If you assume inviscid potential flow, a cylinder rotating forward will create lift. So the counter-clockwise spin on the cheap beach ball is creating lift on i

If you assume inviscid potential flow, a cylinder rotating forward will create lift. So the counter-clockwise spin on the cheap beach ball is creating lift on its right-hand side, so it curves that way. As to why a soccer ball curves the other way, I'm guessing that it's because soccer balls tend to tilt a little, and since they are rotating about that tilted axis, friction pulls them to the left. Even if the same thing happens to the beach ball, it's light enough that friction is small to begin with and the tilt is gonna lift the ball, decreasing friction even more.