That doesn't sound good regardless of how much I spin it around in my head."stupid long mathematical equation"
Anyway, you could just go with some simple conditional statements and inverse the direction of the ball. If you want something more complex you'd have to do some vector maths with at least the ball's direction vector, the paddle's forward vector and the position the ball hit the paddle.
[source lang="cpp"] // edge of playing field if (pong.ball.centre_y > 0.6f) { pong.ball_velocity_y = -ball_speed; } else if (pong.ball.centre_y < -0.6f) { pong.ball_velocity_y = ball_speed; } // ball hit a paddle on the right side if (pong.ball_velocity_x > 0 && collides(&pong.ball, &pong.bats[1]) ) { pong.ball_velocity_x = -pong.ball_velocity_x; } // ball hit a paddle on the left side if (pong.ball_velocity_x < 0 && collides(&pong.ball, &pong.bats[0]) ) { pong.ball_velocity_x = -pong.ball_velocity_x; }[/source]