculous status would be accorded to disasters averted in religiously motivated meetings at other places, like Bible studies in someone's home, at a library, or any other public facility.)

Meetings: Different churches have choir practices different numbers of times per week, so to be generous, I'm assuming that a typical church practices once per week, forty weeks of the year, i.e. 40 choir practices per year. Note that this is a severely low-ball estimate because it's irrelevant that it was a choir practice. All anyone wanting to claim a miracle would need for this to count is any meeting at a church (or almost anywhere else), and those happen several times per week, at least, almost every week of the year at most churches. Even to modify this number to 300 meetings per year is quite generous (many Protestant churches have at least this many outright church services a year with others not far behind).

Time frame: If this had happened in 1565 instead of 1950, we'd still be hearing about it from apologists, probably with similar frequency, so I feel it is generous to extend my focus across one century, 100 years. To stay generous, and because the numbers of churches is likely to drop off drastically before the 1850s, my more realistic assumptions will extend this only by an additional fifty years. Note that under the more generous assumptions, this yields 1,800,000,000 (choir) meetings within the relevant time frame, and on the (still generous) more realistic assumptions, 20,250,000,000 church meetings within the time frame.

Catastrophes: According to FEMA, in the mid-1990s, American churches experienced roughly 1300 church fires per year on average. To be generous, I'll assume that there have been approximately 1000 church catastrophes (of any kind) per year anywhere in the United States, and further that only 1% of those (10) are serious enough to lead to considerable injury or death if any potential victims happen to be present. Again, this assumption is overwhelmingly favorable to the possibility that a miracle happened because there are many other kinds of catastrophes that aren't fires (explosions, obviously, building collapsing, accidents, mass shootings, weather events, etc.) that would all work for the miracle claim. A more realistic, but still generous, number would probably triple this one, 3000 church catastrophes (of any kind) per year anywhere in the U.S., and would double the likelihood of an accident being serious, i.e. with 2% (60) being serious enough to lead to severe injury or death for any victims that are present.

If we assume that these catastrophes occur randomly, this yields a probability of 0.000095 such a serious catastrophe (one entailing serious injury or death to victims) in any given five-minute span anytime on the clock anywhere in the United States for the more generous assumptions, and a probability of 0.00057 in any given five-minute span under more realistic ones. I chose a five-minute span as being relevant because the explosion at the West Side Baptist Church occurred five minutes after choir practice was slated to begin.

Note that it's even very generous to assume that catastrophes like this occur evenly distributed around the clock and throughout the year. This is not the case generally, and it is not the case with the Beatrice explosion. In Beatrice, the exploding furnace had been lit specifically for the choir practice, so catastrophes like fires and certain kinds of explosions are more likely when people are scheduled to be there, say for choir practice. This is also true of intentional attacks like mass shootings. Further, other than arson (the leading cause of church fires, incidentally), we should expect most human-caused church catastrophes to happen during hours when people would also schedule events like choir practices or church services. All of these factors indicate that to be fully realistic to this problem, the odds approximated in this section should be higher than they are.

Being late: A quick Google search about how often people are tardy led me to a survey regarding how often people are late to work (note: punctuality at work is more important than at church choir practices) and determined the following low-ball estimates by making them more generous:
  • 10% of people are chronically late, to which I give a 90% chance of lateness;
  • 20% of people are sometimes late, with 75% chance of lateness;
  • 20% of people are occasionally late, with 50% chance of lateness;
  • 20% of people are rarely late, with 25% chance of lateness;
  • 30% of people are very rarely late, with 10% chance of lateness.
Putting all of these numbers together by their weights gives us a 42% chance that an "average" person will be late to any given event.

I do not feel like this number is out of the ballpark in how realistic it is, particularly for something of low importance like church choir practice, but I will not separate it into very generous and more realistic numbers. I will note, however, that the lateness likelihood given in the Snopes entry is stated in two incompatible ways. The article insists a 25% chance of lateness for any given member and on a one-in-a-million chance of lateness for the whole group of fifteen, but these numbers are incompatible. For a group of fifteen independent people to have a one-in-a-million chance of all being late simultaneously, the individual tardiness rate would have to be 40%, not 25%.

With a 42% chance of an average person being late, the odds that everyone would miss all at once, just by chance, is 1 in 447,982, or 0.00000223. Since this means that out of every 447,982 times that fifteen average people get together at a scheduled time, one of those times will result in all fifteen being simultaneously a few minutes late, this really isn't that ridiculous an assumption. Note also that this assumes that the choir members have independent reasons for being late, which is also generous. Bad traffic on the way to the church holding up several would destroy independence, as would carpooling members or two members coming from the same household and carrying the same excuse. Any dependence in lateness between members would raise the odds that all would be tardy simultaneously.

Crunching the numbers

Here's what we're looking at. I have calculated the odds that all fifteen members of the church choir would independently and simultaneously be late to an event at their church thereby missing the five-minute-long span of time in which a serious enough catastrophe occurs that, were the present, it would result in serious injury or death for some or all of them.

Then, I use that number to find the odds that such an event would occur merely by chance anytime in the last century. To do so, I determined the chance of it occurring at any given time (as just above), then used the complement of that to evaluate the chance that it would not occur at any point whatsoever over the stated time frames. The complement of that number is the odds that we'd see at least one Beatrice, Nebraska, event purely by chance.

Math: If we call the probability of such an event occurring by chance p, and we say that the number of meetings over the given time frame is m, the number I have calculated is 1-((1-p)^m). The chance p is calculated by multiplying the individual probabilities from above, using the (generous) assumption that all of these factors are independent.

Super-generous assumptions: In the case that we use the far more generous assumptions above (40 meetings per year per church and 10 would-be-serious catastrophes per year in churches anywhere in the U.S., evaluated over a century), the chance that we would see at least one event like occurred in Beatrice, Nebraska, sometime within the last century are 31.7%.

What this means is that even under ridiculously generous assumptions, there's nearly a one in three chance that just by utter chance, we would have on record something as freaky-rare, in seeming, as the event on March 1, 1950, in Beatrice, Nebraska, where an serious accident at a church occurred but was missed by all fifteen choir members because they were all simultaneously late. This doesn't look like divine intervention by any stretch, particularly when we keep in mind how generous the assumptions are. It's more likely than having two children, both of whom are girls.

More realistic assumptions that are still very generous: In the case where we use the generous, but more realistic, assumptions mentioned (300 meetings per year per church with 60 would-be-serious incidents per year, evaluated over a century and a half), the chance that we would see at least one event like occurred in Beatrice, Nebraska, sometime roughly since the Civil War is a virtual certainty--the probability isn't worth reporting because it's of the form 99.99...9%. Instead, the odds are all but one in roughly 151 billion. These are the same odds as, given a typical circular above-ground swimming pool filled with white granulated sugar and a single grain of salt, when choosing a single grain at random, you'd choose sugar. No sign of divine intervention here at all. (You're more likely win the lottery by making the decision to buy the lottery ticket by flipping a quarter nine times, buying it only if you get heads on every flip, and then winning the lottery with that ticket.)

Nota bene: Because of the values I chose in my super-generous assumptions, the number calculated in that case is right on the cusp where the probabilities change very rapidly by fiddling only in small ways with the assumptions. The less-generous assumptions are included here primarily to illustrate that this phenomenon is mostly an artifact of trying to be extraordinarily generous to the case of the miracle-claimant. I plainly admit, however, that being even a little more generous in my assumptions would yield a low (but not necessarily miraculously low) chance of such an event happening by coincidence. For example, if we use all of the other super-generous assumptions and assume a ~30% chance that a typical person would be late to church practice (splitting the middle of the two values given in Snopes slightly to the generous side), we only have about a 0.3% chance of seeing an event like the Beatrice, NE, explosion. Even then, we should expect such an event roughly once every three or four hundred years or so, so divine intervention still seems to be a hasty conclusion.

It simply cannot be overstated that the generous assumptions here are ridiculously generous, and even the more realistic assumptions are still quite generous, given the circumstances. We have every reason to believe that realistic numbers are nothing like my very generous assumptions and are far nearer the more realistic ones. Simply put, we have every good reason to believe that some event like this would have happened at least once within American history. I've only included the above note for full integrity of my presentation.

The overall takeaway from this assessment is that under truly realistic assumptions, we shouldn't really be surprised about the story of the Beatrice, Nebraska, West Side Baptist Church explosion on March 1, 1950, and we certainly have no good reasons to accept it as some kind of miracle claim.

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