Entropi temelli Lanchester Savaş Modeli ile bir futbol maçının analizi

Yıl 2021, , 800 - 821, 31.07.2021

Nuri Ömürbek , Gamze Kılınç , Meltem Karaatlı

https://doi.org/10.25287/ohuiibf.776905

Öz

Eskiden beri kullanılmakta olan savaş strateji modelleri karar vermeye yardımcı modellerdir. Lanchester savaş kanunları, Frederick Lanchester’ın II. Dünya Savaşı sırasında geliştirmiş olduğu savunma stratejilerini temel alan matematiksel bir savaş modelidir. Bu model savaş ya da mücadele içeren olaylarda matematiksel bir analiz ile simülatör görevi görmektedir. Diferansiyel denklemler yardımıyla, tarafların çeşitli durumlar altındaki yıpranma oranları hesaplanır ve olay matematiksel olarak canlandırılır. Böylece, tarafların farklı senaryolar altında vereceği tepkilerin öngörülmesi ile risk analizi ve karar verme aşamaları daha sağlıklı bir şekilde gerçekleştirilmiş olacaktır. Günümüzde Lanchester’ın savaş modelleri sadece savaş stratejilerinde değil aynı zamanda karşılıklı rekabet halinde olan tüm durumlarda kullanılmaktadır. Lanchester denklemleri; işletmelerin risk analizi ve pazar paylarının belirlenmesinde, hayvan gruplarının mücadelesinde, biyoloji ve sağlık gibi çeşitli alanlarda kullanılmaktadır. Bu çalışmada ise Lanchester savaş modeli Süper Lig kapsamında 23.02.2020 tarihinde oynanan Fenerbahçe-Galatasaray maçına uyarlanmıştır. Çalışmanın amacı, Lanchester denklemleri yardımıyla çeşitli durumlar altında tarafların saldırı-savunma stratejilerinin incelenmesidir. Bu model kapsamında senaryo niteliği taşıyan Fenerbahçe’nin favori olduğu durum ile Galatasaray’ın kazandığı mevcut durumların matematiksel analizi yapılmıştır. Analizler sonucunda; senaryo niteliği taşıyan modelde Fenerbahçe takımı kazanmıştır. Mevcut durum analizinde ise gerçekleşen durumla uyumlu sonuçlara ulaşıldığı görülmüştür.

Anahtar Kelimeler

Senaryo Analizi, Strateji, Lanchester Savaş Modeli, FB-GS Maçı

Analysis of a football match with the entropy based Lanchester War Model

Öz

Warfare strategy models that have been used since the past are models that help decision making. Lanchester’s war laws are a mathematical model of warfare based on the defense strategies developed during II. World War by Frederick Lanchester. This model acts as a simulator with a mathematical analysis in events involving war or struggle. With the help of differential equations, the attrition rates of the parties under various conditions are calculated and the event is mathematically animated. Thus, risk analysis and decision-making stages will be carried out in a healthier way by predicting the reactions of the parties under different scenarios. Today, Lanchester's war models are used not only in war strategies, but also in all cases where there is mutual competition. Lanchester equations are used in various fields such as in risk analysis of enterprises and in determining market shares, in the struggle of animal groups, biology and health. In this study, Lanchester war model was adapted to Fenerbahçe-Galatasaray match played on 23.02.2020 within the scope of Super League. The aim of this study is to examine the attack-defense strategies of the parties under various cases with the help of Lanchester equations. Within the scope of this model, a mathematical analysis of the scenario situation in which Fenerbahçe was the favorite and the current situation in which Galatasaray won. As a result of the analysis; Fenerbahçe team won in the model which is a scenario. In the current situation analysis, it was seen that results compatible with the actual situation were achieved.

Anahtar Kelimeler

Scenario analysis, Strategy, Lanchester War Model, FB-GS Match

Kaynakça

• Bauer, H. (2019). Mathematical models: the lanchester equations and the zombie apocalypse, Undergraduate Theses and Capstone Projects, 3-39. https://digitalshowcase.lynchburg.edu/cgi/viewcontent.cgi?article=1122&context=utcp
• Cerny, D., Lee, K., Medal, J., & Blumstein, D.T. (2019). Applying lanchester’s laws to the interspecific competition of coral reef fish. Behavioral Ecology, 30(2), 426-433. DOI: 10.1093/beheco/ary182
• Chalikias, M., & Skordoulis, M. (2017). Implementation of F.W. lanchester’s combat model in a supply chain in duopoly: the case of coca-cola and pepsi in greece. Operational Research, 17(3), 737-745. DOI: 10.1007/s12351-016-0226-0
• Clausius, R. (1879). The mechanical theory of heat. Macmillan. DOI: 10.1038/021367a0
• Deitchman, S.J. (1962). A Lanchester model of guerrilla warfare. Operations Research, 10(6), 818-827. DOI: 10.1287/opre.10.6.818
• Dockner, E.J., & Jorgensen, S. (2018). Strategic rivalry for market share: a contest theory approach to dynamic advertising competition. Dynamic Games and Applications, 8(3), 468-489. DOI: 10.1007/s13235-018-0242-1
• Engel, J.H. (1954). A verification of Lanchester's law. Journal of the Operations Research Society of America, 2(2), 163-171. DOI: 10.1287/opre.2.2.163
• Flores, J.C. (2017). Trojan war displayed as a full annihilation–diffusion–reaction model. Physica A: Statistical Mechanics and its Applications, 467, 432-435. DOI: 10.1016/j.physa.2016.10.049
• Hohzaki, R., & Higashio, T. (2016). An attrition game on a network ruled by lanchester’s square law. Journal of the Operational Research Society, 67(5), 691-707. DOI :10.1057/jors.2015.87
• https://www.mackolik.com/, Erişim Tarihi: 01.03.2020.
• Jaynes, E.T. (1957). Information theory and statistical mechanics. Physical review, 106(4), 620-630. DOI: 10.1103/PhysRev.106.620
• Johnson, D.D., & MacKay, N.J. (2015). Fight the power: Lanchester's laws of combat in human evolution. Evolution and Human Behavior, 36(2), 152-163. DOI: 10.1016/j.evolhumbehav.2014.11.001
• Jorgensen, S., & Sigue, S. (2020). A lanchester-type dynamic game of advertising and pricing. In Games in Management Science, 1-14. DOI: 10.1007/978-3-030-19107-8_1
• Kress, M., Caulkins, J.P., Feichtinger, G., Grass, D., & Seidl, A. (2018). Lanchester model for three-way combat. European Journal of Operational Research, 264(1), 46-54. DOI: 10.1016/j.ejor.2017.07.026
• Lebowitz, J.L. (1993). Boltzmann's entropy and time's arrow. Physics today, 46, 32-38. DOI: 10.1063/1.881363
• Mon, D.L., Cheng, C.H., & Lin, J.C. (1994). Evaluating weapon system using fuzzy analytic hierarchy process based on entropy weight. Fuzzy sets and systems, 62(2), 127-134. DOI: 10.1016/0165-0114(94)90052-3
• Özdağoğlu, A. (2013). Lanchester stratejisi ve sistem dinamikleri: büyük taarruz üzerinde inceleme. Savunma Bilimleri Dergisi, 12(2), 63-94. DOI: 10.17134/sbd.68945
• Özdağoğlu, A. (2019). Lanchester N2 kanununun preveze deniz zaferine uyarlanması ve alternatif senaryoların analizi. Izmir Democracy University Social Sciences Journal, 2(1), 18-40. https://dergipark.org.tr/tr/download/article-file/751705
• Özdağoğlu, A., Özdağoğlu, G., Göktepe, E., & Eyüboğlu, K. (2013). İlaç sektöründe pazar paylarının analizi: yeni lanchester stratejisi ve sistem dinamikleri. Yönetim ve Ekonomi: Celal Bayar Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 20(2), 51-65. https://dergipark.org.tr/tr/download/article-file/146134
• Shannon, C.E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423. DOI: 10.1002/j.1538-7305.1948.tb01338.x
• Sheeba, P.S., & Ghose, D. (2008). Optimal resource allocation and redistribution strategy in military conflicts with Lanchester square law attrition. Naval Research Logistics , 55(6), 581-591. DOI: 10.1002/nav.20303
• Stanescu, M. A., Barriga, N., & Buro, M. (2015, Eylül). Using Lanchester attrition laws for combat prediction in StarCraft. In Eleventh artificial intelligence and interactive digital entertainment conference. https://skatgame.net/mburo/ps/aiide15-combat.pdf
• Tang, J., Leu, G., & Abbass, H.A. (2019). Simulation and Computational Red Teaming for Problem Solving. John Wiley & Sons. DOI:10.1002/9781119527183
• Wiper, M.P., Pettit, L.I., & Young, K.D. (2000). Bayesian inference for a Lanchester type combat model. Naval Research Logistics, 47(7), 541-558. DOI: 10.1002/1520-6750(200010)47:7<541::AID-NAV1>3.0.CO;2-0