You outsiders there have an idiom such as "pee race" ?

We got the exact idiom in Turkish which refers to somehow apparently immature/childish competition of knowledge/power/whatever etc. between two (or more) people.

Some Turkish guy claims that he had seen the one-on-one translation, used as "pee race" among you English-speakers too.

Is that it ? Does English have the exact idiom of "pee race" ?