When 2 + 2 = 5

Artwork by Joe, age 41 3/4

The last post was a little rushed, but as at least one person is looking forward to an update I thought I'd clarify some of my thinking.

@CatsofOxford pointed out that because of the partial correlation between the two individual Senate races, no bookie would offer the double, and that's true, but we can still use the implied probabilities in each market to calculate the outcome in terms of overall seats.

It was very strange to me that the odds for the Special race Democrat were so much shorter than for the Democrat in the Regular race. There were differences of course, mostly that while both Republican candidates were incumbents, usually a big advantage, one (Loeffler in the Special) was appointed, and the incumbency advantage is usually lower. Perdue in the Regular race, had name recognition, but even so, for the two Democrats to be separated by so much seemed odd. The majority of voters would be expected to vote by party, so why did one Democratic candidate have an implied probability of 0.62 and another just 0.465? 

Anyway, the point I wanted to make was that these races only had four possible results and with the Democrats starting from 46 seats and the Republicans on 50, the Senate makeup could be easily projected. Two coin tosses have three net outcomes - Two Heads, Two Tails, One of Each, with the latter most likely at evens. 

To stay on 46 seats the Democrats would need to lose both races, a probability we can calculate from the odds available as 0.2033 (0.38 * 0.535).

To move to 48 seats, the Democrats would need to win both races, a probability of 0.28 (0.62 * 0.465), and to end up with 47 seats, and the Republicans with 51 seats, the probability would be 0.5167 (or 1.93 in Betfair terms), yet the price for this last outcome was 4.9. 

What gives? Even allowing for some wiggle in the prices, that's a big difference but if 4.9 intuitively seemed to high, what price was fair? And if 4.9 was too high, then the other outcomes must have been too low. Or the root prices of 1.61 and 2.15 were wrong. Warnock's (1.61) was probably reasonable, but Ossoff should have been closer to 1.94. Something to watch in the future perhaps, but as these events are so rare there's not much to be gained from analysing them to death. I made a little on all three markets by betting with my heart rather than finding an edge, but I can't help thinking I was too late looking at these markets and missed a bigger opportunity. It happens. The bigger picture is that the Democrats look to have secured control of Congress and the Presidency, a nice turnaround from four years ago when the Republicans ruled the roost. So much for all this winning by Donald Trump.