The distribution of the number of runs is best described as skewed (if there are more lower runs and fewer higher runs, or symmetrical if the runs are evenly distributed). So, the mean may not be an appropriate measure of center if the distribution is highly skewed; in such cases, the median might be a better measure.
If you have specific information about Trudy's runs in each game, I can provide a more accurate description of the distribution and the reasoning behind the appropriateness of measures of center.