Q: iPhone data conservation

Hi, P B Leopard.  

Thank you for visiting Apple Support Communities.  

I understand that you are concerned with the amount of data being used with a specific website using Safari.  While there isn't a specific setting to limit the amount of data being used by a website, you can adjust settings to disable cellular data for certain applications and features.  Another option would be to make sure you are connected to Wi-Fi when accessing that specific website.  

About cellular data settings and usage on your iPhone and iPad

Connect to Wi-Fi on your iPhone, iPad, or iPod touch

Another option may be to use the free ESPN application available from the App Store.  While I am not sure about the amount of data this application uses, it may be worth a shot to test.  

ESPN

Cheers