Harry and Meghan - divorce odds

After Harry and Meghan stepped back from the British royal family, UK bookmakers started offering odds on various other scenarios that might occur to the couple. The most interesting of these to analyse are the odds of them getting divorced, in part because there are good datasets on divorce rates.

How should you think about analysing the probability of this?

3/1 are the bookmakers odds on them being divorced by 2025. For simplicity let's assume this is a 5 year time horizon. For this to be an attractive proposition you would want the probability of them getting divorced to be materially higher than the 25% implied probability the 3/1 bet offers. If the true probability was exactly 25%, out of 4 trials, 3 times you would lose your stake and 1 time you would make 3 times your stake.

In analysing a proposition like this you want to first establish a base rate; an average probability across the population that gives you a starting point from which you can bias your estimate of the "true" probability up or down depending on specific factors to the case in hand. The UK Office of National Statistics has good datasets on divorce, broken down by the time since the couple has been married.

Harry and Meghan were married more than a year and a half ago, the marriage data is grouped by year of marriage, for simplicity we will assume that they have been married for 2 years.

The base rate we would like to know is what is the probability of a British couple who has been married for 2 years getting divorced over the next 5? Table 2 of the ONS link posted below has the relevant data, with the most recent year that this figure is available for as couples married in 2006 - at a 13% probability. The number has been on the decline from peaks of 16% in the late 1980s.

This figure is much lower than the level at which the bet might have value, however I would suggest it should be biased upwards for one key reason - celebrity couples are more likely to get divorced for reasons I won't speculate on here. A study done by the Marriage Foundation found that celebrity marriages are twice as likely to end in divorce as the general population for a 14 year period they studied. If we conservatively bias our base rate higher, based on this, by say 10ppts, we are still short of the proposition being attractive (23% calculated vs. 25% implied) and even if we double our estimate it is still not enough margin for error to percieve the bet as attractive (26% calculated vs. 25% implied).

This isn't an unexpected outcome, given bookies are good price makers, but I hope it was useful in showing how one might think about similar propositions.

Links:

https://www.dailymail.co.uk/news/article-7883397/Prince-Harry-Meghan-Markle-likely-divorce-rejoin-Royals-time-bookmakers-say.html
https://www.forbes.com/sites/guymartin/2020/01/15/the-megxit-fallout-day-7-what-the-british-bookmakers-are-telling-us-with-their-odds-on-a-divorce-for-prince-harry/#39ca9a030185
https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/divorce/datasets/divorcesinenglandandwalesageatmarriagedurationofmarriageandcohortanalyses
https://marriagefoundation.org.uk/celebrity-marriages-2/