William M. Briggs

Statistician to the Stars!

Author: Briggs (page 151 of 536)

How Long Do Popes Serve? Update

Update 14 March 2013. The Guardian has released the data on the popes. Its list and mine differ trivially, except that they were able to include the popes’ ages (starting from around 1400). It’s fun to compare the graphs they derived versus mine below. God bless Pope Francis.

Update 11 February 2013 (original date: 12 November 2012): Pope Benedict to Resign.

Easy stuff

Here, for no particular reason other than curiosity and because it’s Saturday, is a brief analysis on how long Popes have served. All data was retrieved from New Advent’s Catholic Encyclopedia.

The first Pope, St Peter, a buff fisherman nicknamed “The Rock”, had the longest go thus far, at about 36 years; perhaps not precisely 36 years because of course dates that far back are imprecise. Still, he had a good, long run.

The shortest term of office, rounded to the nearest year, was 0 years was by Stephen II in Anno Domini 752, who was made Chief “but on the third day after his election, whilst transacting some domestic affairs, he was struck with apoplexy, and expired on the next day.” And this was in the time before twenty-four cable news programs.

This picture shows the frequency of term of service in years (all dates rounded up to the nearest year; so that somebody serving 0 up to 12 months is counted as one year, etc.).

Frequency of Papal Years of Service

Serving just 2 years was the most common, with about half of all Popes serving 6 or fewer years Pope is a stress filled job, which might be why so many don’t last so long.

Blessed Pius IX, with 33 years served from 1846 to 1878 came in second place behind St Peter. Blessed John Paul II was second runner up and sat in office from 1978 to 2005. Lucky us! These last two data might indicate that Popes are serving longer terms lately. This next picture examines that.

Timeline of Papal Service Length

A vertical line representing the years of service for each Pope is drawn at the year in which they began office. Again, St Peter sticks above all the rest. A black dot is indicated for Benedict XVI, as he is still, thank God, beavering away. Update He made it eight years! The plots reveals that after about 1600 or 1700, longer terms of office were more common. Well, no surprise. This is when health took a turn to the north for all mankind on average.

Not for everybody, naturally. John Paul I served for only 33 days in 1978. And Pius VIII made it only 2 years starting in 1829. But all the other gents from 1670 onwards cruised through 6 or more years. Things were dicier for Popes between roughly 500 to 1200, but then this was a tumultuous time in history. Somehow, even with diets nearer to what is nowadays close to scientifically said to be ideal, people didn’t live as long as they do now. Science has no answer.

Natural comparisons to Popes would be presidents, kings and other leaders of large organizations. I’m guessing the distribution in length of service won’t be too different, especially in those institutions which appoint members for life.

I’m still collecting the birth years of the Popes and other information. When I have it (or people can point me to data sources where the collection is already done?) I’ll post new entries.

Update Not all Popes served for life, like Supreme Court judges. Example: Benedict IX took his turn in the Chair three separate times (he’s only given one entry for his total above).

Not so easy stuff

I wondered whether long periods of service were followed by short periods, perhaps because of institutional fatigue or suspicion. Or maybe the opposite was true and long periods were followed by long periods, perhaps because of good will. It could even be that both tendencies held but at different eras. The following picture helps.

Changes in Papal Service Length

St Peter served 36 years and his successor, St Linus, served only 10. Thus the first line is at -26, indicating the successor served twenty-six years fewer. And so on for the remainder of the Popes. The little “blips” at 0 indicate successors who served identical terms to their predecessors.

I can’t see any pattern, which doesn’t say too much, except that there is no pattern which strikes the eye. Counting shows that 123 successions were shorter, 17 were the same, and 122 were longer as their predecessors. The obvious and expected conclusion is that succession is a far more difficult process than captured in these simple numbers.

Paddy Power’s Pope Predictions—Update

Father Dougal is the farthest left

Update See below for main update.

The odds of Father Dougal Maguire (Craggy Island) being the next Pope are 1,000 to 1. You may say this is small, but it’s orders of magnitude a better chance than you have, or has Your Truly, who meets all the qualifications for the office: being a man and Catholic.

Don’t look for me in sitting in St Peter’s chair because, according to the odds maker Paddy Power, even Richard Dawkins has a better chance than I. He’s currently at 666 to 1.

Clearly, Paddy Power is posting these bets (he also has Bono at 1000 to 1) as a novelty, assuming people would pay a Euro or two for the joy of having a slip with Christianity’s self-appointed nemesis’s name printed on it as being the next Pope.

In top spot, as of this writing, Power puts Archbishop Angelo Scola (Italy) in the lead at 3 to 1. This translates into a probability of 0.25 (or 25%). Number two is Cardinal Peter Turkson (Ghana) at 3.5 to 1 (or 7 to 2), which is a probability of 0.222 (22.2%). These two gentleman have been switching places with other for the past couple of weeks. Now one will lead the betting, now the other.

The odds are set by Power with two constraints: the amount of money attracted by each of the various candidates and his (Power’s) goal of making a profit—not to say prophet. (That one is up to the Lord.)

If punters had a fly (or a bug) on the wall of the Conclave, and all their money was flowing to Candidate A, then Power would be forced to change the odds of this candidate. For example, if all the money were going to Turkson, and none to any other candidate, Power would put the odds of Turkson at (say) 1 to 10,000, which means betting 10,000 Euros would win you 1 if Turkson were elected. This would discourage most bettors, which is the point.

But suppose there were only two candidates (Turkson and Scola, say), and that money was flowing to both equally. Then Power would put his odds at close to, but not equaling 1 to 1. Odds of 1 to 1 translate to a probability of 50%. That 50/50 would reflect the “wisdom of the crowd” all right, but it would not allow Power to make any money. This is because all the money that was bet for the losing candidate would have to be paid out to those who picked the winner.

Power, like all bookies, makes his money by creating a “Dutch book” against the bettors. That is, he has to adjust the odds so that, no matter who wins, he takes a profit. That link explains the mathematics of Dutch books, but all we have to know is that the probabilities implied by the odds must add to more than 1. If they do, then Power is guaranteed to make money no matter which man is elected Pope.

This is why if there were only two candidates in the pool, setting them both at 1 to 1, which is 0.50 for each, is not a Dutch book. Obviously, (but not to graduates of New York City high schools) 0.5 + 0.5 = 1, which is not greater than 1. But if both had odds of 1 to 2, which is a probability of 0.66 (66%), then 0.66 + 0.66 = 1.33, which is greater than 1 and thus guarantees a profit for the bookie.

Having the sum greater than 1 implies the amount of money paid out by the bookie must necessarily be less than the amount of money he collected in the form of bets. And this is so no matter who wins. Without going into the guts of it, the further the sum of the implied probabilities are from 1, the more money the bookie keeps.

The sum for Paddy Power’s (current) Pope pool is 1.88, which is very far from 1, and which means that Power will make a profit, and a healthy one, no matter who is picked to serve (this assumes he is also adjusting the odds by the money bet, as discussed above, and which he is surely doing for the top candidates, but probably not for the bottom ones, meaning his profit will be less than the 1.88 implies). Discounting the three novelty bets (Maguire, Dawkins, and Bono) changes the conclusion not at all, since the odds for these non-starters is so long. Indeed, as said above, money for these gents is pure profit for Power (only Bono is eligible).

The mathematics thus hints at a strategy for the bookie: increase the number of candidates. On average, the wider the field the large the sum of the implied probabilities. Of course, the bookie has to have actual money bet on each of the candidates in the field. If he didn’t, then he could just put odds of a million to one on each member of the phone book (a strategy which would push the implied probability sum greater than 1 every time).

For what it’s worth, my money is on Turkson—but there may be a bit of wishcasting there, too.

Update If we assume only the top n candidates are having actual bets placed on them, then the sum of implied probabilities first rises above 1 for n = 8 (it’s 1.03). The lowest rank candidate of the eight has odds of 18 to 1. But this would leave out Cardinal Dolan at 20 to 1, who we can guess is drawing bets. If we include all those candidates 20 to 1 or better, then the sum is 1.22; a good profit.

Update I can’t believe I forgot renormalization! It’s a way to more closely estimate probabilities given the “vig” (one of the insider names for the Dutch book), and assuming calibration and other things that we’ll deal with another day. Idea is to take every implied probability and divide by the sum of probabilities. Assuming the 20 to 1 odds cutoff mentioned in the last update, this means that Scola has probability 0.21 (21%), Turkson 0.18 (18%), and anybody but these two 1 – 0.21 – 0.18 = 0.61 (61%).

If the implied probabilities already sum to 1 then renormalization does nothing, as it shouldn’t.

Update Since Power had (now) Pope Francis at 33 to 1, some are asking how much did Power lose since a long-shot came in. None. Power made a profit on the bets. That’s the point of making Dutch book against his punters. Power wins no matter what. See the link to Dutch Book for the mathematical details.

This is the same reason brokers charge “transaction fees.”

Feds Spend $1.5 Million to Study Why Lesbians Are Fat?

Obesity in lesbians is a health crisis

The title was taken from the CNS News story of the same name, which made ripples in the news yesterday (Drudge linked to it).

The National Institutes of Health (NIH) has awarded $1.5 million to study biological and social factors for why “three-quarters” of lesbians are obese and why gay males are not, calling it an issue of “high public-health significance.”

If this is true, you know what it means, of course. It means that TV and the movies have lied to us. Systematically, and over a long period of time.

When was the last time you saw a show or movie in which a woman oriented towards other women wasn’t hot, svelte, able to wiggle into hipster jeans without grunting? I’ll tell you when. Never. There’s even a popular sub-genre, which I’ve heard is distributed on the internet, which delights in displaying actively oriented non-obese non-heterosexual females. Our first clue should have been that the audience for such fare was (obese or not) men oriented towards women.

Science however can’t be wrong, or questioned. According to the well-funded grant (to the tune of $741,378 of your money—where was the sequester when it was needed?) Sexual Orientation and Obesity: Test of a Gendered Biopsychosocial Model Obesity “nearly three-quarters of adult lesbians [are] overweight or obese.”

S. Bryn Austin, Director of Fellowship Research Training in the Division of Adolescent and Young Adult Medicine at Boston Children’s Hospital, used that scientific statistic to convince the government to part with money to study the statistics of overweight lesbians. In other words, Austin claims already to know lesbians are fatter than normal women, but he wants (and got) three-quarters of a million to verify it.

Some of that money will be spent studying why, “[i]n stark contrast, among men, heterosexual males have nearly double the risk of obesity compared to gay males.” Austin even has a theory. He and his group “will rigorously test our innovative gendered biopsychosocial model to explain sexual orientation disparities in obesity with prospective, repeated measures survey data and biological data from three national youth cohorts.”

Sounds like the solution to the obesity “epidemic” is to have heterosexual men and non-heterosexual women switch their orientations. Maybe science can develop a pill? Or is the education provided in our public schools sufficient?

Anyway, if you’re upset about the money Austin gets, consider these facts. Austin himself only keeps half a million. He has to hand over the other quarter-mill as “protection” to his Dean (funds which are euphemistically called “overhead”). Plus, Austin was only being smart. Turns out the government issued an announcement begging people to take its money to study these things. If it wasn’t Austin, it would have been somebody else.

Yes. “PA-07-409″, or Health Research with Diverse Populations, was government instigated. It’s focus “is on research that bears upon on the health of lesbian, gay, bisexual, transgender, intersex, and other diverse populations.”

I know, or think I know, the meaning of the first four terms, but I haven’t any idea what “intersex” means, and I’m leery of typing it into a browser. I notice, however, that it’s at the end of a list which is ordered by increasing unusualness. This is why “other diverse populations”, which could mean anything, comes last.

Oh, the $1.5 million in the title arises because the government, in its ever-increasing benevolence, handed out more than one grant on the subject. If anything, the figure is a gross understatement. On just the first page of grants “similar to” Austin’s, at least $10 million more was spent.

We glean from these grants that the preferred term for non-heterosexuality is “sexual minority”, which has a pleasing, civil rights, social justice ring to it.

A couple of other awards: Stress Reactivity and Substance Use Among Sexual Minority Girls ($339,887; boys, you’ll have to wait), Risk and Protective Factors for Suicide Among Sexual Minority Youth ($598,609), Cumulative Stress and Hazardous Drinking in a Community Sample of Adult Lesbians ($602,989), etc. forever.

What the novice reader might not understand is that all these grants are in the pipeline, thus that each will result in many to dozens of papers, and that each of these will call for more research, which itself will seem justified because the mass of “work” in the field makes the field appear important. The thing is self-perpetuating.

Doomed Planet: Changing Sun, Changing Climate

Today’s post is at Quadrant. Have you been there before? If not, you have a treat in store.

The editors supplied this quotation:

“Today’s debate about global warming is essentially a debate about freedom. The environmentalists would like to mastermind each and every possible (and impossible) aspect of our lives.”

Vaclav Klaus
Blue Planet in Green Shackles

Bob Carter, Willie Soon, and I provided this start:

Scientists have been studying solar influences on the climate for more than 5000 years.Chinese imperial astronomers kept detailed sunspot records, and noticed that more sunspots meant warmer weather. In 1801, celebrated astronomer William Herschel, the first to observe Uranus, noted that when there were fewer spots the price of wheat soared. He surmised that less “light and heat” from the sun resulted in reduced harvests.

Head over, then come back here to leave comments.

But while you’re there, stay and read Keith Windschuttle’s piece “Inventing massacre stories“, tales the Left uses to induce pleasurable guilt and sense of purpose.

See also the (not-too-often updated) Quandrant TV page, and watch Jim Franklin’s video, “What Science Knows.”

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