Passing plays the central role in the coordination among the team-mates in a soccer game. The present study gives a mathematical theory for the safety of two types of passes: near-ground (Type I) passes and flying (Type II) passes. The influence of each of the related geometric and kinetic parameters to the safety of passing is quantitatively discussed. It is pointed out how the improvements of all the related factors, e.g., the running speeds of players, the muscle strength, the ball speed, the favourable geometrical pattern for passing, the accuracy of the direction of passing, etc., in the everyday training under the guidance of the coach, would help to create both a safe passing sequence and a good “attacking speed”. This would generate more shots with favourable shooting conditions and a good chance to win the game. In the meantime, the rate of injury would also be reduced. The present study also suggests that the improvement of the passing techniques has the potential to significantly raise the attacking speed and the level of world-wide soccer game as a whole.

mathematical theory, soccer game, passing, coordination, attacking speed.