When a character is far off in the distance, essentially taking up few pixels on the screen, there is no need for the character to have 4000 polygons when 100 or less will do.
This is where LODs come into play. What you do is take your main model and create four versions, or five, or however many are needed, each one stepping down in its polygon count. As the character moves away from the camera, a different version of the model is loaded in its place. The farther away from the camera, the lower the version, until the character can no longer be seen.
If we use Kila as an example, her main model of 4094 polygons would more than likely be used for close-up shots, or maybe just in cut scenes. The next LOD for Kila, then, would be the main one used in game, since we could remove around 1000 polygons and still retain all the detail needed. The LOD after that would comprise 1000 polygons; then we'd drop down to around 500; and the last one would be about 100 or 200. As you can see, we step down gradually at first, before dropping dramatically as distance from the character increases. We can do this because there will be decreasing need for detail as the character moves farther away.
The graphics programmer usually sets the number of LODs and the number of polygons in each LOD. The trick is to have as few LODs as possible. One rule of thumb in the industry is "The sum polycount of all LODs shouldn't exceed the main game model."
You can see Kila with her levels of detail in Figure 10.1. Although there are fewer polygons in the versions that are farther away, you cannot tell.
Figure 10.1. Kila with levels of detail
Check out the games you play. Look carefully, and you will see characters or objects "pop" as they move away from the camera. This is the game engine swapping the current model for a lower LOD.