MPLC does not currently licence sports so if you are only showing sports programmes you do not need an MPLC licence.
However to avoid a copyright infringement you would need a mechanism in place to avoid the accidental or occasional showing of non sporting programmes. If you do not have that then an MPLC licence will cover you for that liability,
MPLC Public Performance Licences are affordable, easy to buy and can be put in place immediately. They are the legal way to show movies and TV programmes in a public or commercial space.