There is a famous conjecture called the Doomsday Argument, which will be discussed below. It can be used to predict the future remaining existence of the Major Leagues. Here’s how.

Before reading, come up with an off the cuff estimate for how long you think Major League Baseball will last. Think of it in terms of if you were betting, and you wanted to know how many years it had left, so that half the time you would win and half the time you would lose.

For reference, lets assume that the Major Leagues started in 1869 with the first Cincinnati Reds game, though other games such as the first game played by Alexander Cartwright may have an equal claim. So baseball has been around for 139 years. Based on this, do you have an estimate? Do you feel like you need more information? Well, it turns out that it can be estimated based solely on how long it has existed so far, with no other information needed!

If you have an estimate in your head, feel free to read on.

There is a famous conjecture called The Doomsday Argument. Click on the link to read more about it. Below is a summary. Note that there is no math involved, though it may appear that way, it is only grade school subtraction. If you are interested in the math to derive the formula it is here.

Suppose we want to estimate how long something will last, such as the Major Leagues. When I use the symbol “T” it is only meant to be a shorthand for any year in the lifespan of whatever we are examining. What follows the “T” in parenthesis is the specific year in the lifespan that we are measuring, i.e. T (now) is the current year, T(begin) is year one and T(end) is the last year.

We can say that whatever we are measuring can be observed only in the interval between T (begin) and T(end) i.e simply from its beginning to its end. If there is nothing special about the time right now in terms of the lifespan (and there isn’t in MLB’s case since there is no reason to think that we are any closer to the beginning or end of baseball), then we can say that we expect T(now) to be randomly located in this interval.

That is, since we have no idea whether we are closer to the beginning or end, all we can say is that the current year is randomly located somewhere in MLB’s lifespan. Fair enough?? I think this is eminently fair, and there is no good reason to thnk that we are anywhere closer to the beginning or end of Major League Baseball’s lifespan.

Using this randomness assumption, we can say that T(future) = T(end) – T(now). This means that the remaining years are what is left after subtracting the current year from the last year of MLB’s lifespan. Since we have no idea if we are any closer to the end or the beginning, we can also say that T(future) equals T(past), which is equal to the difference between T(now) – T(begin).

From this it follows that a 50% confidence interval is given by

1/3[T(past)] < T(future) < 3[T(past)]

Similarly (and I will spare you the math) a 95% confidence interval is given by

1/39 T(past) < T (Future) < 39 T(Past)

Simply put, assuming that there is nothing special about a specific observation, then you can estimate with 95% certainty the range of what is remaining by applying the formulas above. It is very intuitive: since there is nothing special about the current time (or observation) then you are equally likely to be at any point along its existence timeline. From that fact the 95% confidence interval is easily derived.

The author of the first paper on the subject, J. Richard Gott, applied this to the remaining lifespan of the human race. When challenged, he used the formula to predict the lifespan of 45 Broadway shows. He correctly identified the lifespan in almost exactly 95% of the cases.

Gott apparently discovered the principle while at the Berlin Wall. Using his ignorance of anything other than how long the wall existed, he assumed that as long as there was nothing special about the time he was there, approximately 8 years after it was built, this meant that there was a 75% chance that he was seeing it after the first quarter of its life. So he thought that there was a 75% chance that it wouldn’t exist in 1993. It was demolished in 1989.

Philosophical objections aside, the formula predicts with 95% confidence that the time remaining of Major League Baseball is 139/39 < T(Future) < 39*139. Baseball will last anywhere from 3.56 years to 5,421 years. Not too unbelievable. But what about my first question, namely how many years remain so that you would break even on a bet?

A 50% confidence interval has 25% on each side of the bell curve. That translates to 139/.25 or 139 times 4. This is 556 years. That is the 50% confidence interval for the entire lifespan of baseball. Applying the 50% confidence formula above, namely:

1/3[T(past)] < T(future) < 3[T(past)]

We can say that the time remaining is somewhere between 1/3 of the time it has lasted and 3 times the time it has lasted. This means the remaining years of the MLB are 139*3 or 417 years.

Is this a surprising result? It sure was to me when I thought about it. But then I realized that there are many things that can go wrong; annihilation of the human race, a new version of the Federal League, a worldwide depression, nuclear attacks and a whole host of things that could end baseball other than a general disinterest.

That is the whole point of the Doomsday Argument, we do not know whether or how these things will occur, we only know that it has lasted for X years and that there is nothing special about the time right now in terms of its lifespan.

One more point. When I say that there is nothing special in terms of lifespan, think of it this way: in a human life we know that one’s lifespan is not random; no one can live 1000 or 1,000,000 years. So if I am 38 (which I am) I know that I am roughly 1/2 of the way through my lifespan. The mere fact that I am 38 reveals that there is something significant about T(now) in my life. Not so with the Berlin Wall or baseball, or the human race for that matter.

My thanks go out to Phil Birnbaum of the SABR Statistical Analysis Committee for assisting me with this article. Thanks Phil!

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