In a previous post, I demonstrated how the conventional wisdom of “any bet that is -EV must be a bad bet” is really just a myth. Another example of conventional wisdom that should be examined more closely is the idea that the larger hold percentage in multiway markets makes them much tougher to beat. In markets with more than two choices, like EPL futures markets or outrights for a golf tournament, the total hold (or margin) is typically much larger than it is for a two-way market when the break-even percentages for all selections are summed up. At sharp books, it can be in the 15–20% range, and at soft ones it can be 30–50% or more. What a rip-off! It seems like those greedy books are charging each bettor a much larger vig to bet in those markets. But is that really true? As they say in the sports world, let’s break it down.

The first thing we need to do is figure out how the line on each individual runner compares to its corresponding vig-free line. The traditional method of calculating the vig-free line is simply converting each line to a break-even percentage, divide it by the overround (e.g., 120%, if that’s what the implied percentages add up to), and then turn it back into odds. For example, a 1.91 (or -110) line on each side of a two-way market has a break-even percentage of 52.4%, and the total implied probability of that market is 104.8%, so the vig-free probability is simply 52.4%/104.8% = 50%. Thus, the fair line is 2.0 (+100) in odds. And it works the same way for all odds, right?

Well, for that hypothesis to be true, the favorite-longshot bias (FLB) would have to be false. But, there is ample evidence to show that it’s a real effect at sports books. The FLB states that the vig isn’t distributed in proportion to the odds, but instead a higher proportion is placed on the longshots. So, in order to calculate the vig-free lines, we need to model the distribution of the margin in the correct way. One thoroughly tested way to do this is to assume that the break-even percentage is determined by adding the same small percentage to the true win percentage of each runner in the market before converting into odds. This distributes the margin equally in absolute terms over each runner (as described by Joseph Buchdahl in his book Squares and Sharps, Suckers and Sharks), so that what you would expect is a total margin for the market of n*m, where n is the number of runners and m is the margin added per runner.

In our typical two-way market example, m= 52.4% — 50% = 2.4%, so if we extrapolate that amount of margin into an 11-way futures market, then we should expect a total margin of about 11 * 2.4% = 26.4%. Obviously, with that many runners, some of them will usually be extreme longshots, and their lines won’t support 2.4% margin (or else the odds would be capped at around 40.0, even for runners with 0% chance of winning). So, with reduced margin applied to the longer shots, one might expect a total margin of about 20%.

That’s exactly what you’d have found a few months ago if you had looked at the odds for the Eastern Conference winner in the 2021 NBA playoffs. Shortly before the playoffs started, 11 teams were still in contention, with the Brooklyn Nets posted as prohibitive favourites. Based on the following odds from DraftKings, the overround was 118.6% (i.e., the market had 18.6% margin or hold). Hypothetically, if a field bet vs. the Nets had been offered as a two-way market, we can presume it would have had a line around 1.935 (-107) and a two-way market margin of 4.5%. I backed out the margin from each line approximately according to the method above, and ensured that the total true win percentage came out to 100%, for both the two-way and multiway markets. My results are in the following table: