Arturo Yee, Eunice Campirán, Matías Alvarado



Gaming and Strategic Choices to American Football

pdf PDF


We propose American football (AF) modeling by means of a context-free grammar (CFG) that cores correct combination of players’ actions to algorithmic simulation. For strategic choices, the Nash equilibrium (NE) and the Pareto efficiency (PE) are used to select AF strategy profiles having better percentage to success games: results from game simulations show that the AF team with a coach who uses NE or PE wins more games than teams that not use strategic reasoning. The team using strategic reasoning has an advantage that ranges from 30% to 65%. Using a single NE, the corresponding advantage is approximately 60% on average. Using a single PE, the corresponding advantage is approximately 35% on average. Feeding simulations with National Football League (NFL) statistics for particular teams and specific players, results close-fit to the real games played by them. Moreover, statistics confidence intervals and credible intervals support conclusions. On the base of CFG modeling and use of statistics (history of teams and players), forecasting results on future games is settled.


American football computer simulation, strategic choices, Nash equilibrium, Pareto efficiency, CFG-statistics-based prediction


[1] Lindsey GR, An Investigation of Strategies in Baseball, Journal of Operation Research, Vol. 11, No. 4, 1963, pp. 477-501. [1] Lindsey GR, An Investigation of Strategies in Baseball, Journal of Operation Research, Vol. 11, No. 4, 1963, pp. 477-501. 

[2] Williams T., Winning Strategies for Offense and Defense, Publishing Baseball’s Best, 2005. 

[3] Yee A, Alvarado M., Methodology for the Modeling of Multi-Player Games, Proceedings of the 18th International Conference on Computers (CSCC '14). Santorini Island, Greece, July 17-21, 2014, pp. 353 - 8. 

[4] Alvarado M, Yee A, Fernández J., Simulation of American football gaming, Advances in Sport Science and Computer Science, Vol. 57, 2014. 

[5] Gonzalez AJ, Gross DL., Learning tactics from a sports game-based simulation, International Journal of Computer Simulation, Vol.5, No.2, 1995, pp. 127-48. 

[6] Alaways LW, Hubbard M., Experimental determination of baseball spin and lift, Journal of Sport Science, Vol. 19, No. 5, 2001, pp. 349- 58. 

[7] Yee A, Rodríguez R, Alvarado M., Analysis of Strategies in American Football Using Nash Equilibrium. In: Agre G, Hitzler P, Krisnadhi A, Kuznetsov S, (Eds.) Artificial Intelligence: Methodology, Systems, and Applications: Springer International Publishing, 2014, pp. 286-94. 

[8] McMillan J., Games strategies and managers, Publishing Oxford University Press, 1996. 

[9] Song C, Boulier BL, Stekler HO., The comparative accuracy of judgmental and model forecasts of American football games, International Journal of Forecasting, Vol. 23, No. 3, 2007, pp. 405-13. 

[10] Baker RD, McHale IG., Forecasting exact scores in National Football League games, International Journal of Forecasting, Vol. 29, No. 1, 2013, pp. 122-30. 

[11] Deutsch SJ, Bradburn PM., A simulation model for American football plays, Applied Mathematical Model, Vol. 5, No. 1, 1981, pp. 13-23. 

[12] Janssen CTL, Daniel TE., A Decision Theory Example in Football, Decision Science, Vol. 15, No. 2, 1984, pp. 253-9. 

[13] Association AFC., Offensive Football Strategies, Champaign, IL, Human Kinetics, 2000. 

[14] Camp W, Badgley CS., American Football, Publishing Createspace Independent Pub, 2009. 

[15] Gifford C., American Football Tell me about Sport, London, U.K., Publishing Evans, 2009. 

[16] AL-Mutairi MS., Two-decision-maker cooperative games with fuzzy preferences, Proceedings of the Industrial Engineering and Engineering Management (IEEM), 2010, pp. 6- 12. 

[17] Mintzberg H, Quinn JB., The Strategy Process: Concepts, Context, Cases. 2nd ed. Englewood Cliffs, N. J., Publishing Pretice Hall, 1991. 

[18] Redondo FV., Economy and Games, Spain, Publishing Antoni Bosh, 2000. 

[19] Nisan N, Roughgarden T, Tardos E, Vazirani VV., Algorithmic Game Theory, Cambridge Publishing University Press, 2007. 

[20] Chalkiadakis G, Elkind E, Wooldridge M., Computational Aspects of Cooperative Game Theory, Publishing Morgan and Claypool, 2011. 

[21] Bell D, Raiffa H, Tversky A., Decision Making, Publishing Cambridge University Press, 1999. 

[22] Dutta PK., Strategies and games: theory and practice, USA, Publishing Massachusetts Institute of Tecnology, 1999. 

[23] McGrew AG, Wilson MJ., Decision making: approaches and analysis, Publishing Manchester University Press, 1982. 

[24] Nash J., Non-Cooperative Games, The annals of Mathematics, Vol. 54, No. 2, 1951, pp. 286- 95. 

[25] Pareto V. Cours d'économie politique. F Rouge Lausanne, 1896, pp. 1-2. 

[26] Alvarado M, Rendón AY., Nash equilibrium for collective strategic reasoning, Expert Systems with Applications, Vol. 3, No. 15, 2012, pp.12014-25. 

[27] Miettinen K., Nonlinear Multiobjective Optimization, Publishing Springer US, 1998. 

[28] Sipser M., Introduction to Theory of Computation., 2nd ed: Thomson Course Thechnology, 2006. 

[29] Young KD, Lewis RJ., What Is Confidence? Part 2: Detailed Definition and Determination of Confidence Intervals, Annals of Emergency Medicine, Vol. 30, No. 3, 1997, pp. 311-8. 

[30] Scott A, Seber G., Difference of Proportions from the Same Survey, The American Statistician, Vol. 37, No. 4,. 1983, pp. 319-20. 

[31] Price RM, Bonett DG., Confidence intervals for a ratio of two independent binomial proportions, Statistics in Medicine, Vol. 27, No. 26, 2008, pp. 497-508. 

[32] Alvarado M, Yee A, Cocho G., Simulation of Baseball Gaming by Cooperation and NonCooperation Strategies, Computación y Sistemas, Vol. 18, No. 4, 2014, pp. 693 - 708. 

[33] Yee A, Alvarado M., Methodology for the Modeling of Multi-Player Games, Proceedings of the 18th International Conference on Computers (part of CSCC '14), Santorini Island, Greece, July 17-21, 2014, pp. 353 - 8. 

[34] Coen C., Mixing rules: When to cooperate in a multiple-team competition, Simulation Modelling Practice and Theory, Vol. 14, No.4,. 2006, pp. 423-37. 

[35] Capraro V, Venanzi M, Polukarov M, Jennings N. Cooperative Equilibria in Iterated Social Dilemmas. In: Vöcking B, (Ed.). Algorithmic Game Theory: Springer Berlin Heidelberg, 2013, pp. 146-58. 

[36] Corley HW, Kwain P., A Cooperative Dual to the Nash Equilibrium for Two-Person Prescriptive Games, Journal of Applied Mathematics, 2014, pp. 1-4. 

[37] Konrad KA., Altruism and envy in contests: An evolutionarily stable symbiosis. Social Choice Welfare, Vol. 22, No. 3, 2004, pp. 479-90. 

[38] Roy Fl., The rise and fall of collective strategies: a case study, International Journal of Entrepreneurship and Small Business, Vol. 5, No. 2, 2008, pp. 124-42. 

[39] Viguier L, Vielle M, Haurie A, Bernard A., A two-level computable equilibrium model to assess the strategic allocation of emission allowances within the European union, Computer and Operations Research, Vol. 33, No. 2, 2006, pp. 369-85. 

[40] Flåm SD. Balanced environmental games. Computer and Operations Research, Vol. 33, No. 2, 2006, pp. 401-8. 

[41] Dornhaus A., Finding optimal collective strategies using individual-based simulations: colony organization in social insects, Mathematical and Computer Modelling of Dynamical Systems, Vol. 18, No. 1, 2012, pp. 25-37.

Cite this paper

Arturo Yee, Eunice Campirán, Matías Alvarado. (2016) Gaming and Strategic Choices to American Football. International Journal of Mathematical and Computational Methods, 1, 355-371


Copyright © 2016 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0