I like your "2." suggestion more, because the initial sentiment score distribution can be not normal.
So there is an option to try making it normal by taking logarithm for example and calculating mean, etc. after that.
So there is an option to try making it normal by taking logarithm for example and calculating mean, etc. after that.
A simple 1-gram model like in the question does not model many complexities of natural language e.g. negation ("not bad" != "bad") so you would expect your estimator to over-represent the dictionary with more words that are equal to their adverb-adjusted equivalent. e.g. "not bad" can be described as 'terrible' more readily than 'very good' can be described as excellent since people assign a hyperbolic weighting to their own happiness (utility theory 101)
The sentiment would only tend to a normal distribution if we had perfect estimators for document sentiment which requires advanced POS tagging and models more complex than a 1-gram bag of words aggregation :)