"If the deer is running, the cloud of pellets will not all hit the deer. Some of the forward pellets will miss the dear, some in the middle of the cloud will hit the deer the length of the body, some in the rear of the cloud will not miss the deer. Being "cloud" shaped some will miss above and below the deer. The only way all of the pellets could hit the deer is at extremely close range to the deer while it was standing still."
I have to disagree on this point. Yes there is some small horizontal shift effect due to shot stringing. However high speed photography gives a better view of what the "cloud" shape really means. Bottom line, the speed of the game vs the speed of the shot makes the effect rather minimal - to the point it can be ignored.
Here is a good short explanation: