***** VARYING WAGER AMOUNTS *****
E = W - ((1 - W) / O)
If you ever want to truly maximize your bankroll, you simply must get in touch with "E". "E" is the result of the above formula, which is arguably the most important mathematical formula available for the purpose of bankroll management. In this case:
E = Edge (optimal wager as a percentage of your bankroll)
W = Winning percentage
O = Odds (in decimal form)
For example, let's say you start the NFL season with $1,000. Let's say you just know that you will hit 55% of your plays this year. Based on betting all -110 point spreads, the formula would grade out as follows:
E = [0.055] (5.5%)
W = [0.55] (55%)
O = [0.90909] (10/11)
[0.55] - ((1 - [0.55]) / [0.90909]) = [0.055]
0.055 is equal to 5.5%. Therefore, if you want to bet the same amount on each game, you start with $1,000 and you are absolutely sure that you will hit 55% of your games, you will maximize your bankroll by wagering 5.5% of your bankroll (or a starting number of $55) on each game.
There are some flaws to this formula. First of all, NFL games are not bet sequentially. That is, most people have more than one game going at the same time. This formula is meant to be used with only one wager in action at a time so the bankroll number can be adjusted before each bet. In addition, nobody *really* knows what percentage they are going to hit in a given year. If you happen to be off by a few percentage points, the results can be destructive. In addition, it is better for most gamblers' mental health to keep wager amounts relatively standard or on a unit system rather than recalculating minute percentages with each play. Wagering $58.54 on a game just doesn't have the panache of wagering $50.
What I do like about this formula, however, is that it concretely shows that if you are serious about making money on sports, adjusting your wager to your winning percentage is a good idea. It is this concept which leads to the topic of varying one's bet size to determine the optimal "E" value for each wager.
Though nobody likes to use the "L" word, everyone has a few games a year that they feel are "locks". Not locks in the tout sense of the word but at least very very strong plays. Unless you are a long time handicapper it is a tough feeling to describe but there are certain times when you feel so confident that you just know that you are going to destroy your book on a certain play.
Human nature dictates that you will want to load up on that one play. Easy money. How can you pass it up? You are not so much *wagering* $1000, you are simply *taking* $1000 from the book because there is no way on earth this game will lose.
I have had that feeling many times, and of course, it does not always guarantee a winner. But I would modestly say that it hits more than it missed by a good margin. The hard part is not so much pinpointing these games, as those feelings will come naturally. The hard part is playing your bankroll right to hit the winners hardest and increase your bankroll.
Where should the line between aggressiveness and foolishness be drawn? If a player has a unit value system between 1 and 5 that is used regularly, that seems a bit odd. How can one play in the same sport warrant five times as much action as another play? A loss on the five unit play would seem to be absolutely devastating. In that case a 5-1 ATS record could still result in a small loss.
If you look at the above formula, though, maybe it is not so odd. I think everyone would agree that if they played less action, that they could hit a higher percentage. That would logically be true. That is not to say that everyone should play less action. If you make a profit on plays 3-7 each day as well as plays 1-2, then keep playing seven games per day. But most people probably feel that if they only played plays 1-2, then their percentage will be higher.
So what would it take to warrant a 5 unit play? If you hit 55% on your average one unit play, then a five unit play would require an E = 0.275. E=0.055 (5.5% of bankroll) when hitting 55%, so a five unit play would have to have you theoretically wagering 27.5% of your bankroll.
Plug in E=0.275 into the formula, we come up with a W (winning %) = 65.5%. For a reference, if you entered the Hilton contest and hit 65.5%, you would have won 3rd place last year. Certainly that means that 65.5% can be done. In fact, it can even be done by wagering the 85 games in one year that the Hilton contest requires.
It is not going to happen year after year, though. The 1999 Hilton contest winner, Russell Culver, went a mediocre 42-43 in this year's contest. Now, it is true that many tout services reportedly enter multiple times in order to claim a high winning percentage in the contest to fish, but Culver's results still show the volatility of gambling on sports.
The point of all this is, if you do vary your wagers, consider lowering the variance and be careful of falling prey to makeup bets. Making one wager worth five times more than another is a very risky proposition. It takes a losing streak of only four or five games with those top plays to really hurt someone's bankroll. Though the formula shows mathematical support for raising the stakes on wagers that have historically been strong, most gamblers are not disciplined or experienced enough to effectively use widely varying wagers without eventually collapsing.
Many successful handicappers have suggested keeping a standard value for all wagers. In fact, I strongly support that myself. Though it is frustrating when one of your strong plays hits and a 2-2 day results in a small loss instead of a big win, over the long haul keeping wager amounts consistent is a smart move for most gamblers.
Even if a standard value is not kept, perhaps lowering the variance is a sound idea. If a person is a $50 bettor, I would argue that many times each year they wager at least $100 on a game. That is a huge variance. Those $100+ games will have an enormous amount of control of your overall success. Instead of varying the wagers to two or three times a standard wager, perhaps keeping everything within 100% would be a good idea. If your standard wager is $50, play your stronger plays at $60 or $70 rather than $100 or more. Certainly your hot streaks will not be as satisfying, but at least cold streaks won't have the potential to bankrupt you.
Realistically, very few gamblers have the discipline to keep their wager standard. When a hot or cold streak comes, the natural inclination to strike while the iron is hot or to make up losses in one play makes most gamblers adjust their wager amounts in some way. And heck, there are a good number of players who are simply disciplined enough that they can regularly vary their unit amounts and find success long term. But if you are one of the vast majority who loves the NFL but struggles to make money on a regular basis, consider setting a flat amount for all of your wagers. Failing that, at least keep track of your actual results compared to what your results would have been had you set a flat wager amount. At the end of the season, the results may surprise you.
E = W - ((1 - W) / O)
If you ever want to truly maximize your bankroll, you simply must get in touch with "E". "E" is the result of the above formula, which is arguably the most important mathematical formula available for the purpose of bankroll management. In this case:
E = Edge (optimal wager as a percentage of your bankroll)
W = Winning percentage
O = Odds (in decimal form)
For example, let's say you start the NFL season with $1,000. Let's say you just know that you will hit 55% of your plays this year. Based on betting all -110 point spreads, the formula would grade out as follows:
E = [0.055] (5.5%)
W = [0.55] (55%)
O = [0.90909] (10/11)
[0.55] - ((1 - [0.55]) / [0.90909]) = [0.055]
0.055 is equal to 5.5%. Therefore, if you want to bet the same amount on each game, you start with $1,000 and you are absolutely sure that you will hit 55% of your games, you will maximize your bankroll by wagering 5.5% of your bankroll (or a starting number of $55) on each game.
There are some flaws to this formula. First of all, NFL games are not bet sequentially. That is, most people have more than one game going at the same time. This formula is meant to be used with only one wager in action at a time so the bankroll number can be adjusted before each bet. In addition, nobody *really* knows what percentage they are going to hit in a given year. If you happen to be off by a few percentage points, the results can be destructive. In addition, it is better for most gamblers' mental health to keep wager amounts relatively standard or on a unit system rather than recalculating minute percentages with each play. Wagering $58.54 on a game just doesn't have the panache of wagering $50.
What I do like about this formula, however, is that it concretely shows that if you are serious about making money on sports, adjusting your wager to your winning percentage is a good idea. It is this concept which leads to the topic of varying one's bet size to determine the optimal "E" value for each wager.
Though nobody likes to use the "L" word, everyone has a few games a year that they feel are "locks". Not locks in the tout sense of the word but at least very very strong plays. Unless you are a long time handicapper it is a tough feeling to describe but there are certain times when you feel so confident that you just know that you are going to destroy your book on a certain play.
Human nature dictates that you will want to load up on that one play. Easy money. How can you pass it up? You are not so much *wagering* $1000, you are simply *taking* $1000 from the book because there is no way on earth this game will lose.
I have had that feeling many times, and of course, it does not always guarantee a winner. But I would modestly say that it hits more than it missed by a good margin. The hard part is not so much pinpointing these games, as those feelings will come naturally. The hard part is playing your bankroll right to hit the winners hardest and increase your bankroll.
Where should the line between aggressiveness and foolishness be drawn? If a player has a unit value system between 1 and 5 that is used regularly, that seems a bit odd. How can one play in the same sport warrant five times as much action as another play? A loss on the five unit play would seem to be absolutely devastating. In that case a 5-1 ATS record could still result in a small loss.
If you look at the above formula, though, maybe it is not so odd. I think everyone would agree that if they played less action, that they could hit a higher percentage. That would logically be true. That is not to say that everyone should play less action. If you make a profit on plays 3-7 each day as well as plays 1-2, then keep playing seven games per day. But most people probably feel that if they only played plays 1-2, then their percentage will be higher.
So what would it take to warrant a 5 unit play? If you hit 55% on your average one unit play, then a five unit play would require an E = 0.275. E=0.055 (5.5% of bankroll) when hitting 55%, so a five unit play would have to have you theoretically wagering 27.5% of your bankroll.
Plug in E=0.275 into the formula, we come up with a W (winning %) = 65.5%. For a reference, if you entered the Hilton contest and hit 65.5%, you would have won 3rd place last year. Certainly that means that 65.5% can be done. In fact, it can even be done by wagering the 85 games in one year that the Hilton contest requires.
It is not going to happen year after year, though. The 1999 Hilton contest winner, Russell Culver, went a mediocre 42-43 in this year's contest. Now, it is true that many tout services reportedly enter multiple times in order to claim a high winning percentage in the contest to fish, but Culver's results still show the volatility of gambling on sports.
The point of all this is, if you do vary your wagers, consider lowering the variance and be careful of falling prey to makeup bets. Making one wager worth five times more than another is a very risky proposition. It takes a losing streak of only four or five games with those top plays to really hurt someone's bankroll. Though the formula shows mathematical support for raising the stakes on wagers that have historically been strong, most gamblers are not disciplined or experienced enough to effectively use widely varying wagers without eventually collapsing.
Many successful handicappers have suggested keeping a standard value for all wagers. In fact, I strongly support that myself. Though it is frustrating when one of your strong plays hits and a 2-2 day results in a small loss instead of a big win, over the long haul keeping wager amounts consistent is a smart move for most gamblers.
Even if a standard value is not kept, perhaps lowering the variance is a sound idea. If a person is a $50 bettor, I would argue that many times each year they wager at least $100 on a game. That is a huge variance. Those $100+ games will have an enormous amount of control of your overall success. Instead of varying the wagers to two or three times a standard wager, perhaps keeping everything within 100% would be a good idea. If your standard wager is $50, play your stronger plays at $60 or $70 rather than $100 or more. Certainly your hot streaks will not be as satisfying, but at least cold streaks won't have the potential to bankrupt you.
Realistically, very few gamblers have the discipline to keep their wager standard. When a hot or cold streak comes, the natural inclination to strike while the iron is hot or to make up losses in one play makes most gamblers adjust their wager amounts in some way. And heck, there are a good number of players who are simply disciplined enough that they can regularly vary their unit amounts and find success long term. But if you are one of the vast majority who loves the NFL but struggles to make money on a regular basis, consider setting a flat amount for all of your wagers. Failing that, at least keep track of your actual results compared to what your results would have been had you set a flat wager amount. At the end of the season, the results may surprise you.
