What happens in Vegas stays in Vegas, and in most cases that means your money. It’s hard to beat the house. These casinos, bookies, and online sportsbooks hire Ivy League-educated statisticians and make preliminary lines through the use of some of the most profitable and experienced gamblers in the world. Winning in Vegas is no easy feat, but that doesn’t mean it can’t be done.
Lines are created by getting the same amount of action on both sides. A spread or line isn’t necessarily the best indicator of the outcome of a game. It just shows where the sportsbooks could get the least amount of exposure, by getting the same amount of money on both sides of the bet, so that they can simply take profit off the juice with no risk.
I think most of you out there know what I mean when I say “the juice,” but for those of you who have never placed a bet or just never cared to find out how it works, when you make a spread bet, it is basically considered even money, but not quite. You put down $110 to win $100 depending on the bet. If the Casino can get all the bets to cancel out they will profit on the fact that you paid $110 to win $100. The losers will pay the winners, and the Casino will collect the rest. That is the ideal situation for the casino, and they make their lines and spreads based on that, not necessarily what the score will be or how likely it is that a team will win. The spreads reflect the prevailing wisdom of the gamblers placing the bets, and often times that means big-time experienced gamblers who have inside information as well as in-depth statistical analysis. So the lines might still be tough to beat, especially since you have to be right enough to overcome the handicap that the casino has placed on you--which of course is that pesky juice.
That being said, there are several games in which the prevailing wisdom comes from the dumb public rather than brainy professionals. This happens in popular games, where the amateurs flood the spoortsbooks, such as the Super Bowl, Football Playoffs, World Series, March Madness etc. These are perfects chances for one to put their money down. That is, of course, if you feel you’ve done your research and know the outcome better than the spread.
So you’ve found a bet you like, and you feel you have an edge. Well, there is a bit more to betting than just having an edge. You must decide how much of an edge you have, and subsequently how much you should risk, and that is where Kelly comes in. This is one lucky lady you want blowing on your dice, if you know what I mean. The Kelly Criterion is a mathematical formula that is used by gamblers, as wells as big name investors such as Warren Buffet and Bill Gross. This is an essential part to both investing and gambling. The formula will tell you how much of your bankroll to risk on a given wager or investment.
where
* f* is the fraction of the current bankroll to wager;
* b is the net odds received on the wager (that is, odds are usually quoted as "b to 1")
* p is the probability of winning;
* q is the probability of losing, which is 1 − p.
Here is the formula. Use it as your guide. Let me break it down for those you who are less mathematically inclined. You take the odds that you are given from the sportsbooks (e.g. Raiders 14 to 1 to win the division)--that is your b. Then multiply that by the chance you think your team has of winning (e.g. 10%)--p. Then subtract from that the chance that they won’t win the division (90%). And finally divide that by b again which of course is 14 to 1. So that is
(14 X 1) = 1.4 - 0.9 = .5/14= .0357.
This formula has concluded that if you believe that the Raiders have a 10% chance of winning the division and you are getting 14 to 1 odds, then you should risk 3.57% of your bankroll on that chance.
I know what you’re thinking. Where did you get 10%? That seems like a bit of an arbitrary number. Well that is true. It is arbitrary. In fact the hardest part of applying the Kelly Formula is determining what percent chance you feel that team has of winning the bet. You can use statistics to determine this number, or simply place a number out there based on the intuition that comes with a vast accumulation of sports knowledge. Here are a few more example bets.
Baseball Prospectus, an organization devoted to in-depth statistical baseball analysis, runs a Monte Carlo simulation (a successful algorithm-based predictor of random events that has been proven to be wildly successful in the areas of space, oil exploration, and physics) on the rest of the baseball season. It simulates the season from where it is now over a million times, and then spits out the percentage chance that every team will win their division, make the playoffs, and get the wild card. As of August 24, 2009, the Rockies are given a 22% chance to win the NL West. There you have it. If you trust Baseball Prospectus and their statistical method than you have a percentage. You have been given p and q : p=.22 and q=.78. The odds as of August 24, 2009 for the Rockies to overtake the Dodgers and win that division are 13/2 or 6.5 to1. That is your b, and now you have all three variables. Simply plug them into the formula.
[(6.5 X .22) - .78]/6.5 = .1 or 10%.
This means that you should bet 10% of your bankroll on the Colorado Rockies to win the NL west.
Now understand that this doesn’t mean that you think that the Colorado Rockies will win the Division. Most likely they will not win the division. We established this when we gave them a 22% chance of winning the division. But if they do win, it will be worth it. This bet has good value, especially given that fact that the Rockies are only three and a half games back. Now to some of you this might make perfect sense, but to others you might be wondering what I mean by good value. If I think the Rockies most likely won’t win the division, why bet on them? This is because if they do win you get paid six and a half times your money.
This brings about another betting principle which I’m sure many of you are familiar with: Expected Value. If we decided to bet on the flip of a coin, and gave each other 1:1 odds, then neither of us would expect a positive or negative expected value. Although the winnings might fluctuate, over the long run we would break even. Now let’s say I now get 2:1 odds every time the coin comes up heads. This is a great deal for me, because I will get two dollars every time it’s heads, but only pay out one dollar when it comes out tails, and yet the outcomes have the exact same chance of coming up.
You have a positive expected value of $.50. That means that on average every time you make that bet you make $.50. Why $.50? When you flip the coin the first time it comes up heads and you win two dollars. When it comes up tails you lose one dollar. So after two bets on average you can to expect to have won once and lost once because the chances are 50/50. Therefore you will have won two dollars and lost one dollar giving you a profit of one dollar over the course of two bets for an average of $0.50 per bet, and there is your expected value. It doesn’t take a genius to figure out that I will soon start to profit. Now the odds of the coin coming up heads didn’t change any, and it doesn’t matter. They don’t have to. I am simply getting paid more than I should, for the likelihood of my success. That is great value.
Now let us look at this Colorado Rockies bet. If the season were played out 100 different times the Rockies would win 22 of those times. For those 22 times that it does happen you make 6.5 times your money. So if we apply this to the same logic we used with the coin, we can see that it works in the same way. If I bet one dollar and win $6.50 every time I win, and I win 22 out of 100 times then I will take in $143. I will, however be expected to lose 78 times. So I can expect to lose $78 at one dollar per loss. This leaves me with a net of $65. I have made the bet 100 times. So on average I can expect to make $65/100, which is $.65. So every time I make this bet for $1 I can expect to win $.65. So it’s worth it.
This same principle can be illustrated in a more drastic example. If someone told you that if you paid them a $100 they could make sure your lottery ticket got put in a vault with five other tickets and then the winner would be drawn out of those five, I think you would do it in a heartbeat. The chances that you win the lottery are still less than likely. You only have a 20% chance. In all likelihood you will have lost $100 dollars, but if you do win, you will get so much more than you put up that it will be worth it. That is why it is crucial to look for value.
Here is another good value divisional bet. The Minnesota twins are given a 21percent chance to win their division by Baseball Prospectus. Once again we are using their Monte Carlo Simulation. The odds for them to win are 10 to one. That is a one in 11 chance or 9.1 percent. All you have to do is believe that the Minnesota Twins have more than a 9 percent chance of winning their division and you have found yourself a good bet. Now it is time to implement the Kelly formula to find out how much of your bankroll you should risk. In this case, b=10, p=.21, q=.79. So
[10(.21)-.79]/10 = .13 or 13 percent.
You should risk 13 percent of your bankroll on the Twins winning their division. Now notice that is not a lot of your bankroll, and once again we know that they most likely won’t win the division, but if you make enough of these good value bets it will pay off in the long run.
The Kelly system already takes into account the expected value. If there isn’t a positive expected value it will give you a negative number. That is to say, if you plug in the numbers to the formula and the result is a negative number, you shouldn’t make the bet at all. Simply follow the formula and you should be fine.
The creators of the Kelly formula found that although the formula creates the highest return on investment it is far more volatile than a sometimes-preferred method called Half Kelly. Half Kelly takes the Kelly percentage and splits it in half. This has been shown a tad--3/4--less effective than the Kelly System but far less volatile, so if you consider yourself to be more risk averse than perhaps using the Half Kelly would be better.
So if you are indeed more risk averse and you want to implement half Kelly, then you would bet 5 percent of your bankroll on the Colorado Rockies to win the NL West, and 6.5 percent of your bankroll on the Minnesota Twins to win the AL Central. It seems much safer now. Doesn’t it?
There is more to betting than meets the eye. So if you feel that Lady Luck is against you, it might be time to turn to Lady Kelly.
(This was originally written in the summer of 2009 and posted on my discontinued blog sportscohorts.com. The Raiders and Rockies turned out to be losing bets, but as history shows the Minnesota Twins Miraculously won the AL Central in 2009. The 10 to 1 pay out would have easily covered the losses of the other two bets, and left the bettor with a tidy profit. Now that's what I call value!)
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