Andrew
The crowds will begin to thin around mid-September. A lot depends on where you want to fish. The western side – Firehole-Gibbon-Madison corridor sees good pressure into October but west entrance traffic can be bad between Old Faithful and West Yellowstone. The NE corner — Lamar, Slough and Soda Butte slow significantly into late September and October. The northern section — Gardiner, Yellowstone and Hellroaring stay decent into late fall and generally the traffic between Mammoth and Tower isn’t that bad in the fall. The real key to deal with the crowds (tourists, not anglers) is to get early starts to your fishing destination before the traffic starts to snarl or fish late and well into dusk. Moving around the park between 9AM and 4PM can be like getting out of a packed football stadium parking lot–very slow.
Strategy without Tactics is a Slow Route to Victory, Tactics without Strategy is the Noise Before Defeat - Sun Tzu