Why do you have to change the chain if you change the gearing???

 

To echo Lurch77 - If you ran the chain on sprockets that were toasted, you're throwing good money after bad. It's likely that your rear sprocket teeth are worn, do they look like they are leaning? Asymetrical? Time to replace the sprockets and chain.
As for Will's question - if there is enough adjustment to allow for the larger sprocket, you don't need to change the length. Depending on how many teeth one goes up or down and the available axle movement determines if one needs to add/subtract links.
If you mean why do you need to change the chain with old sprockets, it because as the chain and sprockets wear together, the pitch (5/8") of both get a little longer over time together. If you throw in a new component (sprocket or chain) the pitch doesn't match up and loads aren't spread out evenly. Individual links or teeth get loaded heavier, accelerating wear until the parts wear in to redistribute the loads. Things will work, but life is sarificed.
This is particulary true for chain/sprocket systems in abrasive environments(ATV/dirt bikes). Systems that are sealed and well lubricated (industrial applications,etc) can run sprockets longer, say for every 2 or 3 chain replacements.

 

HEY IF I HAD A 13F WITH A 38R, HOW MUCH LOW END WOULD I LOSE?

 

adding 1 tooth to the front is the same as taking 4 off of the rear
you do the math

hope this helps