Mathematical Considerations For Teasers

Following on from last week's post on parlays on Sportspicks I'd like to explore the mathematical underpinnings of teasers. This is prompted partially by Robert Barnes' allusion to teasers showing an edge in college football last season and Will from Game On's analysis on teasers for NFL. I'll be posting this on Game On too so that hopefully we'll all find a good edge on teasers this year in college football and NFL.

A teaser is an adjusted parlay that combines spreads and totals from either American football or basketball leagues. Whatever line you take, you adjust it by the same number in the same direction of action. Since spreads and totals are generally quoted on average a little bit below even money, parlays and teasers are quoted at odds that lengthen exponentially with each added leg. The primary difference is that teasers lengthen slower such that a two leg teaser has a similar price to its original constituent spreads and subsequent legs will diverge from even money more slowly.

Why might this be important? The crucial component to profitable parlays is having a positive edge compounded over all legs (preferably every leg should have a consistent edge). The drawback is that since parlays tend to be very much plus money, the iteration to iteration variance is rougher so you have to contend with feasts and famines. Teasers can give you the same compounded edge but with the more even short term returns of regular spread betting.

In order to evaluate the profitability of teasers compared to straights and parlays, you will have to estimate the probabilities of each leg hitting as well as the break even probabilities from the quoted odds. The shorthand for the break even probability is to take decimal odds and take it's reciprocal (divide the number one by it). Multiply the probability for each leg together and convert back to whichever odds format you're comfortable with. Compare this with the quoted teaser/parlay odds and you will know at a glance whether the bookmaker is ripping you off or not. To do this calculation for teasers, you will need to look up the relevant alt lines. Not all bookmakers do this but many do. Whichever of these gives the lowest implied probabilities (and hence best odds) is your candidate.

Now to calculate expected value. Here you will need your own estimates for the probabilities that the base spreads hit as well as the alt spreads used in the teaser. Expectation value is stake multiplied by decimal odds multiplied by estimated probability, then minus your original stake. Divide result by stake and that is your edge.

This may seem tedious but it's key to determining if a bookmaker has mispriced a derivative betting option. I've posted before about how draw no bets and double chances can be better or worse value than betting synthetic moneylines. Similarly, Will has posted that teasing a 6 point favourite down to moneyline can be worse value than taking them moneyline. Since a two leg teaser roughly corresponds to parlaying two bets at about -280 odds each, this is something you'll want to check for yourself because every bit of edge counts. You can't directly evaluate a teaser this way but you can cross reference it against the other leg alt lines and determine which is the best option to take.

So if you made it through all that, I will go through a little more practical stuff. It has become very popular to tease lines through magic numbers as Wong teasers do. This involves teasing a line to +3.5, +7.5 and some others as these are very common margins. Correspondingly, teasing through 0 is not recommended by this logic since a draw is a very low probability outcome.

From my preliminary investigations, I would disagree with the above logic (or at least caution that it may be dated). Bookmakers are well aware of Wong Teasers and will make you pay a premium to put them on. You can verify this by noting the odds on alt spreads, translating them into implied probabilities and observing the jumps over magic numbers. It generally gets priced in. Correspondingly, I think bookmakers may be discounting the jump over the 0 line as they can't totally rip you off. They have to make the lines tempting enough for you to bite.

More generally, I suspect that alt spreads are not as tightly set as there's way more betting action on the primary lines. Teasing may well be a good way of taking advantage of inefficiencies on these lines and compounding the edge in a similar way to parlays. Perhaps multiple teasers can function similar round robin parlays where you distribute the risk over multiple fixtures but collect the compounded edge on them all.

Anyway it's early in the season and I'm still learning the ropes of teasers so hopefully we'll all find some good edges over the coming months!