Contrary to common belief there isn't too much of a relationship between ping and the amount of bandwidth your Internet connection can handle. Most people believe that the higher your download speeds are the lower your ping must be. This is NOT the case.
You could have a 12Mbps Internet connection that gets 5ms to game servers whereas you could have a 1Gbps Internet connection at the same address and get 200ms to the same game servers. The 1Gbps Internet connection could be routing your packets around the world before sending them to the game servers whereas the 12Mbps Internet connection could be routing your packets via the shortest path to provide the lowest ping. This is an extreme example, but it conveys the concept that download speeds and ping aren't linked to one another.
The scenario where there is a relationship between ping and download speeds is if you are maxing out your download speeds. If you max out your download speeds then routers will hold your packets in a queue which adds ping to your connection. The higher download speeds you have the less likely you are to encounter additional ping due to packets being held in a queue. If your Internet provider prioritises game traffic over other traffic then your packets won't be held in this queue so you shouldn't encounter addition ping when someone is maxing our your download speeds.