Not sure if youâve seen this, but I wrote a blog post a while back about the fav-longshot bias. Itâs a bit involved and maybe not worth your time, but what Iâve written below is coming from that post for the most part.
Re your first point about exchanges versus books: one key thing that seems overlooked is what the definition of the FLB is in an exchange versus a bookmaker market. With bookmaker markets, people typically define the FLB as âdeclining returns as odds lengthenâ (e.g. betting on longshots returns -10% while betting on favourites returns -4%). However, with exchanges, often the FLB is defined using the midpoint of the bid-ask spread. Somehow, in my reading of things, this has gone unnoticed by most people. If the midpoint of the bid-ask is unbiased (which it typically is on an exchange, at least in the more efficient markets), this means that expected returns decline as odds lengthen (which is the definition of a fav-longshot bias in a bookmaker context).
Anyways, my point here is that I would expect to see the FLB in exchanges simply because I think FLB is basically inevitable in any market there is an over-round. I donât think a theory about bettor psychology is required to explain FLB (if we are using the declining returns definition).
Re your second point, yes I think thatâs true, but I donât think there even has to be higher price uncertainty. Hereâs an example this week that I think illustrates why itâs the case:
Consider Valimaki and Dubuisson in the European Tour event. We have Valimakiâs skill at about -0.5 and Dubuissonâs at -1, so a half-shot difference. We have their cut probabilities at 61.3% and 50.5% respectively, and their win probabilities at 0.7% and 0.3%. Suppose there is a bettor who, for some reason, thinks that Dubuissonâs true skill is closer to Valimakiâs this week, while the bookmakers stick with the skill levels listed above to generate their prices. This bettor is going to have a much larger perceived edge betting on Dubuisson to win than betting on him to make the cut, even if the bookmaker puts more vig on the outright price. For example, suppose they price his cut probability at 54% and his win probability at 0.4% (generated based on the true prices of 50.5% and 0.3% listed above). This would give this bettor a perceived edge of 75% on the win bet, but an edge of just 13.5% on the cut bet, even though the vig is much higher (proportionally) on the win bet than the cut bet.
This example is specific to the relationship between underlying skill and finish probabilities in golf, but I think it holds more generally. Basically your disagreements with the bookmaker on a team or a playerâs skill can translate into a way bigger edge in probability terms when those probabilities are very small. It doesnât take that much of a disagreement to move from 0.1% to 0.2% â which is a difference of 100%! â while itâs not even possible to have movements that large once you get to probabilities above 50%.
Iâm also realizing this is closely related to my thinking on the FLB. Basically, at low probabilities expected returns (both positive and negative) get magnified even when there are only minor differences between the true price and the price you are betting at. If you are on the positive side of this, it means big EV! But if you are on the negative side of it, it means youâll lose a large % on each dollar bet (which is how the FLB comes about, IMO). So the result is that in low probability, high vig markets, if you are a sharp bettor you can achieve a high ROI, but if you are betting aimlessly you will lose a lot.
I guess I didnât really address your questions, but I do think your point about higher-vig markets having more price uncertainty is also true â I just donât really have anything useful to add on that front.