I've got time to put the full record update up since games don't start again until Thursday, so I figured I would add to this post from last week.
Since I figured out the expected wins of each team from the totals posted at BetUS, all I needed was a standard deviation to come up with a distribution of the probability of each team having a particular number of wins. I did this by using last year's totals and actual results to come up with a root mean squared error estimate of the standard deviation, which was around 2.16.
I'll let Jonny analyze each particular team, but I came up with an unexpected and almost assuredly erroneous result. The numbers show the expected number of teams that should go undefeated is 4.27.
There a couple of reasons that immediately spring to mind why this number is wrong. First off, my methodology could be wrong. I used a normal distribution to estimate probabilties for discrete data. While not terrible, it's still not good (for math geeks, this is analogous to using the trapezoidal rule for estimating integrals).
Also, it may not be a good idea to use a symmetric, normal distribution for totals that are 10, 11, or 12, since the tails of a normal distribution go to infinity and you are buttressing against the total possible number of wins.
Another reason would be that last year's RMSE is not representative of the true standard deviation of the distribution. The last thing that comes to mind is the books shading the lines high for the expected good teams, expecting to take a lot of over action.
To use a further example, last year Moneyline, when he was still running a blog, estimated USC's chances of going undefeated at 14.8% and their chances of one loss at 32.4%. Using this methodology, 2008 USC had a 31.3% chance of going undefeated and a 17.7% chance of one loss. Obviously, Moneyline's numbers are way closer to reality than these are.
There is quite a bit of room for improvement here, I'm just not sure where.
Showing posts with label props. Show all posts
Showing posts with label props. Show all posts
Future Win Totals Thinking
,
Labels:
2009 college football,
contrarianism,
props
Earlier today, Jonny approached me with a question regarding win totals for the upcoming college football season. BetUS has regular season win totals up for most of the major conference teams for 2009. I was asked to compute win expectancies based off the juice. It seems straightforward at first, but I made some assumptions along the way and I want to make sure they are right.
Here is the methodology: first, find the actual juice adjusted probabilties from each line by adjusting each outcome's odds to probabilties then dividing through each outcome's probability by the sum of the probabilities of the two outcomes.
Then, if the total is a whole number, multiply the over juice adjusted probability by the total plus one and the under juice adjusted probability by the total minus one. If the total is a half number, the procedure is the same, except instead of adding/subtracting by one, I added or subtracted by one-half. Two examples follow.
--------------------------------
Example 1.
Team A o10.5 -130/u10.5 +110
p(-130) = 1.3/2.3 = 56.52%
p(+110) = 1 - (1.1/2.1) = 45.73%
.5652 + .4573 = 1.0414
56.52%/1.0414 = 54.27%
45.73%/1.0414 = 45.73%
E(A) = 11*.5427 + 10*.4573 = 10.54 wins
Example 2.
Team B o10 -130/ u10 +110
E(B) 11*.5427 + 9*.4573 = 10.08 wins
---------------------------------
So, the assumptions I want to check are: the juice adjustment to the probabilities and the calculation of the win expectancies by adding one or one-half.
Obviously, one assumption is that the probability distribution is symmetric, which may not be valid for Florida (o/u 11), for example.
I decided on adding one or one-half because of my SftC experience with soccer odds. When calculating the probabilities for three outcomes (Team A, Team B, or Draw), they are proportional to the Team A pk/Team B pk odds. In other words, If Team A is 35% to win, Team B is 35% to win, and there is a 30% chance of a draw, the odds end up at Team A pk 50% and Team B pk 50%. So, by adding one or one-half, I am calculating the odds of the outcomes that can actually happen, since there is no push option.
The reason why I am questioning myself, beyond never really thinking about it before today, is because the cutoff point for moving a line is different if the total is an integer or a half-number. For a whole number, over -200/under +150 equals a quarter of an expected win. Any higher, and you would expect the book to move it.
---------------------------------
Example 3.
Team C o9 -200/u9 +150
p(-200) = 2/3 = 66.67%
p(+150) = 1- 1.5/2.5 = 40%
66.67%/1.0667 = 62.5%
40%/1.0667 = 37.5%
E(C) = 10*.625 + 8*.375 = 9.25
---------------------------------
If you do the same calculation for a half number line, you don't get to the value to move the line.
---------------------------------
Example 4
Team D o9.5 -200/u9.5 +150
E(D) = 10*.625 + 9*.375 = 9.625
---------------------------------
Obviously, the mathematical reason for this is the larger spread on the endpoints (8 and 10 vs. 9 and 10). But is this right? Should the books be more willing to move the total off an integer than a half-number?
I'm finding myself questioning this outcome, because I think win expectancy should be normally distributed, and therefore the same amount odds should persuade the book to move a number, whether the total is a whole number or a half number.
On the other hand, there is also the push factor that has to be thought about. By moving the line off a half-number, the book creates an opportunity for a push, which I assume would be an undesireable outcome. Does the math prove that or did I make a mistake somewhere? I assume the latter.
In any case, assuming the math is right, Jonny should have win expectancies posted on his blog sometime soon.
Here is the methodology: first, find the actual juice adjusted probabilties from each line by adjusting each outcome's odds to probabilties then dividing through each outcome's probability by the sum of the probabilities of the two outcomes.
Then, if the total is a whole number, multiply the over juice adjusted probability by the total plus one and the under juice adjusted probability by the total minus one. If the total is a half number, the procedure is the same, except instead of adding/subtracting by one, I added or subtracted by one-half. Two examples follow.
--------------------------------
Example 1.
Team A o10.5 -130/u10.5 +110
p(-130) = 1.3/2.3 = 56.52%
p(+110) = 1 - (1.1/2.1) = 45.73%
.5652 + .4573 = 1.0414
56.52%/1.0414 = 54.27%
45.73%/1.0414 = 45.73%
E(A) = 11*.5427 + 10*.4573 = 10.54 wins
Example 2.
Team B o10 -130/ u10 +110
E(B) 11*.5427 + 9*.4573 = 10.08 wins
---------------------------------
So, the assumptions I want to check are: the juice adjustment to the probabilities and the calculation of the win expectancies by adding one or one-half.
Obviously, one assumption is that the probability distribution is symmetric, which may not be valid for Florida (o/u 11), for example.
I decided on adding one or one-half because of my SftC experience with soccer odds. When calculating the probabilities for three outcomes (Team A, Team B, or Draw), they are proportional to the Team A pk/Team B pk odds. In other words, If Team A is 35% to win, Team B is 35% to win, and there is a 30% chance of a draw, the odds end up at Team A pk 50% and Team B pk 50%. So, by adding one or one-half, I am calculating the odds of the outcomes that can actually happen, since there is no push option.
The reason why I am questioning myself, beyond never really thinking about it before today, is because the cutoff point for moving a line is different if the total is an integer or a half-number. For a whole number, over -200/under +150 equals a quarter of an expected win. Any higher, and you would expect the book to move it.
---------------------------------
Example 3.
Team C o9 -200/u9 +150
p(-200) = 2/3 = 66.67%
p(+150) = 1- 1.5/2.5 = 40%
66.67%/1.0667 = 62.5%
40%/1.0667 = 37.5%
E(C) = 10*.625 + 8*.375 = 9.25
---------------------------------
If you do the same calculation for a half number line, you don't get to the value to move the line.
---------------------------------
Example 4
Team D o9.5 -200/u9.5 +150
E(D) = 10*.625 + 9*.375 = 9.625
---------------------------------
Obviously, the mathematical reason for this is the larger spread on the endpoints (8 and 10 vs. 9 and 10). But is this right? Should the books be more willing to move the total off an integer than a half-number?
I'm finding myself questioning this outcome, because I think win expectancy should be normally distributed, and therefore the same amount odds should persuade the book to move a number, whether the total is a whole number or a half number.
On the other hand, there is also the push factor that has to be thought about. By moving the line off a half-number, the book creates an opportunity for a push, which I assume would be an undesireable outcome. Does the math prove that or did I make a mistake somewhere? I assume the latter.
In any case, assuming the math is right, Jonny should have win expectancies posted on his blog sometime soon.
Super Sunday 2/1
,
Labels:
i'm a square,
ncaab week 6,
plays,
props,
super bowl,
waste of money
I guess people are realizing Duke is good again.
2p South Florida +2.5 +103 2x
Pass: Missouri State
Onto the Super Bowl. I hate to say it, but I like the Steelers in this game. All of the hype for Fitzgerald and Warner has actually pushed the non-betting general public to think the Cards are going to win straight up. At most other places, I'm seeing between 55-60% of the action coming in onChicago St. Louis Phoenix Arizona.
620p Pittsburgh -6.5 -104 3x
It wouldn't be the Super Bowl without props either. Matchbook doesn't have a great prop market, but I think I found some lines with value. When I'm out 8 units at the end of the day, everyone can laugh at me.
James O39.5 Rushing Yards +110 1.82x to win 2x
Each Team Scores >14 - No +142 1.41x to win 2x
Fitzgerald U82.5 Receiving Yards +170 1.18x to win 2x - That price is a bit ridiculous
Warner U235 Passing Yards +174 1.15x to win 2x
For the record, +175 equals a break even probability of 36%. Fitzgerald was less than 82.5 yards 9/16 or 56% of regular season games. If you include playoffs, it was still 9/19 or 47% of games. I'm getting good value there.
Warner on the other hand, not so much. There were only 3/16 regular season games where he was less than 235 and one he had exactly 235, so that works out to a probability of 22%. Not good value. I wish I had thought to do these calculations before I placed the bets.
The other two props don't really have a good way of determining the probability. James was non-existent down the stretch for the Cards, but has been getting the bulk of the carries in the post-season. For the team totals prop, I don't think you can really look at it other than to see how many games the Steelers held their opponent under 14 this year. The Steelers did that half the time. So, there might be value in +142, which equals a break even probability of 42%.
Good luck with whatever you choose to play tonight.
2p South Florida +2.5 +103 2x
Pass: Missouri State
Onto the Super Bowl. I hate to say it, but I like the Steelers in this game. All of the hype for Fitzgerald and Warner has actually pushed the non-betting general public to think the Cards are going to win straight up. At most other places, I'm seeing between 55-60% of the action coming in on
620p Pittsburgh -6.5 -104 3x
It wouldn't be the Super Bowl without props either. Matchbook doesn't have a great prop market, but I think I found some lines with value. When I'm out 8 units at the end of the day, everyone can laugh at me.
James O39.5 Rushing Yards +110 1.82x to win 2x
Each Team Scores >14 - No +142 1.41x to win 2x
Fitzgerald U82.5 Receiving Yards +170 1.18x to win 2x - That price is a bit ridiculous
Warner U235 Passing Yards +174 1.15x to win 2x
For the record, +175 equals a break even probability of 36%. Fitzgerald was less than 82.5 yards 9/16 or 56% of regular season games. If you include playoffs, it was still 9/19 or 47% of games. I'm getting good value there.
Warner on the other hand, not so much. There were only 3/16 regular season games where he was less than 235 and one he had exactly 235, so that works out to a probability of 22%. Not good value. I wish I had thought to do these calculations before I placed the bets.
The other two props don't really have a good way of determining the probability. James was non-existent down the stretch for the Cards, but has been getting the bulk of the carries in the post-season. For the team totals prop, I don't think you can really look at it other than to see how many games the Steelers held their opponent under 14 this year. The Steelers did that half the time. So, there might be value in +142, which equals a break even probability of 42%.
Good luck with whatever you choose to play tonight.
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