Host Latency

Hey guys i am new to the forum i would like to hear your opinion or experiences on this concerning question i have in regards to game hosting in games like black ops 2 or world at war. My question is there a relation to the latency i encounter to the host framerate or their PC performance i noticed that people who say that their connection is decent but they are running a game on a inadequate computer such as  media laptop. i don't know if their video card performance impacting my latency or their wifi connectivity or both in that matter.

Thanks in advance

PS i am not an expert in networking i just have a very vague background of a course i've taken in the past