US Presidential odds update - Bloomberg odds shortening

It has been a month since I last aggregated the probabilities associated with the US election (linked here) and in that time Peter Buttigieg won the most votes in the Iowa caucus, the result of which was delayed due to technical issues.

Of the updated data below, the most interesting change has been in the betting market's probability for Mike Bloomberg to become President. Bloomberg now sits at an 11% implied probability from 5% a month ago. This is the second highest amongst the Democratic candidates. However, it is in sharp contrast to the 538 primary forecasting model which sees his chances of winning the Democratic nomination first as just 2%.

Bloomberg's primary strategy is untested - he will only begin campaigning on the Super Tuesday states, missing out earlier chances to pickup delegates. He is outspending the rest of the field put together, a strategy only possible due to his personal financial position. This could backfire given the focus in recent years on rising inequality and the behaviour of the very wealthy. The narrative of him trying to "buy" the election is something I would expect to see other Democratic candidates using if he began winning delegates. However, the betting markets clearly give him a lot of credit for being able to bring those resources to bear, and for what he brings as a candidate as a successful businessman and ex mayor of New York.

My personal view is that it is an interesting bet to lay against him winning the presidency, taking the 538 forecasting model as more likely to reflect the true probability of his chances over the betting market, given their data driven approach.

Betting market probabilities

Probabilities across sources

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/