Evidence to Convict?

[Mister Agenda]

I prefer the Tony Hancock version.

I prefer the Amy Schumer version.

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How would you honestly answer, This is only about this scenario, not considering anything else.

Surely it's a straightforward question to answer, namely that if I saw you smash somebody over the head I'd make a statement to the police saying exactly that, but if I didn't see you do it I'd tell them that instead.
Or am I missing some hidden depth or something in your question?

That's great as long as you couldn't be mistaken, deceived, misremembering, coerced, or have your own motivation to lie.

Your testimony is a good reason to investigate to determine if a crime has been committed, and if so, by whom. If it was good enough to convict, our jails would be filled with victims of false accusations, as it would be an easy way to get rid of people you don't want around.

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Your comment brings to mind however;  if testimony is not evidence at all, then why would the police bother gathering it and have procedures to keep it from becoming contaminated. 
The second part of the question is if it is sufficient to come to a reasonable conclusion based on testimony alone.  In this case, we have the testimony of a number of independent witnesses.

Why would the police investigate a claim that a crime has been committed and preserve the exact words of the claim? That's what you're asking?

Evidence is what makes it more or less likely that a particular claim is true. Ten more people telling the same story is just ten more claims in and of themselves, but there can be elements of the testimony that detract from the probability that it's an honest or accurate report, or elements of comparing the testimonies that can add to the probability that the testifiers are being truthful to the best of their knowledge. However the most you can get from that which would support a conviction is textual and contextual evidence that the testifiers are actually reporting the story sincerely and that their reports are similar enough (but not too similar!) to conclude that they're describing the same event.

I still don't think it would be sufficient evidence to convict without cross-examination, an injured party, and a very good reason why physical evidence is not available.