As tonight's Duke/St. John's game shows, the books do occasionally set bad lines. I've been thinking about this topic framed in terms of line movement. What causes the line move and, more importantly, how does it affect the expected value of both sides?

As I wrote yesterday, I've yet to be convinced that value does not exist on sides with reverse line movement. That seems like an odd null hypothesis at first glance. As I've mentioned previously, my H0 is mainly anecdotal with some small sample empirical evidence thrown in. Most other gamblers I think take the opposite null hypothesis, which makes sense without taking the book's logic into account. If you are betting on a dog, would you rather have +7 or +6.5, knowing that your EV falls by a certain amount by taking the 6.5?

Let's take yesterday's WVU-Notre Dame line as an example. The line opened Tuesday night at 8.5 and closed at 9.5. Without thinking too much about it, you obviously would have rather had WVU -8.5. The more important question, particularly if you are stuck at work all day while the line moves, is whether there is still value at 9.5, not whether you lost some EV in the move (which you obviously did). Using the half point calculator, a true line of -8.5 +100 works out to -9.5 +118.2. From that, you can infer that you are losing 4.18% in probability by taking the line at 9.5. That calculation also implies that you needed to have a >55% chance of that line hitting at 8.5.

So, is there a >55% chance of WVU covering at 8.5? I acknowldege that contrarians are working within a tight margin, but I think, because of the line movement, the margin is a bit looser in this case. The "public" was backing Notre Dame yesterday at a 63.13% clip (from close at Wagerline). Why would the books move the line, exposing themselves to 4.18% chance of a middle? I think the answer has to be they realized an error in the line and WVU was overvalued at 8.5. That is, there was a significantly greater than 50% chance that WVU covers 8.5, and sharps knew it and hammered the line, facilitating the move to 9.5. Even if big money was coming in, if the books were attracting equal action from sharps (thereby validating their line), they never would have moved it, no matter what the "public" was on.

Here is some math to back me up (all at -110 juice for the book). I'm going to go through the first example spelling things out, from there you should pick it up. As you look through the numbers, ask yourself if you were the bookmaker, would you move the line to change your EV or variance?

Example 1

Probabilities held constant at 60% chance WVU covers at -8.5 and a 40% chance that Notre Dame covers at +8.5

80% of the money is coming in on WVU

EV = .6 (-800+220) + .4 (880-200)

= .6 (-580) + .4 (680)

= -76

70% of the money is coming in on WVU

EV = .6 (-370) + .4 (470) = -34

60% of the money is coming in on WVU

EV = .6 (-160) + .4 (260) = +8

I could solve an equation for percentage of money that needs to be wagered on WVU for the books to break even, but I'm lazy and it's fairly obvious that the number is slightly above 60%.

Example 2

WVU is attracting a constant 70% of the money and the probabilities of a WVU cover vary

WVU covers 70% of the time

EV = .7 (-370) + .3 (470) = -118

WVU covers 65% of the time

EV = .65 (-370) + .35 (470) = -76

WVU covers 60% of the time

EV = .6 (-370) + .4 (470) = -34

WVU covers 55% of the time

EV = .55 (-370) + .45 (470) = +8

Clearly, if the books are taking a ton of money on WVU, they are at risk of taking loss. WVU needs to cover a little under 60% of the time for the books to take wash here.

Example 3

WVU is attracting a constant 60% of the money and the probabilities of a WVU cover vary

WVU covers 70% of the time

EV = .7 (-160) + .3 (260) = -34

WVU covers 65% of the time

EV = .65 (-160) + .35 (260) = -13

WVU covers 60% of the time

EV = .6 (-160) + .4 (260) = +8

WVU covers 55% of the time

EV = .55 (-160) + .45 (260) = +29

I have no idea how much risk the books tolerate. But I think it is pretty clear looking through these examples that action doesn't have to be all that one sided if the probabilities aren't even. So, why would a book move a line by a point if they weren't uncomfortable with the risk? And inherently, will there still be value in the new line? I'll leave the math to you, but it obviously depends on how one-sided the action was. Remember, for there to be value (without considering juice), the probability for WVU to cover at 8.5 has to be greater than 54.18%. Overall, I think when the line moves more than a point, it is a signal that value remains on the contrarian side.

Finally, how bad did the books screw up with their Duke/SJU line given this analysis? The books opened themselves up to a huge middle opportunity. There must have been a ton of action on Duke and they realized the Duke was probably going to cover.

## 3 comments:

I'm remaining political and staying on the fence with this issue. I have a few months before I'm investing not my student loans(the payment of them, I guess). Respond however, thinking out loud. Seems to be the way to go:

I think we have A LOT more to work with in football than we do in basketball, and I'm meaning value. Football is about beating joe public and pretty much only joe public. I feel like smart money can outweigh public money in basketball in certain instances. Because of this books set sharper lines and have a lot less leeway. So if they get hit hard by someone, they are forced to move it.

Then again, I also firmly believe that someone banging a side for 10K that also causes a move knows what they are doing.

"WVU was overvalued at 8.5"Undervalued, I think you mean.

"Overall, I think when the line moves more than a point, it is a signal that value remains on the contrarian side."Lost me here. So you're saying that a two point "reverse" move would cause you to be more interested in a play than a one point move?

I may write more about this at a later time, but I figured the email dialogue VW and I had today may spark more conversation.

19:I probably need to work the math out more.Obviously, the original edge needs to be larger (say 58% instead of 54%). As I showed in my post, there are two variables at play, how one-sided the action is and if the books change their mind on the fair line (which I assume would be validated by sharp gamblers, and that's kind of the essence of the post).

If the original WVU cover probability is 55%, even attracting 70% of the money on WVU is still profitable for the book thanks to the juice. So, in order for them to rationally move the line one point, they need some combination of a ton of money on WVU and a significant difference in cover probability for WVU.

If they move the line two points, doesn't that indicate that they are taking way more total money and sharp money (again, as a proxy for probability) than they are comfortable with? And shouldn't that probability have to be larger than 58%, at least in a general case?

These are definitely more thoughts and ideas than they are hard and fast rules, so I'm happy for you to chime in and let me know where my analysis is wrong.

VW:If the original WVU cover probability is 55%, even attracting 70% of the money on WVU is still profitable for the book thanks to the juice. So, in order for them to rationally move the line one point, they need some combination of a ton of money on WVU and a significant difference in cover probability for WVU.But why would they settle for it being only "slightly profitable thanks to the juice"? If they are in that situation, and are aware of both those numbers, I see no reason why they wouldn't move the line.

I also think it's unrealistic to think that the books know exactly what % of a time a team is going to cover. IMO, after the line is initially released, the market is set a lot more by the actions of sharps than book's opinion on the games.

19:You are saying that if they are +8 in EV at the current line at 55%, why wouldn't they adjust there, rather than wait for EV to go negative? In which case, there is significantly less value than what I am indicating.Post a Comment