{"id":2174,"date":"2024-06-01T15:47:48","date_gmt":"2024-06-01T15:47:48","guid":{"rendered":"https:\/\/egoanalytics.me\/?page_id=2174"},"modified":"2026-04-09T14:34:52","modified_gmt":"2026-04-09T14:34:52","slug":"binomial-probability-explanation","status":"publish","type":"page","link":"https:\/\/egoanalytics.me\/index.php\/binomial-probability-explanation\/","title":{"rendered":"Binomial Probability Explanation"},"content":{"rendered":"\n
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What’s the Optimal Betting Strategy?<\/strong><\/p>\n\n\n\n

Once the predictions are made, how does one determine the quality of the bets? As seen by the Gambling Performances page<\/a>, the simplest way would be to calculate the absolute difference between the ego predictions and the Win Total line for each organization, and then sort the bets by that metric in descending order. By doing so, one would think that the bets with the best chance of winning are at the top, and the bets with the lowest chance of winning are at the bottom. But is that true? If it is, would it be worth taking all 32 bets? If it is not worth doing 32, then how would one know which bets to take and which to avoid?<\/p>\n\n\n\n

The goal of a bettor is to have a betting portfolio that maximizes Units<\/a>, as that is viewed by many as the universal measure of gambling success. While Return on Investment is a valuable measure, the amount of money (or portion of bankroll) that goes into those Returns also matters. Units is a function with two variables: Return on Investment (ROI)<\/strong> and Number of Bets<\/strong>. The formula is [Total Units = ROI * Number of Bets]. In terms of Win Total Futures, one could maximize Number of Bets by taking all 32 bets, but the Return on Investment would theoretically decrease as one would be taking on bets with a higher chance of losing (based on the difference between prediction and line, not in terms of odds). Or one could try to maximize ROI by taking fewer, theoretically safer bets (again, in terms of difference, not in terms of odds), but obviously Number of Bets would decrease as a result. One’s strategy could depend on several factors, two main ones being Betting Style<\/strong> and Risk Aversion<\/strong>. Betting Style here refers to how one bets in terms of Fixed Amount <\/strong>and Variable Amount<\/strong>. Fixed Amount means that the bettor has a set amount of money to put on each bet, and Variable Amount means that he or she alters the amount of money that they put in depending on the specific bet. The more bets that a Fixed Amount bettor adds to their portfolio, the larger the total bankroll that he or she is putting into their portfolio. For a Variable Amount bettor, the number of bets is not as relevant with regard to risk (as you could put any amount on any of the bets), so for this section, I’m going to assume that everyone is a Fixed Amount bettor. Part of this reason is that sportsbooks are suspicious of gamblers that use various, specific amounts for each bet, so allocating a flat, round amount across bets should help the successful gambler fly under the radar. Sportsbooks are known for having a history of limiting successful gamblers in order to stem losses, so the Fixed Amount method is most applicable for the widest spectrum of gamblers. Risk Aversion for a Fixed Amount gambler would then be how far down the chart that one would go in order to build their portfolio of bets. The more bets one adds, the more money that they are gambling with, and therefore, the risker that their portfolio becomes overall. For a Variable Amount gambler, risk is much more complicated in terms of how much of one’s total bankroll goes towards a specific bet and how many bets one makes. <\/p>\n\n\n\n

Before I go into the actual content of this page, I just want to stop down and explain how I view this model and its relationship to gambling. To me, there is little difference between investing in stocks and gambling on sports. In the same way that an investor uses some information (typically some research done by the investor or a stock broker) to make an investment in a stock or a group of stocks (or other types of investments), a sports bettor is using information (typically “gut feeling” for a casual gambler) in order to gamble on a bet or a series of bets. The key difference, as alluded to in the previous sentence, is that sports gambling has a reputation of most participants using little to no actual research, which is one reason why people are much better at losing money through gambling than in the stock market. This distinction makes people think that investing in stocks is responsible, while gambling your money on sports is irresponsible. But the core “game” is still the same in many ways. Banks (Sportsbooks) set a value level for a company (a Win Total line for a NFL organization) that can go up or down based on the public’s perception of how the company (NFL organization) will actually perform. If one thinks that a company (NFL organization) is being undervalued (has a low Win Total line in relation to expectation), he or she purchase stock in the company (take the Over bet). If the investor turns out to be right, then he or she gains value (the bet pays out). If the investor is wrong, then he or she will lose value (the bet does not pay out). Once again, investing can be (and often is) much more complex, but at its roots, it is very similar to the type of gambling that is being conducted via this project. In this project, when I say “portfolio” like an investor, I am referring to a set of bets. And when I say “bets” like a gambler, I am referring to investments. So what are the ways to determine the optimal portfolio of bets?<\/p>\n\n\n\n

Method #1 – All 32<\/strong><\/p>\n\n\n\n

Method #1<\/em><\/strong> – Take all 32 bets. It may seem counterintuitive, but this method is the least risk averse, or, in other words, the riskiest for a Fixed Amount bettor. This would require the bettor to put in the maximum amount of money into the portfolio, taking on riskier and riskier bets as they build up to the total 32. On the other hand, for a Variable Amount gambler, it could be the most risk averse option, as they can spread the total amount with which he or she is planning to use across the largest number of bets. This is, of course, assuming that the Fixed Amount bettor has a variable total bankroll with which to gamble, and that the Variable Amount bettor has a fixed total bankroll with which to gamble. The Fixed Amount bettor bets the same amount per bet, so increasing the number of bets adds money to the portfolio. The Variable Amount bettor has a set total amount that they are willing to put into the portfolio and is spreading that total amount across those bets in different individual allocations. The lower the number of bets, the less money the Fixed Amount bettor puts into the portfolio, which contains (theoretically) more reliable bets, lessening the risk. The fewer the number of bets, the more money (or weight) that the Variable bettor puts on individual bets, putting his or her eggs in fewer baskets, therefore increasing the risk. <\/p>\n\n\n\n

The results of this betting method can be seen on the website homepage in Green on the left side of the chart. A sign of the riskiness of the style is that when things go well (like in 2020) the Units are higher than the other methods, and when things don’t go well (like in 2023), the Units are lower than the other methods.<\/p>\n\n\n\n

Method #2 – (ego – Line) Absolute Difference<\/strong><\/p>\n\n\n\n

Method #2a<\/em><\/strong> – Take a specific Number of Bets after sorting by the absolute difference between the ego prediction and the line from the sportsbook. For example, one could simply take the top 20 bets based on the (ego – Line) difference. The results of taking the top 20 bets each season can be seen in the chart on the homepage in orange on the right side of the chart at the bottom of the page. Using a cutoff of the top 20 is not optimal given the 4 seasons of data, as seen by a lower Total Units compared to Method #1. Looking at the chart below, the optimal Number of Bets each season would have been 16, resulting an an average Rate of Return of 24.30% and Total Units of 15.55.<\/p>\n<\/div>\n<\/div>\n\n\n\n

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*Diff represents the absolute difference between ego and the sportsbooks’ lines*<\/p>\n<\/div>\n<\/div>\n\n\n\n

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\n\n\n \n\n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
<\/th>\n20Diff<\/th>\nResult<\/th>\nROI<\/th>\nRROI<\/th>\nUnits<\/th>\nRUnits<\/th>\n<\/th>\n21Diff<\/th>\nResult<\/th>\nROI<\/th>\nRROI<\/th>\nUnits<\/th>\nRUnits<\/th>\n<\/th>\n22Diff<\/th>\nResult<\/th>\nROI<\/th>\nRROI<\/th>\nUnits<\/th>\nRUnits<\/th>\n<\/th>\n23Diff<\/th>\nResult<\/th>\nROI<\/th>\nRROI<\/th>\nUnits<\/th>\nRUnits<\/th>\n<\/th>\nRROI<\/th>\nRUnits<\/th>\n<\/tr>\n<\/thead>\n
1<\/td>\n 2.54<\/td>\n 19.09<\/td>\n 90.9%<\/td>\n 90.91%<\/td>\n 0.91<\/td>\n 0.91<\/td>\n 1<\/td>\n 3.45<\/td>\n 20.4<\/td>\n 104%<\/td>\n 104%<\/td>\n 1.04<\/td>\n 1.04<\/td>\n 1<\/td>\n 2.42<\/td>\n 0<\/td>\n -100%<\/td>\n -100%<\/td>\n -1<\/td>\n -1<\/td>\n 1<\/td>\n 2.46<\/td>\n 0<\/td>\n -100%<\/td>\n -100%<\/td>\n -1<\/td>\n -1<\/td>\n 1<\/td>\n -1.27%<\/td>\n -0.05<\/td>\n <\/tr>\n
2<\/td>\n 2.33<\/td>\n 0<\/td>\n -100%<\/td>\n -100%<\/td>\n -1<\/td>\n -0.09<\/td>\n 2<\/td>\n 2.98<\/td>\n 17.69<\/td>\n 76.9%<\/td>\n 90.45%<\/td>\n 0.77<\/td>\n 1.81<\/td>\n 2<\/td>\n 2.35<\/td>\n 0<\/td>\n -100%<\/td>\n -100%<\/td>\n -1<\/td>\n -2<\/td>\n 2<\/td>\n 1.61<\/td>\n 0<\/td>\n -100%<\/td>\n -100%<\/td>\n -1<\/td>\n -2<\/td>\n 2<\/td>\n -28.53%<\/td>\n -2.28<\/td>\n <\/tr>\n
3<\/td>\n 2.22<\/td>\n 21.5<\/td>\n 115%<\/td>\n 35.30%<\/td>\n 1.15<\/td>\n 1.06<\/td>\n 3<\/td>\n 2.70<\/td>\n 20.5<\/td>\n 105%<\/td>\n 95.30%<\/td>\n 1.05<\/td>\n 2.86<\/td>\n 3<\/td>\n 2.33<\/td>\n 0<\/td>\n -100%<\/td>\n -100%<\/td>\n -1<\/td>\n -3<\/td>\n 3<\/td>\n 1.43<\/td>\n 16.67<\/td>\n 66.7%<\/td>\n -44.33%<\/td>\n 0.67<\/td>\n -1.33<\/td>\n 3<\/td>\n -3.43%<\/td>\n -0.42<\/td>\n <\/tr>\n
4<\/td>\n 2.22<\/td>\n 21.5<\/td>\n 115%<\/td>\n 55.23%<\/td>\n 1.15<\/td>\n 2.21<\/td>\n 4<\/td>\n 2.28<\/td>\n 20.2<\/td>\n 102%<\/td>\n 96.98%<\/td>\n 1.02<\/td>\n 3.88<\/td>\n 4<\/td>\n 2.29<\/td>\n 0<\/td>\n -100%<\/td>\n -100%<\/td>\n -1<\/td>\n -4<\/td>\n 4<\/td>\n 1.28<\/td>\n 20.4<\/td>\n 104%<\/td>\n -7.33%<\/td>\n 1.04<\/td>\n -0.29<\/td>\n 4<\/td>\n 11.22%<\/td>\n 1.80<\/td>\n <\/tr>\n
5<\/td>\n 1.92<\/td>\n 21.5<\/td>\n 115%<\/td>\n 67.18%<\/td>\n 1.15<\/td>\n 3.36<\/td>\n 5<\/td>\n 2.18<\/td>\n 21<\/td>\n 110%<\/td>\n 99.58%<\/td>\n 1.10<\/td>\n 4.98<\/td>\n 5<\/td>\n 1.75<\/td>\n 19.52<\/td>\n 95.2%<\/td>\n -60.96%<\/td>\n 0.95<\/td>\n -3.05<\/td>\n 5<\/td>\n 1.22<\/td>\n 0<\/td>\n -100%<\/td>\n -25.86%<\/td>\n -1<\/td>\n -1.29<\/td>\n 5<\/td>\n 19.99%<\/td>\n 4.00<\/td>\n <\/tr>\n
6<\/td>\n 1.78<\/td>\n 0<\/td>\n -100%<\/td>\n 39.32%<\/td>\n -1<\/td>\n 2.36<\/td>\n 6<\/td>\n 2.17<\/td>\n 0<\/td>\n -100%<\/td>\n 66.32%<\/td>\n -1<\/td>\n 3.98<\/td>\n 6<\/td>\n 1.51<\/td>\n 18<\/td>\n 80%<\/td>\n -37.47%<\/td>\n 0.80<\/td>\n -2.25<\/td>\n 6<\/td>\n 1.20<\/td>\n 15.59<\/td>\n 55.9%<\/td>\n -12.23%<\/td>\n 0.56<\/td>\n -0.73<\/td>\n 6<\/td>\n 13.98%<\/td>\n 3.36<\/td>\n <\/tr>\n
7<\/td>\n 1.69<\/td>\n 17.19<\/td>\n 71.9%<\/td>\n 43.97%<\/td>\n 0.72<\/td>\n 3.08<\/td>\n 7<\/td>\n 2.16<\/td>\n 19.52<\/td>\n 95.2%<\/td>\n 70.44%<\/td>\n 0.95<\/td>\n 4.93<\/td>\n 7<\/td>\n 1.47<\/td>\n 0<\/td>\n -100%<\/td>\n -46.40%<\/td>\n -1<\/td>\n -3.25<\/td>\n 7<\/td>\n 1.17<\/td>\n 16.99<\/td>\n 69.9%<\/td>\n -0.50%<\/td>\n 0.70<\/td>\n -0.03<\/td>\n 7<\/td>\n 16.88%<\/td>\n 4.73<\/td>\n <\/tr>\n
8<\/td>\n 1.47<\/td>\n 21<\/td>\n 110%<\/td>\n 52.23%<\/td>\n 1.10<\/td>\n 4.18<\/td>\n 8<\/td>\n 2.11<\/td>\n 21<\/td>\n 110%<\/td>\n 75.39%<\/td>\n 1.10<\/td>\n 6.03<\/td>\n 8<\/td>\n 1.43<\/td>\n 10<\/td>\n 0%<\/td>\n -40.60%<\/td>\n 0<\/td>\n -3.25<\/td>\n 8<\/td>\n 1.16<\/td>\n 17.04<\/td>\n 70.4%<\/td>\n 8.36%<\/td>\n 0.70<\/td>\n 0.67<\/td>\n 8<\/td>\n 23.84%<\/td>\n 7.63<\/td>\n <\/tr>\n
9<\/td>\n 1.46<\/td>\n 18.7<\/td>\n 87%<\/td>\n 56.09%<\/td>\n 0.87<\/td>\n 5.05<\/td>\n 9<\/td>\n 2.10<\/td>\n 18.7<\/td>\n 87%<\/td>\n 76.68%<\/td>\n 0.87<\/td>\n 6.90<\/td>\n 9<\/td>\n 1.30<\/td>\n 18<\/td>\n 80%<\/td>\n -27.20%<\/td>\n 0.80<\/td>\n -2.45<\/td>\n 9<\/td>\n 1.12<\/td>\n 0<\/td>\n -100%<\/td>\n -3.68%<\/td>\n -1<\/td>\n -0.33<\/td>\n 9<\/td>\n 25.47%<\/td>\n 9.17<\/td>\n <\/tr>\n
10<\/td>\n 1.25<\/td>\n 18.33<\/td>\n 83.3%<\/td>\n 58.81%<\/td>\n 0.83<\/td>\n 5.88<\/td>\n 10<\/td>\n 1.98<\/td>\n 0<\/td>\n -100%<\/td>\n 59.01%<\/td>\n -1<\/td>\n 5.90<\/td>\n 10<\/td>\n 1.17<\/td>\n 18.33<\/td>\n 83.3%<\/td>\n -16.15%<\/td>\n 0.83<\/td>\n -1.62<\/td>\n 10<\/td>\n 1.07<\/td>\n 0<\/td>\n -100%<\/td>\n -13.31%<\/td>\n -1<\/td>\n -1.33<\/td>\n 10<\/td>\n 22.09%<\/td>\n 8.84<\/td>\n <\/tr>\n
11<\/td>\n 1.12<\/td>\n 19.52<\/td>\n 95.2%<\/td>\n 62.12%<\/td>\n 0.95<\/td>\n 6.83<\/td>\n 11<\/td>\n 1.93<\/td>\n 18.7<\/td>\n 87%<\/td>\n 61.55%<\/td>\n 0.87<\/td>\n 6.77<\/td>\n 11<\/td>\n 1.14<\/td>\n 0<\/td>\n -100%<\/td>\n -23.77%<\/td>\n -1<\/td>\n -2.62<\/td>\n 11<\/td>\n 1.03<\/td>\n 0<\/td>\n -100%<\/td>\n -21.29%<\/td>\n -1<\/td>\n -2.33<\/td>\n 11<\/td>\n 19.65%<\/td>\n 8.66<\/td>\n <\/tr>\n
12<\/td>\n 1.12<\/td>\n 16.45<\/td>\n 64.5%<\/td>\n 62.32%<\/td>\n 0.65<\/td>\n 7.48<\/td>\n 12<\/td>\n 1.89<\/td>\n 10<\/td>\n 0%<\/td>\n 56.43%<\/td>\n 0<\/td>\n 6.77<\/td>\n 12<\/td>\n 1.14<\/td>\n 18.7<\/td>\n 87%<\/td>\n -14.54%<\/td>\n 0.87<\/td>\n -1.75<\/td>\n 12<\/td>\n 0.96<\/td>\n 21<\/td>\n 110%<\/td>\n -10.26%<\/td>\n 1.10<\/td>\n -1.23<\/td>\n 12<\/td>\n 23.49%<\/td>\n 11.27<\/td>\n <\/tr>\n
13<\/td>\n 0.95<\/td>\n 17.52<\/td>\n 75.2%<\/td>\n 63.31%<\/td>\n 0.75<\/td>\n 8.23<\/td>\n 13<\/td>\n 1.85<\/td>\n 17.14<\/td>\n 71.4%<\/td>\n 57.58%<\/td>\n 0.71<\/td>\n 7.49<\/td>\n 13<\/td>\n 1.13<\/td>\n 21<\/td>\n 110%<\/td>\n -4.96%<\/td>\n 1.10<\/td>\n -0.65<\/td>\n 13<\/td>\n 0.94<\/td>\n 17.04<\/td>\n 70.4%<\/td>\n -4.05%<\/td>\n 0.70<\/td>\n -0.53<\/td>\n 13<\/td>\n 27.97%<\/td>\n 14.54<\/td>\n <\/tr>\n
14<\/td>\n 0.90<\/td>\n 0<\/td>\n -100%<\/td>\n 52.64%<\/td>\n -1<\/td>\n 7.23<\/td>\n 14<\/td>\n 1.72<\/td>\n 20<\/td>\n 100%<\/td>\n 60.61%<\/td>\n 1<\/td>\n 8.49<\/td>\n 14<\/td>\n 1.08<\/td>\n 0<\/td>\n -100%<\/td>\n -11.75%<\/td>\n -1<\/td>\n -1.65<\/td>\n 14<\/td>\n 0.91<\/td>\n 0<\/td>\n -100%<\/td>\n -10.91%<\/td>\n -1<\/td>\n -1.53<\/td>\n 14<\/td>\n 22.65%<\/td>\n 12.54<\/td>\n <\/tr>\n
15<\/td>\n 0.90<\/td>\n 0<\/td>\n -100%<\/td>\n 41.53%<\/td>\n -1<\/td>\n 6.23<\/td>\n 15<\/td>\n 1.71<\/td>\n 18.33<\/td>\n 83.3%<\/td>\n 62.12%<\/td>\n 0.83<\/td>\n 9.32<\/td>\n 15<\/td>\n 1.07<\/td>\n 16.45<\/td>\n 64.5%<\/td>\n -6.67%<\/td>\n 0.65<\/td>\n -1.00<\/td>\n 15<\/td>\n 0.86<\/td>\n 18.33<\/td>\n 83.3%<\/td>\n -4.63%<\/td>\n 0.83<\/td>\n -0.69<\/td>\n 15<\/td>\n 23.09%<\/td>\n 13.85<\/td>\n <\/tr>\n
16<\/td>\n 0.85<\/td>\n 22.5<\/td>\n 125%<\/td>\n 46.75%<\/td>\n 1.25<\/td>\n 7.48<\/td>\n 16<\/td>\n 1.67<\/td>\n 16.76<\/td>\n 67.6%<\/td>\n 62.46%<\/td>\n 0.68<\/td>\n 9.99<\/td>\n 16<\/td>\n 1.05<\/td>\n 17.69<\/td>\n 76.9%<\/td>\n -1.44%<\/td>\n 0.77<\/td>\n -0.23<\/td>\n 16<\/td>\n 0.83<\/td>\n 0<\/td>\n -100%<\/td>\n -10.59%<\/td>\n -1<\/td>\n -1.69<\/td>\n 16<\/td>\n 24.30%<\/td>\n 15.55<\/td>\n <\/tr>\n
17<\/td>\n 0.82<\/td>\n 10<\/td>\n 0%<\/td>\n 44.00%<\/td>\n 1.25<\/td>\n 7.48<\/td>\n 17<\/td>\n 1.55<\/td>\n 21<\/td>\n 110%<\/td>\n 65.26%<\/td>\n 1.10<\/td>\n 11.09<\/td>\n 17<\/td>\n 1.04<\/td>\n 0<\/td>\n -100%<\/td>\n -7.24%<\/td>\n -1<\/td>\n -1.23<\/td>\n 17<\/td>\n 0.82<\/td>\n 0<\/td>\n -100%<\/td>\n -15.85%<\/td>\n -1<\/td>\n -2.69<\/td>\n 17<\/td>\n 21.54%<\/td>\n 14.65<\/td>\n <\/tr>\n
18<\/td>\n 0.82<\/td>\n 18.7<\/td>\n 87%<\/td>\n 46.39%<\/td>\n 0.87<\/td>\n 8.35<\/td>\n 18<\/td>\n 1.50<\/td>\n 0<\/td>\n -100%<\/td>\n 56.08%<\/td>\n -1<\/td>\n 10.09<\/td>\n 18<\/td>\n 0.98<\/td>\n 0<\/td>\n -100%<\/td>\n -12.39%<\/td>\n -1<\/td>\n -2.23<\/td>\n 18<\/td>\n 0.82<\/td>\n 18.47<\/td>\n 84.7%<\/td>\n -10.26%<\/td>\n 0.85<\/td>\n -1.85<\/td>\n 18<\/td>\n 19.95%<\/td>\n 14.37<\/td>\n <\/tr>\n
19<\/td>\n 0.79<\/td>\n 18.33<\/td>\n 83.3%<\/td>\n 48.33%<\/td>\n 0.83<\/td>\n 9.18<\/td>\n 19<\/td>\n 1.47<\/td>\n 0<\/td>\n -100%<\/td>\n 47.86%<\/td>\n -1<\/td>\n 9.09<\/td>\n 19<\/td>\n 0.95<\/td>\n 17.41<\/td>\n 74.1%<\/td>\n -7.84%<\/td>\n 0.74<\/td>\n -1.49<\/td>\n 19<\/td>\n 0.75<\/td>\n 0<\/td>\n -100%<\/td>\n -14.98%<\/td>\n -1<\/td>\n -2.85<\/td>\n 19<\/td>\n 18.34%<\/td>\n 13.94<\/td>\n <\/tr>\n
20<\/td>\n 0.74<\/td>\n 0<\/td>\n -100%<\/td>\n 40.91%<\/td>\n -1<\/td>\n 8.18<\/td>\n 20<\/td>\n 1.39<\/td>\n 0<\/td>\n -100%<\/td>\n 40.47%<\/td>\n -1<\/td>\n 8.09<\/td>\n 20<\/td>\n 0.87<\/td>\n 16.67<\/td>\n 66.7%<\/td>\n -4.12%<\/td>\n 0.67<\/td>\n -0.82<\/td>\n 20<\/td>\n 0.67<\/td>\n 0<\/td>\n -100%<\/td>\n -19.24%<\/td>\n -1<\/td>\n -3.85<\/td>\n 20<\/td>\n 14.51%<\/td>\n 11.61<\/td>\n <\/tr>\n
21<\/td>\n 0.69<\/td>\n 0<\/td>\n -100%<\/td>\n 34.20%<\/td>\n -1<\/td>\n 7.18<\/td>\n 21<\/td>\n 1.29<\/td>\n 10<\/td>\n 0%<\/td>\n 38.54%<\/td>\n 0<\/td>\n 8.09<\/td>\n 21<\/td>\n 0.85<\/td>\n 20<\/td>\n 100%<\/td>\n 0.84%<\/td>\n 1<\/td>\n 0.18<\/td>\n 21<\/td>\n 0.62<\/td>\n 0<\/td>\n -100%<\/td>\n -23.08%<\/td>\n -1<\/td>\n -4.65<\/td>\n 21<\/td>\n 12.63%<\/td>\n 10.61<\/td>\n <\/tr>\n
22<\/td>\n 0.64<\/td>\n 19.09<\/td>\n 90.9%<\/td>\n 36.78%<\/td>\n 0.91<\/td>\n 8.09<\/td>\n 22<\/td>\n 1.20<\/td>\n 0<\/td>\n -100%<\/td>\n 32.25%<\/td>\n -1<\/td>\n 7.09<\/td>\n 22<\/td>\n 0.85<\/td>\n 17.14<\/td>\n 71.4%<\/td>\n 4.05%<\/td>\n 0.71<\/td>\n 0.89<\/td>\n 22<\/td>\n 0.51<\/td>\n 18.77<\/td>\n 87.7%<\/td>\n -18.05%<\/td>\n 0.88<\/td>\n -3.97<\/td>\n 22<\/td>\n 13.76%<\/td>\n 12.11<\/td>\n <\/tr>\n
23<\/td>\n 0.55<\/td>\n 21<\/td>\n 110%<\/td>\n 39.96%<\/td>\n 1.10<\/td>\n 9.19<\/td>\n 23<\/td>\n 1.10<\/td>\n 18.77<\/td>\n 87.7%<\/td>\n 34.66%<\/td>\n 0.88<\/td>\n 7.97<\/td>\n 23<\/td>\n 0.77<\/td>\n 18.7<\/td>\n 87%<\/td>\n 7.66%<\/td>\n 0.87<\/td>\n 1.76<\/td>\n 23<\/td>\n 0.49<\/td>\n 0<\/td>\n -100%<\/td>\n -21.61%<\/td>\n -1<\/td>\n -4.97<\/td>\n 23<\/td>\n 15.17%<\/td>\n 13.95<\/td>\n <\/tr>\n
24<\/td>\n 0.50<\/td>\n 18.33<\/td>\n 83.3%<\/td>\n 41.77%<\/td>\n 0.83<\/td>\n 10.03<\/td>\n 24<\/td>\n 1.01<\/td>\n 16.25<\/td>\n 62.5%<\/td>\n 35.82%<\/td>\n 0.63<\/td>\n 8.60<\/td>\n 24<\/td>\n 0.76<\/td>\n 0<\/td>\n -100%<\/td>\n 3.17%<\/td>\n -1<\/td>\n 0.76<\/td>\n 24<\/td>\n 0.44<\/td>\n 0<\/td>\n -100%<\/td>\n -24.88%<\/td>\n -1<\/td>\n -5.97<\/td>\n 24<\/td>\n 13.97%<\/td>\n 13.41<\/td>\n <\/tr>\n
25<\/td>\n 0.50<\/td>\n 0<\/td>\n -100%<\/td>\n 36.10%<\/td>\n -1<\/td>\n 9.03<\/td>\n 25<\/td>\n 0.77<\/td>\n 0<\/td>\n -100%<\/td>\n 30.38%<\/td>\n -1<\/td>\n 7.60<\/td>\n 25<\/td>\n 0.74<\/td>\n 0<\/td>\n -100%<\/td>\n -0.96%<\/td>\n -1<\/td>\n -0.24<\/td>\n 25<\/td>\n 0.43<\/td>\n 16.17<\/td>\n 61.7%<\/td>\n -21.41%<\/td>\n 0.62<\/td>\n -5.35<\/td>\n 25<\/td>\n 11.03%<\/td>\n 11.03<\/td>\n <\/tr>\n
26<\/td>\n 0.46<\/td>\n 23.5<\/td>\n 135%<\/td>\n 39.90%<\/td>\n 1.35<\/td>\n 10.38<\/td>\n 26<\/td>\n 0.73<\/td>\n 10<\/td>\n 0%<\/td>\n 29.22%<\/td>\n 0<\/td>\n 7.60<\/td>\n 26<\/td>\n 0.73<\/td>\n 17.69<\/td>\n 76.9%<\/td>\n 2.04%<\/td>\n 0.77<\/td>\n 0.53<\/td>\n 26<\/td>\n 0.28<\/td>\n 20.6<\/td>\n 106%<\/td>\n -16.51%<\/td>\n 1.06<\/td>\n -4.29<\/td>\n 26<\/td>\n 13.66%<\/td>\n 14.21<\/td>\n <\/tr>\n
27<\/td>\n 0.37<\/td>\n 18.33<\/td>\n 83.3%<\/td>\n 41.51%<\/td>\n 0.83<\/td>\n 11.21<\/td>\n 27<\/td>\n 0.48<\/td>\n 0<\/td>\n -100%<\/td>\n 24.43%<\/td>\n -1<\/td>\n 6.60<\/td>\n 27<\/td>\n 0.60<\/td>\n 0<\/td>\n -100%<\/td>\n -1.74%<\/td>\n -1<\/td>\n -0.47<\/td>\n 27<\/td>\n 0.27<\/td>\n 0<\/td>\n -100%<\/td>\n -19.60%<\/td>\n -1<\/td>\n -5.29<\/td>\n 27<\/td>\n 11.15%<\/td>\n 12.04<\/td>\n <\/tr>\n
28<\/td>\n 0.22<\/td>\n 19.09<\/td>\n 90.9%<\/td>\n 43.27%<\/td>\n 0.91<\/td>\n 12.12<\/td>\n 28<\/td>\n 0.38<\/td>\n 0<\/td>\n -100%<\/td>\n 19.99%<\/td>\n -1<\/td>\n 5.60<\/td>\n 28<\/td>\n 0.48<\/td>\n 18<\/td>\n 80%<\/td>\n 1.18%<\/td>\n 0.80<\/td>\n 0.33<\/td>\n 28<\/td>\n 0.20<\/td>\n 17.14<\/td>\n 71.4%<\/td>\n -16.35%<\/td>\n 0.71<\/td>\n -4.58<\/td>\n 28<\/td>\n 12.02%<\/td>\n 13.46<\/td>\n <\/tr>\n
29<\/td>\n 0.21<\/td>\n 20<\/td>\n 100%<\/td>\n 45.23%<\/td>\n 1<\/td>\n 13.12<\/td>\n 29<\/td>\n 0.29<\/td>\n 0<\/td>\n -100%<\/td>\n 15.85%<\/td>\n -1<\/td>\n 4.60<\/td>\n 29<\/td>\n 0.42<\/td>\n 0<\/td>\n -100%<\/td>\n -2.31%<\/td>\n -1<\/td>\n -0.67<\/td>\n 29<\/td>\n 0.17<\/td>\n 0<\/td>\n -100%<\/td>\n -19.24%<\/td>\n -1<\/td>\n -5.58<\/td>\n 29<\/td>\n 9.88%<\/td>\n 11.46<\/td>\n <\/tr>\n
30<\/td>\n 0.11<\/td>\n 21.5<\/td>\n 115%<\/td>\n 47.56%<\/td>\n 1.15<\/td>\n 14.27<\/td>\n 30<\/td>\n 0.24<\/td>\n 18.33<\/td>\n 83.3%<\/td>\n 18.10%<\/td>\n 0.83<\/td>\n 5.43<\/td>\n 30<\/td>\n 0.37<\/td>\n 18.7<\/td>\n 87%<\/td>\n 0.67%<\/td>\n 0.87<\/td>\n 0.20<\/td>\n 30<\/td>\n 0.15<\/td>\n 0<\/td>\n -100%<\/td>\n -21.93%<\/td>\n -1<\/td>\n -6.58<\/td>\n 30<\/td>\n 11.10%<\/td>\n 13.32<\/td>\n <\/tr>\n
31<\/td>\n 0.07<\/td>\n 0<\/td>\n -100%<\/td>\n 42.80%<\/td>\n -1<\/td>\n 13.27<\/td>\n 31<\/td>\n 0.16<\/td>\n 18<\/td>\n 80%<\/td>\n 20.09%<\/td>\n 0.80<\/td>\n 6.23<\/td>\n 31<\/td>\n 0.35<\/td>\n 17.41<\/td>\n 74.1%<\/td>\n 3.04%<\/td>\n 0.74<\/td>\n 0.94<\/td>\n 31<\/td>\n 0.04<\/td>\n 0<\/td>\n -100%<\/td>\n -24.45%<\/td>\n -1<\/td>\n -7.58<\/td>\n 31<\/td>\n 10.37%<\/td>\n 12.86<\/td>\n <\/tr>\n
32<\/td>\n 0.01<\/td>\n 21<\/td>\n 110%<\/td>\n 44.90%<\/td>\n 1.10<\/td>\n 14.37<\/td>\n 32<\/td>\n 0.07<\/td>\n 0<\/td>\n -100%<\/td>\n 16.34%<\/td>\n -1<\/td>\n 5.23<\/td>\n 32<\/td>\n 0.01<\/td>\n 20.5<\/td>\n 105%<\/td>\n 6.22%<\/td>\n 1.05<\/td>\n 1.99<\/td>\n 32<\/td>\n 0.04<\/td>\n 0<\/td>\n -100%<\/td>\n -26.81%<\/td>\n -1<\/td>\n -8.58<\/td>\n 32<\/td>\n 10.16%<\/td>\n 13.01<\/td>\n <\/tr>\n <\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n
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Method #2b<\/em><\/strong> – Use a cutoff of a specific (ego – Line) difference. For example, only taking the bets with an (ego – line) difference of 1 or more. If one did use this cutoff value of 1 or more between the ego prediction and the line set by the sportsbook for each of the first 4 seasons, he or she would have made 64 total bets with an average (weighted) Return on Investment of 19.54%, generating 12.51 Total Units. Conveniently, 64 bets across 4 seasons is an average of 16 bets per season, matching the Number of Bets from the example from Method #2a. Counter to what I would have thought, simply taking the top 16 bets each season in Method #2a actually results in a higher average ROI, therefore generating a higher Total Units than using the cutoff mark of (ego – line) difference in this Method. Below is a table of results if one were to use the same cutoff for each of the 4 seasons.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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Cutoff<\/th>AVG # of Bets\/Bet # Equivalent<\/th>Total # of Bets<\/th>RROI<\/th>Total Units<\/th><\/tr><\/thead>
2.40<\/td>1.5<\/td>6<\/td>29.47%<\/td>1.77<\/td><\/tr>
2.00<\/td>4.5<\/td>18<\/td>22.83%<\/td>4.11<\/td><\/tr>
1.80<\/td>5.75<\/td>23<\/td>25.83%<\/td>5.84<\/td><\/tr>
1.60<\/td>8<\/td>32<\/td>26.75%<\/td>8.02<\/td><\/tr>
1.40<\/td>9.75<\/td>39<\/td>24.52%<\/td>9.56<\/td><\/tr>
1.20<\/td>11.75<\/td>47<\/td>20.84%<\/td>9.79<\/td><\/tr>
1.10<\/td>14.25<\/td>57<\/td>25.39%<\/td>14.47<\/td><\/tr>
1.00<\/td>16<\/td>64<\/td>19.55%<\/td>12.51<\/td><\/tr>
0.80<\/em><\/td>20.5<\/em><\/td>82<\/em><\/td>19.50%<\/em><\/td>15.99<\/em><\/td><\/tr>
0.75<\/td>21.75<\/td>87<\/td>16.89%<\/td>14.69<\/td><\/tr>
0.60<\/td>24<\/td>96<\/td>10.80%<\/td>10.37<\/td><\/tr>
0.50<\/td>25<\/td>100<\/td>12.18%<\/td>12.18<\/td><\/tr>
0.40<\/td>26.75<\/td>107<\/td>10.23%<\/td>10.95<\/td><\/tr>
0.33<\/td>27.75<\/td>111<\/td>11.16%<\/td>12.39<\/td><\/tr>
0.20<\/td>29.5<\/td>118<\/td>12.63%<\/td>14.91<\/td><\/tr>
0.10<\/strong><\/td>30.5<\/strong><\/td>122<\/strong><\/td>12.18%<\/strong><\/td>14.86<\/strong><\/td><\/tr><\/tbody><\/table>
Highest Total Units of the cutoffs above<\/em> \/ Cutoff equivalent of the 52.4% cutoff for Method #3b<\/strong><\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n
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