Sporting events are either OTC or I'll go with a RL friend. However, it should definitely be done at a social rate. What that rate should be, hard to say.

One gave discounted rate on her hourly for the game an then full hourly for our alone time. Another asked for nothing while at the game but then normal rate off alone time.

For a guesstimate, you should plan on paying her regular multi-hour; the going to the event would be either the same or a couple hundred dollars less.  

E.g. If you want to take a lady for a baseball game, and her 6 hour rate is $2500, you should plan on paying that. In reality it maybe $1800-2500.
Make sure both of you have clarity on how much time you'll spend where- how much time you'll spend at the game and how much time you'll spend alone.  
And also make sure you budget the amount you are paying for tickets and food so you know what you'll be out of pocket!