Millman on Placing Wagers Late

From Millman's latest column:

Bet early in the week and you are essentially betting against an oddsmaker who, with advice from some consultants and his staff, puts up what he considers to be the best number. Bet late in the week and you are betting against the collective IQ of hundreds of wise guys who pounded the value out of the number within the first 48 hours it was up. It's essentially like buying stock in Apple a week after the iPhone comes out, because you really want a chance to research it. Meanwhile, the pros on the Street made their money the first 24 hours and then cashed out.

Which I agree with for the most part. However, for the contrarian, the analogy fails. In the stock market, you don't have a bunch of people coming in and betting against the iPhone after it is released. If that were the case, you would create a market inefficiency between the true and perceived values of Apple. In the sports market, that inefficiency exists and can be leveraged if properly identified.

And that's why I believe contrarianism works. At least for now.

The Plan for 2009-10

Caution: very crude approximations ahead.

My long term winning percentage is around 53.5% in college football, pro football, and college basketball. Using Matchbook over the last two years, I am averaging about -105 on the juice on each bet. Using these approximations, it works out to a Kelly bet of about 3%, since I make many bets simultaneously (I used 10 for the approximation). I recognize that I should be adjusting each bet based on the juice I am getting, but I doubt I that I have exactly a 53.5% chance of winning each bet.

With the above extremely crude approximations, it doesn't make any sense to bet "full Kelly." In fact, I am pretty sure that my efficiency would be way down if I bet the approximate "full Kelly" on each game. So, my plan is to make each unit 0.5% of my Tuesday bankroll. Normal bets will be 3x (or 1.5%) plays and big bets will be 5x (2.5%) plays. Every once in a while, I will break out a personal max when I think the edge is large for 8x (4%), but those will be exceedingly rare. These will all be flat bet in the same manner as baseball was, even though I'm not playing bases ever again.

These will go into effect starting Thursday or Friday, depending if I play Boise or not. Speaking of which, below are my leans for CFB Week 1.

CFB Week 1 Leans
1015p Boise State -4 (Thu.)
8p Tulane +13.5 (Fri.)
12p Syracuse +6.5
10p California -21.5
1030p Washington +17
330p Memphis +16.5 (Sun.)

If this list seems much smaller than year's past, it is, and it is exhaustive. Overall, I am committed to being a bit tighter this year, and even moreso in Weeks 1-3, since I always get my ass handed to me at the beginning of the season, which I don't think is a function of bad luck and small sample size. I'm also putting more emphasis on playing games that are higher volume. That means mainly games featuring BCS teams and off-Saturday games. It seems to me that games that have more volume will have a bigger need to balance square vs. sharp action (when a contrarian angle exists), and therefore, more value on the anti-public side.

Future Win Totals Thinking

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.

Am I Getting Value?

The short answer, I think, is yes, mostly. The chart below illustrates that.




The column labeled "Avg Juice" takes the total amount of money I would have won on each team divided by the amount risked. The next two columns are each team's third order wins and losses. The penultimate column is third order winning percentage and the last column converts that winning percentage into Vegas Odds. In the last column, green means I have been consistently getting better odds than the third order record would suggest, while red is the opposite. (UPDATE: Per request, I put my +/- units in the last column) I only looked at teams I've bet on more than 5 times, and I didn't control for statistical significance in the color coding.

What I find most interesting is that three of the four teams that have taken most of my money are the teams that I haven't been getting better than third order juice on my wagers (with statistical significance issues lingering, particularly with Washington). My initial inclination was that these teams were underperforming, and that I would have at least been getting value recently as their juice should have increased. To test this, I looked at the time series of Washington's juice over the season. The trend was not significant. Same with Oakland.

I'm not entirely sure what this means, other than I have likely been betting on Washington (n=34) and Oakland (n=25) too much, when they don't actually have value. Of course, my other bets are not necessarily +EV because I didn't look at pitching matchups, etc. Particularly because of pitching matchups, I would expect a positive bias to these results, since in Contrarianville, we often bet on the "wrong" side of pitching mismatches. Still, overall, I'm happy with these results.

(UPDATE2: Going off ilike#s comment, here are two graphs comparing the "value" and my unit profit. They show a weak positive correlation.)

Reading Material

One of the things I plan to do while I'm not gambling is... read about gambling. Sports gambling has taken a more academic flavor over the last several years. I've already documented some articles here, but since I plan on using the Googles effectively, I'll link to papers that I think are worthwhile to the mathematically inclined in this post. I'll be updating sporadically and infrequently.

Brandes Inst. - Non-techinical lit review. If you aren't good at the maths, just read this one
Levitt (2004) - Explains why contrarians often bet on dogs
Dare (2006) - Explains why sports betting is a poor investment using Kelly criterion
Fair and Oster (2005) - The books know more than anyone else
Paul and Weinbach (2007) - Follow up to Levitt (2004) using "real" data
Woodland and Woodland (2000) - Weak evidence for betting against winning streaks
Sapra (2008) - Wager against last year's "out of nowhere" teams in the NFL
Paul and Weinbach (2008) - Early forward line movement for dogs is profitable in bases

Abstract for you NBA bettors:

Price Setting in the NBA Gambling Market: Tests of the Levitt Model of Sportsbook Behavior

Levitt (2004) suggested that sportsbooks do not set prices in the NFL to clear markets, as was commonly assumed, but set prices to maximize profits. This paper uses actual betting data from four sportsbooks to test the Levitt (2004) hypothesis in the NBA. For a sample of the 2004-05 to 2006-07 seasons, it is shown that favorites receive a disproportionate share of NBA pointspread bets. In addition, the percentage of bets the favorite receives increases with each additional point of the pointspread. In the totals market, it is shown that overs receive a much higher percentage of bets compared to unders and the percentage bet on the over increases with each point of the total. Unlike the NFL, however, taking a contrarian position and betting against public sentiment is not found to win more often than implied by efficiency.

My basic commentary on all of these articles is that the markets are slightly inefficient, as we've already hypothesized. A simple system is not going to cut it to beat the books, which all of these papers have shown. There obviously is something to thinly slicing lines, if you assume we have enough knowledge about the sports we wager on to find bait lines. I would also suggest that the Paul and Weinbach (2007) paper shows that the betting percentages we all use may have more value than we currently attribute to them. Combining the two strategies in an intelligent and as yet undiscovered way will likely yield the best results.

I'll be away most of the weekend, so feel free to tell me why I'm an idiot and I'll likely agree with you on Sunday night.

A Clarification

I should point out, from the post this morning, I think #1 is mainly responsible for the stuffy 2008-09. That doesn't mean that given the wealth of data available (records, units played, Wagerline, passes), I shouldn't do a post analysis on my results and attempt to find inefficiencies.

Streak for the Cash
10p Sacramento vs. Memphis
Current Streak: 0

Basically playing HCA here, since Sactown is a 3 point favorite. Whatever, we're playing for pride at this point anyway.

Looking at Time Series, Part 2

In part one, I looked at time series analyses of my 2008-09 college gambling results and it wasn't pretty.

Tonight, I'm going to look at 2007-08, since most of my contrarian thoughts were forged during that period and, conveniently, I have statistics for them.

The graph from the 07-08 NCAAB season is shown below. It has an uptrend (that'd be nice), so I'm probably going to have to look at the first differences.



Now here is an interesting result. At first glance, it almost looks like a random walk again.

Type Coef SE Coef T P
AR 1 0.9881 0.0156 63.18 0.000
Constant 0.2549 0.1641 1.55 0.122
Mean 21.34 13.74

But, remember, I said I have to look at the first differences because of the upward trend. Here is the time series analysis on the first differences.

Type Coef SE Coef T P
AR 1 0.1142 0.0631 1.81 0.071
Constant 0.1444 0.1532 0.94 0.347

The constant term is not statistically significant, which kind of sucks. If it were significant, it would indicate skill. Regardless, the AR1 coefficient is marginally significant. I'm not sure if that really means there was predictive ability in 2007-08, but at least it shows statistically that I was more likely to win the game after a win (and lose after a loss).

The college football season from 2007-08 also had a positive trend (below), so a similar analysis will need to be completed on the first differences.



For the 2007-08 NCAAF data, the trend was so severe, the time series program died before converging, so we'll have to go straight to the first differences.

Type Coef SE Coef T P
AR 1 0.0203 0.0838 0.24 0.809
Constant 0.4808 0.2598 1.85 0.066

This is what I wanted to see all along. The AR1 term for the first differences is very close to zero and the constant term is positive and statistically significant. Basically, that is saying that each bet was totally independent and had an expected outcome of 0.5x. Statistical skill, finally.

For completeness, I suppose I should look at 2008-09 college football from Week 3 forward. Intelligently, I didn't even play the NCAAF in Week 2.



Not much change from the original.

Type Coef SE Coef T P
AR 1 0.0095 0.0856 0.11 0.912
Constant 0.5586 0.2693 2.07 0.040

No real change in time series statistics either. Hooray. One good season in the last six.

Clearly, I think the results show I had some skill in 2007-08. Whether that is attributed to blind luck, a different gambling market, or strategy changes causing a decline in my abilities, I'm not sure. Since it seems that contrarians in general have records that are worse this year overall compared to last, I'm hopeful, but not convinced, that 2008-09 is just a hiccup on the path to success.

Looking at Time Series Analysis of am19psu's Results

Well, I went ahead and downloaded Minitab so I could do some ARIMA modeling of my data. I have to admit, the preliminary results are a little disheartening. One thing to keep in mind is that the strategy is ever-evolving, so the results here may not have come from the same distribution, but I doubt that is playing much of a factor.

As you recall, the figure below shows my results through March 1st for 2008-09 basketball season.



I used disheartening above because when I did the time series analysis I came up with this:

Type Coef SECoef T P
AR 1 0.9712 0.0158 61.46 0.000
Constant 0.0645 0.1481 0.44 0.664
Mean 2.235 5.133

Basically, what that means is that my results are a random walk. The AR1 coefficient is the coefficient of the serial correlation term with p-value 0.000 and the constant is not significant (with p-value 0.664). Note that the coefficient is near 1. If it were exactly 1, it would be a true random walk. This pattern is one that is destined to fail over time. It's even been called gambler's ruin.

This result has many names: the level-crossing phenomenon, recurrence or the gambler's ruin. The reason for the last name is as follows: if you are a gambler with a finite amount of money playing a fair game against a bank with an infinite amount of money, you will surely lose.

And in general, we're not even playing a fair game because of juice.

This graph shows the results from 2008-09 college football.



The time series analysis for this sucks even worse.

Type Coef SE Coef T P
AR 1 0.9382 0.0300 31.26 0.000
Constant -0.8430 0.1800 -4.68 0.000
Mean -13.636 2.912

In this particular example, the AR1 term is a bit farther away from 1, meaning it is likely not a random walk, but the constant term is negative. That means I am a loser when it comes to college football, at least in 2008-09. Not that I had any inclination of that from the sidebar.

The next figure shows my NCAAF results with the first two weeks left out. One of the things that I've considered is that contrarian gambling early in the season is not profitable. ML has told me stories about Squeeky cleaning up in college football early in a season, 2004 or 2005, I believe. However, I have not had any luck whatsoever. This graph doesn't necessarily support that hypothesis, but it is fair to say that I never got out of the hole I dug myself the first two weeks.



These results are much more indicative of what I want to see. With a coefficient of AR1 around 0.84 and positive constant, I am showing NCAAF to be profitable for 2008-09 after Week 2.

Type Coef SE Coef T P
AR 1 0.8451 0.0445 18.99 0.000
Constant 1.0931 0.1816 6.02 0.000
Mean 7.056 1.173

Whew. At least, debatably, I'm not completely retarded. That said, when I look at the first differences, the p-value of AR1 is not statistically significant, so it is still possible that results are a random walk.

I'm not even going to look at the last two NFL seasons, since I readily admit I have no skill in that sport.

I'm not entirely sure what to make of these results, other than I have not been gambling skillfully in 2008-09. More questions and suggestions are always welcome in the comments.

In part two of this post, which will run Friday at 6PM, I'll look into my 2007-08 results.

Sportsbook Infallibility and Line Movement

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.

More Thoughts on Strategy

Here is something I wrote last week:

Like other gambling strategies, it will take commitment and intelligence to make it work properly, and not everyone will be able to get it, but those that do will make sports wagering an investment strategy or a job, not unlike poker. In my opinion, it's only a matter of time.

Here is something I wrote three months ago:

What makes me place a bet on one five-point dog receiving 38% of the action at Wagerline versus another? Subjectivity. One of those teams might be Ole Miss the other might be Fresno State. I feel like Ole Miss is an underrated football squad, so there is value in taking their side. The opposite is true of Fresno.

I've taken the subjectivity out of my gambling style. That whole post last week really was blowing sunshine up my ass. Think about it. There a lot of smart people out there who like sports. If it was as easy as looking at Wagerline and Pomeroy numbers, someone would have wrote a regression equation a while ago and made a killing.

Originally, when Moneyline started writing his posts about contrarian strategy, I thought they were a reaction to a crappy season and I had a lot of questions about why he would change a winning strategy. Then I looked to the right of my blog, and to the right of his blog, and the results in everyone's signatures at RMMB and realized, maybe this isn't a winning strategy. Not contrarianism, mind you, but my application of it.

In another post last week, I was starting to question myself:

What was I doing differently last year when my big plays were hitting at such an incredible clip? Is this really all variance?

Obviously, some of it is variance. Even contrarianism applied correctly has had a miserable year this year. But some of it is not letting my own ideas affect my judgment. Inherently, I know the books didn't set up Louisville -2.5 tonight to attract equal action. I don't need Wagerline or SIA to tell me that. Last year, I was doing a lot more of this kind of thinking than I was writing a bunch of numbers down on a sheet.

What does this mean for me? It probably means playing a lot less games. I've been playing a lot of games simply because their stats at Carib, SB, SportsInsights, etc. have looked good. No more. I'll still look at Wagerline and SIA to double check myself, but the first thing a game will have to pass is the sniff test.

Will this mean I miss out on some (a lot?) of contrarian plays, especially in hoops and baseball? Yup. I am willing to admit straight up that most of the time I don't know whether the books are setting a trap in the CAA or Sun Belt. A lot of those games will be falling off my card. Note that I passed YSU and Idaho tonight. They looked funny to me when I looked at the lines, especially Idaho +6 vs. USU, but do I really know the public's reaction to those lines? Not really.

The whole idea is to turn those red numbers green. Time will tell if this the right way or not.

Sports Gambling Strategy

From the post I linked earlier (question from The Blue Horseshoe):

2. am19psu .. why do you think there isnt any decent lit. on sports gaming while I alone have 30+ poker theory books

The obvious answer is it's a lot easier to beat a random donkey at poker than it is to beat a professionally run sports book. That said, some attention has been paid to it, both by gamblers and academics. However, I'm not sure a successful strategy has ever been developed. Certainly, nothing has ever been published with as much mainstream success as card counting in blackjack or "power poker" in Hold 'Em and other no limit games.

I've been of the opinion that VegasWatch and MoneyLine, and to a lesser extent myself, are at the forefront of publicly developing a sports wagering strategy that is quantitative and repeatable. Maybe I'm blowing a little bit too much sunshine up our tails, but I honestly believe we are laying the groundwork for some good analytical research. I know I am not going to find the answer because I am 27 and have a real job, but there are smart people with more time on their hands that are going to stumble across ML's site and start thinking.

Contrarian strategy isn't a new idea, but the ability to employ the concept is greater than ever. With the internet, there is a lot of information out there prior to games. Whether it is consensus information, quantitative predictions, like Pomeroy or Football Outsiders, line movement statistics or even message boards, everything the contrarian gambler could want is at our fingertips.

In the old days, you really had to know the sport you were wagering on to spot a trap line. Squeeky is an example of this type of gambler. When he was playing every sport, he knew intuitively when the books were trying to attract action to a certain side. And this is still true. I can spot a good deal of the trap lines the books set in college football. But now I have a way to back up my ideas quantitatively. Before the internet, unless you knew a bookie, you couldn't get that kind of knowledge. And even then, you couldn't publish literature telling people to befriend a bookie.

Who knows, maybe we'll all end up going broke before we become truly successful, but I'm guessing that somebody, maybe (probably?) not us, figures it out. It's not going to be easy to learn how to do. Like other gambling strategies, it will take commitment and intelligence to make it work properly, and not everyone will be able to get it, but those that do will make sports wagering an investment strategy or a job, not unlike poker. In my opinion, it's only a matter of time.

Of course, even if we or somebody else figures it out, there will be the question of whether people will be allowed to use it. I tend to think they will, at least at small limits. This is unlike card counting in blackjack, where the events being bet on are less dependent on one another. A good card counter can clean out the house in blackjack. With sports gambling, by taking the anti-public side, contrarians are providing a kind of insurance to the risk and variance the books take on by setting a trap line. If people are betting 10 dimes a game and becoming a consistent winner, it wouldn't shock me to see books turn away their business, but at smaller limits, I wouldn't be surprised if books welcomed the contrarian's action.

This post has been more of a stream of thoughts based off The Blue Horseshoe's question, but it is obviously something I've thought about before. I guess the future will tell whether I am full of crap or forseeing where this is heading.

Worth A Read

I don't necessarily agree with all of it, and most of you have already read it, but this is worth a read (including the comments).

Picks up shortly.

More Reading

I'm bored tonight. I decided to look through some of the Wizard of Odds sports betting information, at first to see how it compared to my analysis of 2008 NFL lines. While I was there, I found some other information. Most of this is old hat to most of the people reading this blog, but I thought I would put it out there anyway.

The Power of the Dog
Teasers are Bad
Vegas has covered this more, but Futures are Garbage, too

A well timed post by Sham over at RMMB goes a bit more in-depth than either the WoO or I did in describing the Home Dog Effect.

How Contrarian was the 2008 NFL Season?

Not fucking very, I'll tell you that much.

If you recall, about a month ago, I looked at how win probabilities were spread across different bins of Wagerline percentages for the entire college football season. The results were a lot more cut and dried there. Remember, for each graph, it is the amount of action and win percentage received by the favorite.

For example, if the 53-54 bin has the following record: 8-4-0 0.667, that means that the aggregate of all favorites that received between 52.5 and 54.49% of the action at Wagerline won two-thirds of their twelve games.

Below are the results for all games and some selected discriminators. Red (Green) text indicates results that would be bad (good) for a contrarian. Yellow highlighted boxes show something that I found interesting.



Wow, you think the NFL market was efficient this year? Can't get much more efficient than that.

As a whole, if you weren't betting on the most contrarian sides, favorites receiving less than 40% and dogs receiving less than 30%, you weren't profiting this year, unless you had other strategies. I think one of the things that helped me to my demise this year is that 69-70 bin, where I would imagine I played close to every game.

Home Favorites

Road Favorites

For a while now, it's been touted that in the NFL, home dogs are generally a safe wagering option. Guess who figured that out and changed the market? This year, home favorites had a losing record. On top of that, almost 70% of the games played had a home favorite. So, if you were playing road dogs, opposite of what you would expect, you would have been profitable, barely, at 53.1%. For the road dogs, it was once again the extreme events where the most value was to be found.

When the road team was favored, there was hardly any profitable angle at all. Home anti-public dogs (getting less than 35%) went a miserable 14-16-1 this year. That area is where a lot of money can be made in college, but in the pros, it was worthless.

Spread = 1

Spread between 1.5 and 4.5

Spread between 5 and 7.5

Spread between 8 and 13.5

Spread 14 or Greater

I opted to bin the spreads differently for this exercise. There seemed to be a lot of one point spreads in the NFL this year, and I wanted to capture that. From there, I split them up so the lines were roughly indicative of field goal, touchdown, 10 point and two touchdown lines.

There were two places where I think real money could have been made this year. The first is the anti-public favorite when the spread was one. Up through 54%, anti-pub chalk was 15-6-1. If your personal cutoff was 52%, that rose to 15-3-1. Beyond that, just about every other aggregate was garbage in the NFL this year. The other place that money was to be made was with big dogs, regardless of spread. Old time gamblers bet any line greater than 14 on principle (or so I am told, I don't actually know any old time gamblers). The final table shows that was profitable, at least for this year.

So what does this tell me? First, there is no easy way to beat the system in the NFL. Second, you need more than consensus numbers to make intelligent decisions, whether it's intuition or some other metric. I'd be interested to see somebody take the spreads and see how something like Football Outsiders does ATS. Third, this is my third losing NFL season in a row. I am considering hanging it up in the pros. Why bother if there is no angle? When somebody like Moneyline can't turn a decent profit, why cause myself the aggravation? I will likely stick it out one more year to try to get better, but if results like this come back next year, I'll be happy to watch the NFL for pleasure in 2010.

I should point out that I think this year was particularly bad to contrarians, though I have neither the time nor patience to go back and compile previous years' statistics. Feel free to do so on your own and let me know what you find.

Are the Playoffs Different than the Regular Season?

After posting my leans yesterday, a decent discussion started in the comments. The Saw thought it was interesting that all of my leans were favorites. I responded by saying this:

I feel very uncomfortable with it. Here is a thought experiment I might post about:

Premises:
1. NFL playoff games generate more action than any other game all year, leading up to the Super Bowl

2. Books will be less willing to expose themselves with such large action, i.e. happier to take the rake versus setting trap lines.

If those are true, then I would conclude there is more value available on a split action dog, since the books know that favorites attract more action by nature.

That said, I have a hard time believing that Ten -3 and especially Car -9.5 were set to attract split action.

I'm happy to hear other opinions on it, though.

I think what I wrote here is generally true (see e.g. Super Bowl XLII line). However, Moneyline pointed out that the opposite can also be true:

I like your list. If forced to decide right now, Tenny would be my only play.

Try thinking of the Tennessee line this way:

Let's say that the books know, based on all the info that they undoubtedly possess, that Baltimore as underdog is going to be much more attractive to bettors than Tennessee as a favorite.

They don't want to be exposed in this big of a spot, so what do they do?

They shrink the price on Tennessee to increase the # of dollars that are wagered on the Titans.

I'm not saying that is definitely what is happening in this case, but it is certainly possible.

It is not unreasonable to think that the "true" line for this game is somewhere between Tenny -3.5 and Tenny -4.5

Eric had his own ideas:

ML, I remember reading something you wrote about the divisional rounds last year that really stuck with me. It boiled down to:

-People were used to betting on 'good' teams against 'bad' teams all year.

-Divisional playoffs normally pit two well regarded teams against each other.

-Public sides with taking the points because both teams are perceived as 'good' (equal).

Maybe there's little chance for the oddsmakers to avoid that bias.

*Also thinking out loud*

So, the hard part is figuring out which side the public will like more. That's always our problem, and the playoffs only compound the problem. I think each line needs to be scrutinized harder in the playoffs to find the angle. For example, listening to what people around the water cooler are saying, what Peter King writes, or what the Gay One and the Dumb One say on ESPN Radio.

A side conversation came up as well. The Saw said:

I certainly don't know the inside workings of books, but the more I thought about it, I think the books setting up trap lines makes more sense in these situations. Yeah they may lose more money over the course of one weekend or a playoff season, but over the course of many seasons wouldn't the books make more by taking a stand against public teams?

Jonny came up with one explanation:

the problem is that books can't set traps whenever they want. Sometimes there is no situation for them to exploit(or it is too small) and they receive a higher expected value keeping the split as small as possible.

I thought something different. Ordinarily, I would agree with The Saw. But in games with such heavy action, the risk involved with setting a trap line would outweigh the +EV. I think. That's at least my rationale for the thoughts above. I'm sure whichever side I choose will be wrong anyway, so all of this will be moot.

Coming later tonight: picks, obviously, and a look at the 2008 NFL regular season.

2008 NFL Line Movement

As you can see to the right, I was absolute chicken garbage wagering on the NFL this year. Which is par for the course. I am always straight up awful the first third of the season. It didn't help this year that the second third of the season was as square as it comes. Just for grins, here are the results for all of my leans this year.



Like I said, chicken garbage. If you recall, I looked at college football line movement a few weeks ago. When looking at the graph below, remember that it is tabulated using only my Tuesday leans from the year. Again, though, I think this is the relevant sample that, at least, I should be looking at. At first glance, the hypothesis that reverse (negative) line movement is good for the contrarian gambler looks decent. When interpreting the results, you should compare what my overall record was (terrible) compared to the winning percentage of lines with reverse movement (marginal).



Unlike college football, in the NFL, the magnitude of the reverse movement doesn't appear to be all that significant.



Also, in the NFL, there are far less lines that move throughout the week than there are in college football, which shouldn't be much of a surprise since teams are much more evenly matched and more about each team is known.

As always, feel free to tell me what a retard I am in the comments.

NCAAF Line Movement Revisited

After Moneyline and I had our discussion about line movement this week, I thought I would update the NCAA statistics. I plan on putting the NFL line movement and contrarian stats together after I get back from the Rose Bowl. Here is the first table:


Recall, that these stats have been compiled from my list of Tuesday leans (Early) and what line the games closed at (Close). The blue indicates the record for the games I actually played.

Moneyline and Vegas have been hinting for a while that line movement scares them away from plays. An initial glance at the table seems to indicate that they are correct in their assessment. However, I remain convinced that reverse (or negative above) line movement remains a solid indicator that a wager should be made.


If the negative line movement was 0.5 or 1 points, then yes, playing those games during the 2008 college football season was a losing proposition (See how I subtly reminded the readers of the sample? That's how you get a Lemmy!). Those games were 29-39 at close. However, if you used games that moved 1.5 points or more, suddenly reverse line movement was a great way of pointing you in the right direction.

Obviously, more extensive research needs to be conducted. I'm particularly interested to see if the NFL, where lines move less often and at a smaller magnitude, shows a similar pattern. Regardless, this is one sport for one season. However, my empirical evidence over the last three years of gambling makes me think that these statistics will be replicated.

Feel free to tell me where I screwed up in the comments.

EDIT: I figured I would throw these together just for completeness. This also seems to follow what I had already thought about positive (or forward) line movement:



It doesn't look there is much +EV for games where the line moves in a contrarian's favor.

How Contrarian Was College Football Season?

The research project I mentioned on Saturday night is a quantitative assessment of the contrarian-ness* of the college football season. There are some huge caveats here. One is, of course, sample size. The second is the binning of Wagerline percentages. Different ways of binning will yield different results.

I think this last caveat is most important. While people like myself, Vegaswatch, Jonny, and Moneyline are attempting to make sports wagering a quantitative exercise, quite obviously there is a lot of subjectivity involved. What makes me place a bet on one five-point dog receiving 38% of the action at Wagerline versus another? Subjectivity. One of those teams might be Ole Miss the other might be Fresno State. I feel like Ole Miss is an underrated football squad, so there is value in taking their side. The opposite is true of Fresno.

In the figure below, "Wagerline %" is the percent of Wagerline users who selected the FAVORITE. Therefore, a value of 39 indicates there is a public dog and a value of 75 indicates the favorite is extremely public. The record and winning percentage are again for the FAVORITES. Here are the results for all 684 Division 1 NCAA Football games that statistics were available for on Wagerline.



Here is a philosophical question. If we agree that contrarians generally bet on anti-public underdogs successfully, and that gambling markets are efficient, then shouldn't there be a way to exploit favorites? The answer could be yes or no. One possibility is that since we know that gamblers tend to bet on favorites, we need to relax our definition of an anti-public favorite. Perhaps 54% on a favorite constitutes being "anti-public," however we define it? The other option is that favorites cover slightly more across all "public" bins.

With the obvious small sample size caveat, I think that, in general, favorites getting less than 55% of the action at Wagerline are worth looking at. It also appears that contrarians using only Wagerline numbers did not do well until the percentages were greater than 68%.

Another factor that I consider when placing a bet is home field advantage. I think it is just anecdotal over the years, but I prefer to be on a home team than a road team. In the figures below, I've separated out the sides for home favorites and road favorites.

HOME FAVORITES

ROAD FAVORITES

EDIT: When you upload more than one image at a time to blogger, they come out in reverse order of the way you uploaded them. Also, proofread your posts before you put them out there for the world to see. Idiot.

In this case, "anti-public" home favorites are even better than an ordinary favorite. Likewise, "anti-public" home dogs (bottom image) are better than an ordinary underdog. While certainly not exhaustive, I think these statistics do show some evidence for home field advantage in football wagering.

Lastly, I looked to see if the percentages changed much given a larger spread. The following four tables show how winning percentages change among consensus numbers for spreads less than 3, between 3.5 and 7, between 7.5 and 14, and greater than 14.5

FAVORITE GIVING 3 OR LESS

FAVORITE GIVING BETWEEN 3.5 AND 7

FAVORITE GIVING BETWEEN 7.5 AND 14

FAVORITE GIVING MORE THAN 14

Because sample sizes start getting really small here, it is difficult to gain a lot of information, but I hypothesize that short "anti-public" favorites and moderate "anti-public" dogs were the most profitable bets to make.

EDIT: It would help if I had uploaded the images correctly. Long (>7 pts) "anti-public" favorites appear to be profitable. The part about moderate "anti-public" dogs still stands, though you can probably add short dogs to the list as well (<14 pts).

Feel free to draw your own conclusions from the data and put them in the comments below.

*I can make new words out of contrarian, too.

Totals

I've been wanting to add totals to my gambling repertoire for some time now. Two things have been keeping me from doing it: 1. early on, I was unwilling to dabble in a new (to me) gambling theory, and 2. by the time I wanted to, I was already deep in the hole. I'm obviously even deeper in the hole now, but I still feel like I am leaving profits on the table by not including them in my wagering strategy.

During the early parts of college basketball season, I will evaluate totals just as I would sides and keep record of them. I won't be posting them, but I will put the results up once I feel I've come to a reasonable conclusion as to whether they are worthwhile to me. This is important, because I plan on playing baseball this summer, and totals were extremely profitable to other contrarians last year during baseball season.

Stay tuned.

More Line Movement Stats

Jonny came up with a good idea for another stat to look at. He wanted to know what effect crossing a key number (3 or 7) had on the records. In this case, I started running into sample size issues. I didn't even bother running the stats for favorites because I play so few of them that results would be worthless. Results are posted below:

Nomenclature:

"7 Dog +" means the line moved from 6.5 or less to 7 or above.
"7 Dog -" means the line moved from 7.5 or more to 7 or below.
"3 Dog +" means the line moved from 2.5 or less to 3 or above
"3 Dog -" means the line moved from 3.5 or more to 3 or below.



I find it very interesting that even with the small sample size, it appears line movement around key numbers is a bad thing for contrarians, at least this season. Again, take this post with the usual caveats of where the sample came from, particularly in this case.

***********************************************

Yes, I am bored tonight. I put together some other relevant stats. First, a frequency distribution of line movement.



I am not at all surprised that this approaches a normal distribution (other nerds know this is due to the law of large numbers and the central limit theorem), but is left skewed, since I am trying to be on the sharp side of games. Note that this is just leans, so I am obviously preferentially picking out the sharp sides on Tuesdays. Which is some decent affirmation that record aside, I know what I am doing.

The other graph shows the record for all line movements. This is basically just expanding on Wednesday's post, but I thought somebody might be interested in it.



Not much really surprising here except for positive and negative line movements of one point. I don't have a good subjective reason for it, so I am just going to chalk it up to small sample size and variance.

If there are any other analyses that seem interesting and won't take an obscene amount of time, throw them in the comments and I'll see what I can do.