The Poologic Calculator now shows the expected points for the recommended bracket. This can be used to compare sheets with different champ picks. The value might be misleading for comparing different models.
Instructions --- How to Use the Results --- Theory of operation --- FAQ --- Model explainer --- Model probabilities
Instructions
- Fill in the standard scoring factors for each round. When you correctly predict a win, the standard scoring points for that game equal the standard scoring factor for the game's round.
- Fill in the seed scoring factors for each round. When you correctly predict a win, the seed scoring points for that game are calculated by multiplying the winning seed times the seed factor for the game's round.
- Fill in the underdog scoring factors for each round. When you correctly predict an upset, the underdog scoring points for that game are calculated by multiplying the difference between the opponent seed and the winning seed times the underdog factor for the game's round.
- Fill in the upset scoring factors for each round. When you correctly predict an upset, the upset scoring points for that game equal to the upset scoring factor for the game's round.
- Fill in the useed scoring factors for each round. Useed scoring factors are used like seed scoring factors, except that they are only awarded for upsets.
- Fill in the bonus scoring factors for each round. Bonus points are awarded if the winning seed is equal to or greater than the limit (see below).
- Fill in the limits for the bonus points for each round. The winning seed must equal or exceed this limit if bonus points are to be awarded.
- If non-zero underdog factors, upset factors, or useed factors are specified, then specify whether the predicted or actual opponent should be used to determine underdog, upset, and useed points.
- If non-zero underdog factors, upset factors, or useed factors are specified, indicate whether both a predicted upset and an actual upset are required (or not required) to award underdog, upset, and useed points.
- Indicate whether standard scoring points are awarded for upsets.
- If you are using a multiple entry or contrarian strategy, then you can constrain the champ to a particular team. By default, the calculator is constrained to "any team" (i.e., unconstrained) and the calculator will pick the champ that provides the overall expected-point-maximizing pool sheet. See the Poologic FAQ for more information on the multiple entry and contrarian strategies.
- Specify the probability model. For a description of the probabilty models, go here. For the probability tables for each model, go here.
- The game score standard deviation (SD) adjustment (%) can be used to see how sensitive this picks are to game score. Reducing the SD tends to reduce the number of upsets and this has little or no effect for pools with no upset incentives. All the unadjusted model-specific SDs are around 11 points, so a 10% adjustment is around 1 point.
- Hit the CALCULATE NOW button.
The points from the different types of round factors are added. The overall formula for the points award for a win not involving an upset is:
standard_factor + seed_factor*seed
If the requirements are met for an upset, then the formula is:
standard_factor + seed_factor*seed + upset_factor + (winner_seed - opponent_seed)*underdog_factor + useed_factor*seed
For example, suppose the standard scoring factor for the final round is 32, the seed scoring factor is 5, the underdog scoring factor is 7,the upset factor is 9, and the useed factor is 11. Suppose that the actual opponent is used in underdog/upset scoring and that both a predicted and an actual upset are not required to award underdog/upset points.
- Suppose that you predict that a 1 seed will beat a 2 seed in the final. Suppose that the team that you pick wins. Then you will be awarded 32 + 5 = 37 points for that game.
- Suppose that you predict that a 3 seed will beat a 4 seed in the final round. Suppose that the team that you pick wins and it's ACTUAL opponent is a 1 seed. Then you will be awarded 32 + 3*5 + 2*7 + 9 + 3*11 = 103 points for that game. (If both a predicted and an actual upset were required, then only 47 points would have been awarded.)
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BACK TO THE CALCULATORHow to Make Best Use of the Results
Submitting multiple pool entries is highly recommended to optimize your chances of winning. In standard-scoring pool with as few as 20 total entries, it is usually a good idea to submit four entries with different teams picked as champion. See the Poologic FAQ for details on the recommended multiple pool sheet strategy. You may be able to use the ROI Calculator to determine the best championship picks.
The real-world application data that I have seems to indicate that a multiple-entry strategy based on betting sheets from the different probability models might be superior to varying the championship pick in a pool with fairly large upset incentives. See this study.
Poologic Calculator does not take local or nationwide favorites into account. You may be able to use the ROI Calculator to adjust for favorites. Check out the Poologic FAQ to learn about contrarian strategy.
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BACK TO THE CALCULATORTheory of Operation
The theory behind the unconstrained calculator is represented by the "Best of All" strategy presented in Breiter and Carlin[1]. Beiter and Carlin used a brute force Monte Carlo calculation to arrive at the sheet that maximizes the expected point total. The Poologic Calculator uses a more efficient direct calculation, based on a recurrence relation, to arrive at the maximizing sheet. The recurrence relation takes advantage of the fact that the maximum expected point total for the subsheet ending at a particular game can be represented as a function of the maximum expected point total for the two sub-sheets that end in the feeder games for that game. See Kaplan and Garstka [2] for a detailed description of the recurrence relation algorithm.
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BACK TO THE CALCULATORMail questions to Tom Adams.
References:
[1] "How to Play Office Pools If You Must" by David Breiter and Bradley Carlin (Chance Vol. 10, No 1, 1997, pp. 5-11)
[2] "March Madness and the Office Pool" by Edward H. Kaplan and Stanley J. Garstka (Management Science Vol. 7, No 3, March 2001, pp. 369-382)
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