math - Calculate likelihood of soccer player to intercept pass

Question

I am working on a soccer game engine in C#, and specifically the safety of a pass along the ground. I'm having a hard time thinking of a suitable formula to indicate how far an opposing player might be from intercepting a pass. I want to be able to give a likelihood between 0 and 1, ignoring all other factors like ball height, player pace/ability/etc. In other words, I'm thinking mostly about current position of the opposing player.

What formula would you deem most appropriate? Perhaps an arc with the possession player at the centre and the recipient player on the radius?

Answer 1

如果我正确理解了您的问题，那么以下几行是否可行：假设一名球员 A 即将将球传给球员 B，然后一名球员 C 试图拦截传球。由于您想忽略球高度等变量，因此您只需要一些相当简单的二维数学。

从 A 点到 B 点有一条线段 AB。如果球员 C 想要拦截传球，他最有可能在属于线段 AB 并且与点 C 的距离最近的 P 点进行。如果球员 C 能够在球从 A 点移动到 P 点之前从 C 点移动到 P 点，他将能够拦截传球。同样，这很容易找出，你只需要知道球的速度以及试图拦截传球的对方球员的速度。

现在，如果你知道，假设传球和对方球员的速度的平均值和标准差，以及如果球员能及时到达那里成功拦截传球的平均机会，你可以应用一些统计数据得到一些伪有意义的估计。