If you’ve been following the news, or twitter, you’ll have noticed that the current pope, Pope Benedict XVI (pronounces *Kss-vee*) has decided to retire at the end of the month, to spend more time with his twitter account. Anyway, the Grauniad had an interactive thingy up, which, they suggested, “illustrates the idea that a long-serving pope is often followed by one whose papacy is much shorter”. Well, possibly. But you really need to do a bit more than stare at a fancy graphic. You actually need to do some analysis of the data.

Of course, first one has to grab the data. Then we can plot it:

and we can see that there is a lot of variation, and possibly some long-term trends (e.g. recently popes seem to have survived longer). But is a long-lasting pope followed by one who keels over quickly? Well, in statistical terms that would mean that lengths of papal reigns would be negatively auto-correlated. And we have a nice tool to look at that sort of thing: it’s called the autocorrelation function, or ACF. Our hypothesis is, in technical language, that the lag one ACF is negative.

We can calculate that, and we find that it is 0.15. So, it is (a) small, and (b) in the wrong direction. No p-values needed. But this might be an effect of the longer-term trends in the data. We can remove this by fitting a suitable smooth curve (a spline, for those who want to know), and look at that:

The pink line is the fitted line, with the (approximate) 95% confidence interval.

We can see the long-term trends: from about 600AD to 1100AD was not a good period for popes. And, but for a blip around the 15th Century life seems to be improving. But what about the lag 1 acf? Well, that is 0.02, so basically zero, and also still in the wrong direction.

All in all, I think this disproves the notion that long reigns are followed by short ones. Except, it might be that this has changed over time. If we only look at the residuals for popes who started their papacy from after 1800 (i.e. the last 14 popes), we get an estimate of -0.09, which is at least in the right direction. Except that the approximate standard deviation is 0.29, so much larger. If we only look at the 9 popes who started poping after 1900, we get an acf of -0.62, with a standard error of 0.30. So we might just about have crept up to statistical significance (the z-statistic is -2.1, so less than -1.96 for a 5% significance), but (a) the sample size is small, (b) the significance is marginal, and the large-sample used may be way off, and (c) I’ve had to poke around a bit to get to something which might be marginally significant, so there is a certain amount of data dredging: looking for rubies in the rubbish and not stopping until I find one.

All in all, a pope will not spring eternal. Sorry.

Classic nerd-ery, Bob. Bless you.

Yes, yes. But how long (or short) should the pope’s reins be?

All the way to the end of his rein, deer.

Seriously, though – I wonder how the pattern compares with that of other, similar, roles – the reigns of heads of other religious and other organisations, monarchs, etc…

Well, if you can get the data…

For monarchs it’s a bit different, as they can become king/queen at a very young age, but popes for the last few hundred years have had to prove their worth, so have tended to be older.

Also, historically, you couldn’t be made a priest until you were 30, so because Popes are usually cardinals first, you’ve got a higher cut-off age than you’d think. (This was the case from at least 700AD; these days you’re expected to do at least 5-6 years of study, sometimes more, meaning a minimum age of around 25.)

Personally I think both their reins and their reigns should be short. But I guess that’d be waiting for a not-so rainy day.

I misplaced this – it was meant to be a reply to Cath@VWXYNot?’s comments. (Sorry.)

If a Pope met an anti-Pope would they both vanish in a puff of incense? If I were one or the other I’d be fairly incensed.

That could b why the Western Schism took so long to resolve – they didn’t want to end up as some sweet smelling smoke.

The Western Schism is, of course, the last time a pope resigned. It really does sound like a playground spat.

I am (more than) a bit dubious about the data you are using. I presume that the first pope in your list is St Peter, but he didn’t found the church in Rome immediately after Christ’s death. He was certainly at the Council of Jerusalem (c 50 AD -see Acts 15) and some church traditions include a seven-year period as Bishop of Antioch. Together this would suggest a term as Bishop of Rome of no more than about 7 years, not inconsistent with the terms of other early popes.

OK, I think that’s a fair point. I suspect a few of the dates for the early popes are a bit here or there. I’ve just re-run the code, and it doesn’t make much difference to the main results.

BTW, if anyone wants the code and data, just ask me.

I’m sure the effect is caused by “papal mourning…”

And if all of the times were the same, would that be Papal evening?