Ddakota
09-13-2004, 06:33 PM
BETTING SYSTEM....
POINTS SCORED = 11.74
PENALTY YDS = 7.1
RUSHING YDS = 12.45
FG MADE = 9.6
RETURN YDS = 15.3
YARDS PER GM = 14.47
PASSING ATT = 8.95
YARDS PER PUNT = 9.72
TIMES SACKED = 10.2
PASSING PERCENT = 0.47
HOME FIELD = 3.45
PT SPREAD MULTIPLIER = 1.14
LOWER LINE DIFF = 0
UPPER LINE DIFF = 12
DATABASE: ROLLING AVERAGE LAST 16 GAMES
There's a reason its my favorite formula. It did great! It picked 147 winners and just 85 losers for a winning percentage of 63.4%. Since it generated so many plays, it racked up a staggering number of net units, 53.5 to be exact.
Once you've developed a system with a high winning percentage, the question becomes how to manage your bankroll so you can optimize your profits. Gamblers often discuss "money management systems" which provide the guidelines for establishing an "optimal wager". The optimum wager is computed as a percentage of your available bankroll. This type of wagering is best optimized in a sequential environment such as horse racing, but can serve quite well in football or basketball or any other sport where you can establish a good estimate of your expected winning percentage.
Keep in mind that you need a fairly large database of past plays to get a reliable estimate of your expected winning percentage. That's why the formula listed above uses a betting window of from 0 to12 points, so that we get a lot of plays. However, once you have a good estimate of winning percentage, a good money management system can save you from self-destruction whe the probabilities get skewed (bound to happen sooner or later). A good money management system has definite advantages over a "star-unit" system (wager 4 units on a 4-star game, 3 units on a 3-star game, and so on). Some star-unit players hit over 60% and still wind up losing money if they do poorly on their highest-rated plays.
To explain the system, we need to use the following variables.
W = Winning percentage against the spread
O = True Odds
E = Edge (optimal wager as a percentage of your bankroll)
G = Growth rate of bankroll
N = Number of events
B = Amount added to bankroll
As all gamblers know, in Las Vegas you pay a 10% vigorish ("juice") on every wager, or in other words, you lay $11 to win $10. This means that the true odds (O) will have a constant value of 10/11 or .90909. The O variable reflects the built-in advantage that the sports book has. The average gambler will win 50% of the time, and be payed about 91 cents for every dollar that they risk.
The equation to compute E (the optimum wager) is:
E = W - ((1-W) / O)
When we plug in the 63.4% winning percentage from the above formula, we get:
E = .634 - ((1-.634) / .90909), or E equals .2314
This means that the optimum bet is 23.14% of the bankroll. Now that we know our winning percentage (W) and our optimum wager size (E) we can compute the growth rate (G) of our bankroll:
G = (1-E)^(1-W) * (1+O*E)^W
or:
G = (.7686)^(.366) * (1.2104)^.634, or (.9082 * 1.1286) = 1.0249
G can be thought of as the "interest rate", since in theory it is the same thing as the interest rate payed on a savings account or checking account. In this case, G is equal to about 2.5%, which is about the same rate that a checking account pays. However, insteaded of being compounded monthly or annually, G is compounded with each additional wager. To compute the total amount of our bankroll increase (B), we need this equation, where N is the total number of games wagered on:
B = G ^ N
In our above example, our formula generated 232 plays, so N is equal to 232. This means that B is equal to 307.6, and we would multiply our initial bankroll by a staggering 307.6 times! An initial bankroll of $1000 would be turned into $307,600!
Of course, the Kelly System has many pitfalls. One is that if you risk 23% of your bankroll with every wager, an early losing streak of just 4 games would nearly break the bank. For this reason, we recommend a more modest wager of just 10%, or less than half of the optimized 23.14%. This changes the results as follows:
G = (.9)^(.366) * (1.0909)^.634, or (.9621 * 1.0567) = 1.0166
B = 1.0166 ^ 232 = 46.3
In this case, our "interest rate" drops to 1.66%, but our bankroll still multiplies by 46.3 times, turning $1000 into $46,300. The interesting thing about the Kelly method is that it does not matter where in the sequence the wins or losses occur, the final results will be the same as long as the estimated winning percentage (W) is maintained.
How the Sequencing Works for Football
We mentioned early that the best environment for an establishing an optimum wager is a sequential environment. In horse racing, for example, the races occur one at a time. Football games are not played in a true sequence, since several games are going on at once. However, you can simulate the sequence by grouping games by their kickoff times. For example, 1 group could consist of Sunday games that start at 1 p.m. Eastern time. The second group could consist of games that start at 4 p.m. Eastern and also includes the Sunday night and Monday night games.
To illustrate this, let's look at weeks 1-3 of the 1996 NFL season. We went 9-3 the first week and 9-6 the second week. In week 1, there were 7 games that started at 1 p.m. Since our initial bankroll was $1000, we wagered $100 on all 7 games. When you allow for the vig, this represented an outlay of $770. We hit 5 winners for a return of $500 and 2 losers for a loss of $220, so our net gain was $280. This left our bankroll at $1280. With the adjusted bankroll, we we could wager $128 (vig of $12.80) on the 4 p.m. games and went 4-1, pushing the bankroll to $1651.
If you think about this a little bit, you'll get the idea how it works. The data below shows the results of the first 2 weeks. Our combined record for the 2 weeks is 18-9 (67.3%) and our bankroll has more than doubled (from $1000 to $2032). By the end of the NFL season, the 63.4% formula would have produced a bankroll of $46,300.
WK1 B=1000 1pm wager=100+10vig=110*7wagers=770 b=230 5wins*210=1050+230=$1280 9-3 B=1280 4pm wager=128+13vig=141*5wagers=705 b=575 4wins*269=1076+575=$1651
WK2 B=1651 1pm wager=165+17vig=182*9wagers=1638 b=13 6wins*347=2082+13=$2095 9-6 B=2095 4pm wager=210+21vig=231*6wagers=1386 b=709 3wins*1441=1323+709=$2032
Taking Profits
One final thing we need to address is profit taking. You'll notice that we started out wagering $100 per game, and by the end of week 2, we are already wagering over $200. By somewhere around week 9 or 10, our stake per game will top $1000. Our $46,300 figure is based on letting the entire bankroll ride the entire season. Most intelligent players will start to tuck away some of their profits as they start to win, and play with a smaller roll. Different gamblers have different comfort zones. A good system that I like to follow is when your bankroll reaches 300%, take out at least 1/2. When it reaches 300% take out 1/3. The next time take out 1/2 again, and continue in this rotation
POINTS SCORED = 11.74
PENALTY YDS = 7.1
RUSHING YDS = 12.45
FG MADE = 9.6
RETURN YDS = 15.3
YARDS PER GM = 14.47
PASSING ATT = 8.95
YARDS PER PUNT = 9.72
TIMES SACKED = 10.2
PASSING PERCENT = 0.47
HOME FIELD = 3.45
PT SPREAD MULTIPLIER = 1.14
LOWER LINE DIFF = 0
UPPER LINE DIFF = 12
DATABASE: ROLLING AVERAGE LAST 16 GAMES
There's a reason its my favorite formula. It did great! It picked 147 winners and just 85 losers for a winning percentage of 63.4%. Since it generated so many plays, it racked up a staggering number of net units, 53.5 to be exact.
Once you've developed a system with a high winning percentage, the question becomes how to manage your bankroll so you can optimize your profits. Gamblers often discuss "money management systems" which provide the guidelines for establishing an "optimal wager". The optimum wager is computed as a percentage of your available bankroll. This type of wagering is best optimized in a sequential environment such as horse racing, but can serve quite well in football or basketball or any other sport where you can establish a good estimate of your expected winning percentage.
Keep in mind that you need a fairly large database of past plays to get a reliable estimate of your expected winning percentage. That's why the formula listed above uses a betting window of from 0 to12 points, so that we get a lot of plays. However, once you have a good estimate of winning percentage, a good money management system can save you from self-destruction whe the probabilities get skewed (bound to happen sooner or later). A good money management system has definite advantages over a "star-unit" system (wager 4 units on a 4-star game, 3 units on a 3-star game, and so on). Some star-unit players hit over 60% and still wind up losing money if they do poorly on their highest-rated plays.
To explain the system, we need to use the following variables.
W = Winning percentage against the spread
O = True Odds
E = Edge (optimal wager as a percentage of your bankroll)
G = Growth rate of bankroll
N = Number of events
B = Amount added to bankroll
As all gamblers know, in Las Vegas you pay a 10% vigorish ("juice") on every wager, or in other words, you lay $11 to win $10. This means that the true odds (O) will have a constant value of 10/11 or .90909. The O variable reflects the built-in advantage that the sports book has. The average gambler will win 50% of the time, and be payed about 91 cents for every dollar that they risk.
The equation to compute E (the optimum wager) is:
E = W - ((1-W) / O)
When we plug in the 63.4% winning percentage from the above formula, we get:
E = .634 - ((1-.634) / .90909), or E equals .2314
This means that the optimum bet is 23.14% of the bankroll. Now that we know our winning percentage (W) and our optimum wager size (E) we can compute the growth rate (G) of our bankroll:
G = (1-E)^(1-W) * (1+O*E)^W
or:
G = (.7686)^(.366) * (1.2104)^.634, or (.9082 * 1.1286) = 1.0249
G can be thought of as the "interest rate", since in theory it is the same thing as the interest rate payed on a savings account or checking account. In this case, G is equal to about 2.5%, which is about the same rate that a checking account pays. However, insteaded of being compounded monthly or annually, G is compounded with each additional wager. To compute the total amount of our bankroll increase (B), we need this equation, where N is the total number of games wagered on:
B = G ^ N
In our above example, our formula generated 232 plays, so N is equal to 232. This means that B is equal to 307.6, and we would multiply our initial bankroll by a staggering 307.6 times! An initial bankroll of $1000 would be turned into $307,600!
Of course, the Kelly System has many pitfalls. One is that if you risk 23% of your bankroll with every wager, an early losing streak of just 4 games would nearly break the bank. For this reason, we recommend a more modest wager of just 10%, or less than half of the optimized 23.14%. This changes the results as follows:
G = (.9)^(.366) * (1.0909)^.634, or (.9621 * 1.0567) = 1.0166
B = 1.0166 ^ 232 = 46.3
In this case, our "interest rate" drops to 1.66%, but our bankroll still multiplies by 46.3 times, turning $1000 into $46,300. The interesting thing about the Kelly method is that it does not matter where in the sequence the wins or losses occur, the final results will be the same as long as the estimated winning percentage (W) is maintained.
How the Sequencing Works for Football
We mentioned early that the best environment for an establishing an optimum wager is a sequential environment. In horse racing, for example, the races occur one at a time. Football games are not played in a true sequence, since several games are going on at once. However, you can simulate the sequence by grouping games by their kickoff times. For example, 1 group could consist of Sunday games that start at 1 p.m. Eastern time. The second group could consist of games that start at 4 p.m. Eastern and also includes the Sunday night and Monday night games.
To illustrate this, let's look at weeks 1-3 of the 1996 NFL season. We went 9-3 the first week and 9-6 the second week. In week 1, there were 7 games that started at 1 p.m. Since our initial bankroll was $1000, we wagered $100 on all 7 games. When you allow for the vig, this represented an outlay of $770. We hit 5 winners for a return of $500 and 2 losers for a loss of $220, so our net gain was $280. This left our bankroll at $1280. With the adjusted bankroll, we we could wager $128 (vig of $12.80) on the 4 p.m. games and went 4-1, pushing the bankroll to $1651.
If you think about this a little bit, you'll get the idea how it works. The data below shows the results of the first 2 weeks. Our combined record for the 2 weeks is 18-9 (67.3%) and our bankroll has more than doubled (from $1000 to $2032). By the end of the NFL season, the 63.4% formula would have produced a bankroll of $46,300.
WK1 B=1000 1pm wager=100+10vig=110*7wagers=770 b=230 5wins*210=1050+230=$1280 9-3 B=1280 4pm wager=128+13vig=141*5wagers=705 b=575 4wins*269=1076+575=$1651
WK2 B=1651 1pm wager=165+17vig=182*9wagers=1638 b=13 6wins*347=2082+13=$2095 9-6 B=2095 4pm wager=210+21vig=231*6wagers=1386 b=709 3wins*1441=1323+709=$2032
Taking Profits
One final thing we need to address is profit taking. You'll notice that we started out wagering $100 per game, and by the end of week 2, we are already wagering over $200. By somewhere around week 9 or 10, our stake per game will top $1000. Our $46,300 figure is based on letting the entire bankroll ride the entire season. Most intelligent players will start to tuck away some of their profits as they start to win, and play with a smaller roll. Different gamblers have different comfort zones. A good system that I like to follow is when your bankroll reaches 300%, take out at least 1/2. When it reaches 300% take out 1/3. The next time take out 1/2 again, and continue in this rotation