The pageantry and religious significance of the papal conclave aside, an electoral process that's been around for over 1,000 years provides a lot of data. For those of you interested in historical trends, or those of you betting on voting results, here's the numeric breakdown of what past conclaves have offered.
Unsurprisingly, data on secret meetings that took place in Rome in 1118 is hard to come by. Not that it doesn't exist; there are a number of sites that offer detailed specifics of the 107 conclaves that have occurred since 1061. (Like this site, which must make Nate Silver wish he had some elixir of immortality.) For most gatherings, details are sketchy. But using Wikipedia (in English and Hungarian) and Catholic-Hierarchy.org, we've pieced together the number of electors and length of each conclave since 1455, and the number of ballots cast at each since 1830.
First, the topline numbers. A caveat: What follows is not an even comparison. The church changes the rules for voting with relative frequency (meaning: frequently given the number of conclaves that have been held).
That said, there have been 107 conclaves in the past 952 years, for an average of one every 8.89 years. The frequency of conclaves has slowed considerably since the 1500s, as the graph below suggests.
The chart below shows data since 1455, as available. The orange line shows the length of the conclave in days; the blue line, the number of electors (voting cardinals); the red line, the number of ballots.
Since 1455, the average length of a conclave has been 34.5 days, though the median length has been only 13. This difference is partly due to rules changes that facilitated votes, but it is mostly due to there having been a number of conclaves that stretched for a number of months. The conclave of December 1799 lasted until the following March, probably ruining the cardinals' celebration of the new century. The longest was in 1691, stretching some 150 days.
Since 1830, the average number of ballots cast is 13, while the median is 6.5. This is largely due to the 83 votes cast in 1830 — but it excludes the monster conclave of 1774, which stretched 135 days and comprised 265 votes. Here is a chart of all of the votes after 1830, for clarity …
… since including the two prior ruins the scale.
If you're curious (and as you might suspect), there's no real correlation between how long a conclave lasts and how long the resulting pope serves. On average, the pope will serve for 609 days for each day the conclave lasts, but that varies widely. The graph below indicates that figure for each conclave. The best ratio was in 1846, when a three-day conclave yielded Pius IX, who served 32 years.
Our predictions for this conclave? The past four have averaged 5.5 ballots — meaning that we could see a new pope on Thursday. And if he meets the historical average, there will be another conclave starting March 13, 2018.