Canon Powershot N would be a budget option (only 28mm though). Very small and perfect for a jersey pocket.
http://www.amazon.com/Canon-PowerSho.../dp/B00AWYN2CW
I just bought one for exactly this purpose. Cheap, compact, and just beats my phone for pictures (Nexus 5X, generally considered a good camera).
Smartphones have decent cameras, but usability really fails. Its basically impossible to use a smartphone one-handed (try it). Oh, and if I drop/damage it, it was $130. I've got a 6D for when I really want to take good pictures. The Sony and Ricoh options looked good, but I personally couldn't justify the cost for marginal uses. I've already got a smartphone and DSLR, buying another ~$400 camera is a bit too much.