**Push Probabilities and the Value of a Half Point in NCAA Men’s Basketball**

At its core, sports betting is about estimating the probability of an event occurring and comparing your estimation with the implied probability of the payout that is offered from a sportsbook. For example, if you estimate the probability of Colorado men’s basketball team covering the spread against USC to be 55.0%, it’s probably worth a bet if you can get -110 odds on Oregon (52.4% breakeven probability).

**Conditional Probabilities**

However, what is often oversimplified is the fact that your estimate is actually a **conditional probability**. Your estimate of 55.0% probability of Colorado covering is conditional on the fact that 1) the teams that playing are Colorado and USC, and 2) Colorado is a 9-point favorite and 3) whatever else is an input into your model. If Oregon were a 7-point underdog instead, your probability would be different. This is what makes totals and spreads incrementally harder to model that money lines. Betting a money line,you only need to consider the odds (set by a sportsbook) and the probability of a team winning. Betting the spread, however, requires you to account for the odds and the probability of a team covering the spread, both of which (the odds and the spread) are set by the sportsbook.

Using data from the past two seasons of NCAAB[1],we can estimate the frequency of a game ending in a 9-point margin to be around 4.8% (513/10,810). But Colorado could be on the winning or losing side of that game. **With this data, we should be able to conclude that the likelihood of Colorado winning by 9 points is approximately 2.4%, right? Ehhh not quite.**

Given that Colorado is favored by 9 points, it should be pretty obvious that they have a greater chance of winning by 9 points than losing by 9 points.

Alright, so let’s look at the frequency of winning by 9, conditional on being the favorite. Of the 10,810 games sampled over the last two seasons, 238 games were a pick-em,leaving 10,572 instances where there was a favorite and an underdog. Of those games, 366 ended with the favorite winning by precisely 9 points. Therefore, conditional on being a favorite, the frequency of winning by 9 points has been 3.5% (366/10,572) over the past two seasons.

Unfortunately, this is not enough to say that a team that is favored by 9 points has a 3.5% probability of pushing. Not all favorites are the same, as some are small favorites and some are large favorites. What we’d like to do is isolate the games that feature a 9-point favorite, or there about.

Over the last five seasons, there have been 1,247 games featuring a favorite between 8 and 10 points. (Note: we used 8-10 rather than 9 for the sake of increasing our sample size, and therefore our confidence in these insights.) In those 1,247 games, the favorite won by exactly 9 points on 55 occasions, or **4.4% of the time**. While we don’t know with certainty that this represents the true probability of pushing a bet as a 9-point favorite (as there are many other factors in a game), we are much more comfortable with this figure than any of the figures calculated above.

**Value of a Half Point**

Let’s assume that you want to bet Colorado v USC tonight and most books are dealing Colorado -9/-110. However, some books are moving to -8.5.How much should you be willing to move from -9 to -8.5?

Using our push percentage of 4.4%, this turns into a simple arithmetic problem. We can solve for the odds on -8.5 (and -9.5 for good measure) that gets you to the same expected return as -9/-110. As seen below, -8.5/-120 is approximately the equivalent of -9/-110. Therefore, if a book is offering the -8.5 at less than -120, it’s probably a better bet than the -9/-110.

[1]Courtesy of sportsdatabase.com

**NCAAB Half Point Price**

Cool math, guy. So how does this help me?

Well – by doing this exercise across all the various point spreads, we can come up with a fair price for each half point. The table below should serve as a guide for when you’re shopping various point spreads in NCAAB. You're welcome.

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