I have checked into sound pollution definition and I believe that it any sound that is affecting your quality of life. I’d say sleepless nights and a crying wife qualifies for this….
If it's bad enough to cause you sleepless nights, and assuming your house is built to half-way decent standards, there are a number of avenues to explore. Contact your local authority - county / city council - and ask for the Environmental Health section / officer. Explain the situation to them, and ask them if they can inspect the premises in question for excessive noise. Do it
today - it may take a while for them to schedule a visit, depending on workload. Pending any visit / inspection, keep written records of how often it's on through the night, and records of any efforts you've made to address the issue with the sports complex management.
You can also have an independent company monitor the noise level and check whether it breaches residential area rules, and produce this as evidence to the sports complex. But I recommend starting with the local authority and seeing what they can do for you - they will have the expertise to deal with it, and you won't have the expense of going it alone with monitoring records / legal action.
I have real sympathy for you and your wife in this situation - I have difficulty getting to sleep with high levels of ambient noise (especially low-frequency, which can make it feel like the whole house is resonating), and it would drive me nuts to know that the only reason it's on is that some utter gobdaw forgot to flick a switch. Again.
Good luck.