I haven't found too many problems with the sports arenas that I've been to in the UK, either for sports events or for live music.
However, I do remember going to a gig about 20 years ago at what was then known as the G-MEX in Manchester (UK). It was converted about fifteen years earlier from an old railway station and had a huge Victorian arched glass canopy. The arena had about four sets of men's public toilets around the building, none of which were particularly large (I used two of them during the course of the night). The gig was about 75% attended by guys and the beer outlets were doing great business.
When I went to use one of the toilets I found a fairly sizeable room, consisting of only a single closet (capable of being used by a wheelchair user), eight urinals against one wall and six wash basins on the opposite wall. The place was heaving! There were three guys using the toilet in the closet together, whilst two more were pissing against the wall in there. The eight urinals were being used by about twelve guys, all squeezed up together. Three others had pulled the plastic tub used for disposing of paper towels into the middle of the room and were standing around it, pissing through the holes that you were supposed to put your paper towels in. The six wash basins, meanwhile, had a line of about eight guys pissing into them, whilst another one stood one the end, peeing into the end one from the side (as, in fact, I had to in the end, it being impossible to get any further in). There was quite a view in the mirrors behind them and I caught a few guys looking over the shoulders of the pissers at the reflection in the mirrors! Needless to say, the floor was awash. God knows what state the place was in by the end of the evening or what the cleaners had to face.