Strategy optimization in beachvolleyball applying a two scale - PowerPoint PPT Presentation

Strategy optimization in beachvolleyball – applying a two scale approach to the olympic games Susanne Hoffmeister Jörg Rambau Chair of Buisness Mathematics University of Bayreuth MathSport, Padua 2017 Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 1 / 17

Sport Strategy Optimization Introduction identify a sport strategic decision of your team Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 2 / 17

Sport Strategy Optimization Introduction identify a sport strategic decision of your team ◮ may be opponent dependend Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 2 / 17

Sport Strategy Optimization Introduction identify a sport strategic decision of your team ◮ may be opponent dependend ◮ may change from match to match Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 2 / 17

Sport Strategy Optimization Introduction identify a sport strategic decision of your team ◮ may be opponent dependend ◮ may change from match to match model sport game as Markov Decision Process (MDP) Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 2 / 17

Sport Strategy Optimization Introduction identify a sport strategic decision of your team ◮ may be opponent dependend ◮ may change from match to match model sport game as Markov Decision Process (MDP) ◮ should capture the strategic question Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 2 / 17

Sport Strategy Optimization Introduction identify a sport strategic decision of your team ◮ may be opponent dependend ◮ may change from match to match model sport game as Markov Decision Process (MDP) ◮ should capture the strategic question ◮ can be evaluated for future matches Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 2 / 17

Sport Strategy Optimization Introduction identify a sport strategic decision of your team ◮ may be opponent dependend ◮ may change from match to match model sport game as Markov Decision Process (MDP) ◮ should capture the strategic question ◮ can be evaluated for future matches give recommendations Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 2 / 17

Sport Strategy Optimization Introduction identify a sport strategic decision of your team ◮ may be opponent dependend ◮ may change from match to match model sport game as Markov Decision Process (MDP) ◮ should capture the strategic question ◮ can be evaluated for future matches give recommendations ◮ for past and future matches Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 2 / 17

Sport Strategy Optimization Introduction identify a sport strategic decision of your team ◮ may be opponent dependend ◮ may change from match to match model sport game as Markov Decision Process (MDP) ◮ should capture the strategic question ◮ can be evaluated for future matches give recommendations ◮ for past and future matches ◮ for player performances varying with the day Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 2 / 17

Two Scale Approach Sketch of General Procedure strategic Question strategic recommendation Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 3 / 17

Two Scale Approach Sketch of General Procedure strategic Question strategic recommendation mathematical analysis rough level analytical opt numerical opt model s-MDP solution solution data opponent dependend ? Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 3 / 17

Two Scale Approach Sketch of General Procedure strategic Question strategic recommendation mathematical analysis rough level analytical opt numerical opt model s-MDP solution solution data opponent dependend ? detailled level g-MDP model data Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 3 / 17

Two Scale Approach Sketch of General Procedure strategic Question strategic recommendation mathematical analysis rough level analytical opt numerical opt model s-MDP solution solution data opponent dependend ? detailled level g-MDP model data observation skills Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 3 / 17

Two Scale Approach Sketch of General Procedure strategic Question strategic recommendation mathematical analysis rough level analytical opt numerical opt model s-MDP solution solution data opponent dependend ? detailled level g-MDP model simulation data observation skills Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 3 / 17

Two Scale Approach Sketch of General Procedure strategic Question strategic recommendation mathematical analysis rough level analytical opt numerical opt model s-MDP solution solution data opponent dependend ? detailled level g-MDP model validation simulation � data observation skills Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 3 / 17

Two Scale Approach Sketch of General Procedure strategic Question strategic recommendation mathematical analysis rough level analytical opt numerical opt numerical opt model s-MDP solution solution solution data opponent dependend transition probs ? detailled level g-MDP model validation simulation � data observation skills Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 3 / 17

strategic Question strategic recommendation Example Application s-MDP mathematical analysis optimal solution transition probabilities Beach Volleyball g-MDP validation simulation observation Skills Olympia 2012 : Brink/Reckermann vs. Alison/Emanuel Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 4 / 17

strategic Question strategic recommendation Example Application s-MDP mathematical analysis optimal solution transition probabilities Beach Volleyball g-MDP validation simulation observation Skills Olympia 2012 : Brink/Reckermann vs. Alison/Emanuel Result : 2:1 (23:32, 16:21, 16:14) Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 4 / 17

strategic Question strategic recommendation Example Application s-MDP mathematical analysis optimal solution transition probabilities Beach Volleyball g-MDP validation simulation observation Skills Olympia 2012 : Brink/Reckermann vs. Alison/Emanuel Result : 2:1 (23:32, 16:21, 16:14) Strategic Question – Risky or Safe? Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 4 / 17

strategic Question strategic recommendation Example Application s-MDP mathematical analysis optimal solution transition probabilities Beach Volleyball g-MDP validation simulation observation Skills Olympia 2012 : Brink/Reckermann vs. Alison/Emanuel Result : 2:1 (23:32, 16:21, 16:14) Strategic Question – Risky or Safe? Risky or save serve? (technique and target field) Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 4 / 17

strategic Question strategic recommendation Example Application s-MDP mathematical analysis optimal solution transition probabilities Beach Volleyball g-MDP validation simulation observation Skills Olympia 2012 : Brink/Reckermann vs. Alison/Emanuel Result : 2:1 (23:32, 16:21, 16:14) Strategic Question – Risky or Safe? Risky or save serve? (technique and target field) Risky or field attack? (technique and target field) Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 4 / 17

strategic Question strategic recommendation Example Application s-MDP mathematical analysis optimal solution transition probabilities Beach Volleyball g-MDP validation simulation observation Skills Olympia 2012 : Brink/Reckermann vs. Alison/Emanuel Result : 2:1 (23:32, 16:21, 16:14) Strategic Question – Risky or Safe? Risky or save serve? (technique and target field) Risky or field attack? (technique and target field) Blocking player Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 4 / 17

strategic Question strategic recommendation Example Application s-MDP mathematical analysis optimal solution transition probabilities Beach Volleyball g-MDP validation simulation observation Skills Olympia 2012 : Brink/Reckermann vs. Alison/Emanuel Result : 2:1 (23:32, 16:21, 16:14) Strategic Question – Risky or Safe? Risky or save serve? (technique and target field) Risky or field attack? (technique and target field) Blocking player Serving on which opponent player Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 4 / 17

strategic Question strategic recommendation Example Application – Beach Volleyball s-MDP mathematical analysis optimal solution transition probabilities s-MDP and g-MDP g-MDP validation simulation observation Skills actions are complete attacking sequences small number of states p serve a p serve ˆ a p serve a s-MDP transitions Hoffmeister (Bayreuth) Sport Strategy Optimization MathSport 2017 5 / 17