| On different conditions, the competitive ability of athlete would be in different form, and be expressed in different conception. On this paper, in order to express the athlete's competitive ability or competitive level on competition, "performance" how they show their competitive ability on competition was introduced.Performance of athlete are controlled by variant factors. The best or the worst competitive showing in specified conditions is called condition extremum of performance ,the best is the maximum value of performance and the worst is the minimum value of performance.This paper is began with the conception introduction of performance, then the performance index system and the condition extremum model which is consisted by the performance aim function and the performance restrain function are established. Through the studying on this model ,it is expected to be useful on theory explore and practical apply.In this research, multi-methods, strokes analysis data on 337 competitions in volley ball, table tennis, and basketball were served as sample.The establish of performance index system : the athletes' main competitive ability would take an important role in their performance on competition, so the strokes analysis data which is obtained on competition is the basic information source of performance.The establish of performance condition extremum model : It is established with such methods as multiple linear regression analysis and solve equation, this model is consist of two parts ,one is aim function and the other is restrain function.analysis on performance condition extremum model: it is analysis on two parts ,index system analysis and model system analysis. The model analysis includes maximum , minimum and fixed value.performance condition extremum model of performance could be used in such fields as result forecast ;form diagnose ; competitive aim determine ;skill and tactic determine and winning strategy ,it would have useful value on sports train and competition.
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