Once the police officers are convinced enough that you did it to bring you in for questioning the chances you'll be able to just convince them otherwise are slim and a huge risk.
Watching the first 48 (a show following murder investigations) I'd break it down to:
(1) people that are guilty and think things like "he had it coming" or "my buddy was just supposed to rob him" help their case. They admit to capital crimes when trying to lessen their guilt.
(2) people the police think are guilty and ineffectively lie. They probably don't hurt or help themselves.
(3) people the police aren't sure of. They can talk themselves in or out of suspicion based on their guilt and/or ability to effectively lie.
The group that get coerced into confessing to a crime is a very small percentage of people interviewed.
(1) The police have enough evidence to charge you with a crime
(2) The police do not have enough evidence to charge you with a crime
They do not have to tell you (and can actively lie!) which scenario you are in, and these scenarios are only loosely correlated with whether or not you actually recently committed a crime.
In scenario (1), they're going to charge you with a crime no matter what you say - they already have enough evidence. And anything you say to the police in this scenario can only be used as evidence against you to further strengthen the police's case, it cannot be used in your own defense in court. So it's better to remain silent.
In scenario (2), if you remain silent, they cannot charge you with a crime - they don't have enough evidence and you're not giving them any (asserting your right to remain silent is not evidence). If you answer their questions, you might accidentally give them enough evidence to charge you with a crime, like contradicting your own story because your memory is fallible. The police are allowed to lie to you, ask you trick questions, wear you down, and in general do anything they can to get a confession or other evidence against you. The things you say here can only be used against you to strengthen the police's case. So it's better to remain silent.
If you are being interrogated by the police, they are not your friends and nothing you say can help you. The only person on your side is your lawyer. Stay silent until your lawyer is in the room, and then do exactly what your lawyer says.
It's been linked elsewhere, but https://www.youtube.com/watch?v=d-7o9xYp7eE is a real-life law professor and a police officer both saying exactly the same thing. American TV often includes narratives about the behavior of police officers that do not align with reality or the best interests of people accused of crimes.
There's no advice in my post.
It seems you are OK with this group not being zero.