Entropi temelli Lanchester Savaş Modeli ile bir futbol maçının analizi

Year 2021, , 800 - 821, 31.07.2021

Nuri Ömürbek , Gamze Kılınç , Meltem Karaatlı

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

Abstract

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.

Keywords

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

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

Abstract

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.

Keywords

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

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