I have only watched ESPN games via the web and not via the app on a smart device. The streaming experience is largely dictated by the speed and quality of your Internet connection as others have mentioned. All consumer class Internet is "best effort," meaning it has no service level agreements for latency, pack loss or jitter (all of which play a bigger role with real-time video and real-time audio. Other factors include the infrastructure of the content provider. You can have solid Internet performance on your end but if the content provider's servers, Internet connectivity, etc., are having issues, you will also.
I was without my Spectrum 200Mbps service for a week after my wife cut our service wire while gardening 😕 I ran 1080p over the Wi-fi hotspot on my AT&T phone with little problem. Netflix didn't want to run any higher than 740p, YouTube TV, Hulu, Prime and Disney+ all ran fine with very little pixelating or buffering. That's particularly strange because my voice service over the same phone is often spotty with audio dropping in and out.