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Unpredictable acceleration performace

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I have a 1.5 Roadster from 2008, purchased less than a year ago. This is my first Roadster so I'm not terribly confident in terms of what to expect as "normal" performance vs. "less than normal."

A few months ago I had part of the battery replaced. I'm not positive, but it seems like since then the acceleration performance has varied between driving sessions (much less so within a session).

Sometimes acceleration is what I imagine it should be - BAM - I am thrust back in the driver seat under acceleration from 0-30 and also 50-70.

Sometimes acceleration is less than expected, like there is insufficient traction (when roads are wet, acceleration is affected).

Initially I thought that acceleration was impacted by the battery being less than some threshold, but now I no longer think this is the case (unless the battery is pretty low).

Any thoughts on what might be going on? When should acceleration be affected?