Or, some thoughts on the theory of bid-ask spreads in gambling markets
One of the things I’ve found interesting to think about for a few months now is how spreads and odds get set by bookmakers. I’ve written a bit about this before, in terms of how the line gets set, but also think it’s worth considering how the house edge is set on any given market. In the simplest terms, what determines whether a two-sided market is -110 on both sides1 or -115 on both sides 2, or some other number? Put differently, and more broadly, this can be thought of as a question around efficiency and liquidity in gambling markets, and what determines the bid-ask spread.
It’s useful to start with how lines get set. Broadly speaking, bookmakers begin by opening markets at prices they think reflect the ‘right price’ for a game, based on their actual expectations of performance, expectations of people’s bets, and a variety of other factors3. Gamblers (or market participants, if you prefer to sound more academic) then places wagers in these markets, moving the line one way or another based on their aggregate volumes, and the line eventually moves to a more efficient equilibrium price such that future bets aren’t one-sided and won’t move the market4.
At the highest level: markets which reach that equilibrium price faster should have tighter bid-ask spreads. In a gambling context, that should be reflected in the form of a lower vig; the most efficient market possible would be one offering true odds5, with any house edge eating away at liquidity in some aspect. The key here is that the tightness of a bid-ask spread is reflective of the risk that the marketmaker is taking; in situations where the marketmaker can trust that he is not exposed to as much risk6, then he should be willing to offer a tighter market to attract more bets.
What makes a market reach that price faster? It’s primarily a function of liquidity. A market with a lot of gamblers, a lot of bets, and a lot of dollars at stake has a lot more volume and is a lot more liquid. Consequently, there’s enough activity going on that you’re able to reach the ‘right price’ a lot quicker. It’s not that the prices in these market necessarily start any more accurately than any others; they just move more quickly into equilibrium much more quickly. This is pretty straightforward to see in the gambling world; the most heavily bet markets are generally NFL games (both spreads and totals), and those bets are generally regarded as most efficient and hardest to find an edge on7.
Beyond liquidity, events with more precisely well-known mathematical odds should also be more efficient markets, and this should again be reflected in tighter spreads. However, in this instance the efficiency is a function of the event itself rather than a function of the market participants – if the true odds are particularly well known, the marketmaker can be more confident that his opening lines are already the ‘efficient prices’ and he doesn’t have to rely on gamblers to get him there. As an example, one of the popular Super Bowl prop bets offered every year is whether the coin toss will be Heads or Tails. Prop bets (or derivative bets) tend to get less action than most ‘regular’ bets, and they usually have larger vigs to reflect the fact that they’re less efficient markets. But this is an obviously 50-50 proposition, it’s a literal coin flip – and I think every time I’ve seen the prop offered, it’s been a -105 bet8 on either side, reflecting that fact.
Conversely, less liquid or well-known stuff should in contrast see wider spreads. I already mentioned derivative (or prop) bets as one example here; less money chasing those markets means prices can remain inefficient longer, and there’s a higher risk of one-sided traffic9. In some instances, you can actually see the ‘efficiency as liquidity’ question play out in real time, with not just the lines moving dynamically, but the size of the spreads as well. In college football, for example, while most big college football games are pretty liquid markets, FCS games are much less commonly bet. I’ve very frequently seen markets start at -120 or -125 on Monday morning, but have those spreads shrink to -110 on Saturday around noon when it’s almost gametime. Why are they able to tighten the market? Because by that point they feel pretty good about the quality of the price they’re offering, so they have less need to protect against price risk – despite the fact that it was perfectly logical for them to do so a few days prior.
One particularly interesting ‘less liquid’ example is in futures betting 10, which has two real wrinkles to deal with. First, time lag – these events are all things that happen in the future, not today, and the correct probabilities will evolve over time. This creates some level of uncertainty risk in that the efficient prices will change over time, could change dramatically over time, and even if the market lands on the efficient prices today the marketmaker faces a real risk that in the future the market won’t remain liquid enough to stay efficient as prices evolve. That uncertainty ends up reflected in a wider spread. Secondly, these are typically not 1-on-1 outcomes; there’s a whole field of potential options11. As such, getting to “equilibrium” is a lot harder because it’s not about A vs B, it’s about A, B, C… to Z all being reasonably efficient prices. Liquidity is a lot harder because even with a lot of people betting, there’s no guarantee you’ll receive enough volume on each individual possible outcome of the futures market for the prices to be accurate; it’s a lot easier for a few to be out of whack. Books end up protecting against this by having a much, much higher hold in futures markets than in regular betting – where the house edge is usually something like 4-5% in any typical point spread, the total house edge in most futures markets is often 20-30% or more.
Another example is in live betting, where wagers are accepted during the actual course of play of a game. These markets typically see much wider spreads (something like -120 on each side instead of -110), largely because the timeframe in which bettors can move the price is basically nonexistant – the game is already going on! Bookmakers either have to be very very confident in the prices they offer or offer a less liquid market to protect themselves. They generally choose the latter.
It’s also worth thinking about alternative forms of illiquidity, where you can get tighter spreads at the cost of something else. One example is betting exchanges like Betfair – rather than having a marketmaker take your risk, these exchanges use a peer-to-peer market where your wager remains pending until some other bettor wants to take the other side. Because the exchange isn’t taking any risk themselves, they’re protected against any ‘inefficient prices’ and never have any net exposure, so bettors are able to benefit from tighter spreads12, at the cost of some execution risk (you’re not guaranteed for your wager to be received until someone takes the other side). Another example is in parimutuel betting, where odds are constantly fluctuating and the actual odds at which a bet is locked in are not set until shortly prior to the event occurring (this is pretty popular in horse racing). The house takes a fixed percentage from the total pool of wagers and then pays out according to the final odds, so they’re again not taking any risk. From the bettor’s perspective, you can get a tighter ‘spread’ and you’re guaranteed to have your bet be valid, but you’re not guaranteed on the actual price, since that will still move around even after your bet is placed13.
Okay, now that we’re 1400 words into this – what’re the implications of all of this to the average gambler? In my experience a lot of times people see markets with lines at -115 or -120 and get annoyed at the bookmaker’s apparent stinginess. If that’s happening on a major event like an NFL or college football game, then sure, that doesn’t seem appropriate. But if that’s happening on more obscure events, it’s not indicative of cheapness – it’s indicative of the marketmaker being afraid that their price is wrong, and that means it’s an opportunity. Despite wider spreads, the average bettor is far more likely to be able to profit betting into markets with less efficient prices than they are into markets with tight spreads and perfectly efficient prices. Ed Miller and Matthew Davidow make this point really well in The Logic of Sports Betting14 when they get into the idea of ‘strong markets versus weak markets,’ and the need for savvy gamblers to attack the latter – when markets are less liquid, spreads are often wider, but they’re less efficient, and that means they are much more likely to be beatable.