I have a feeling that serving first in a set is an advantage. Is there a statistic like "X % of the sets were won by the player who served first"?
As of now there are very few standardized statistics taken by the ATP or WTA concerning "percentage of sets won by player who served first". However, Professors Franc Klaassen and Jan R. Magnus recently completed research on a number of Wimbledon tournaments and inspected several questions including the one concerning the outcomes of sets depending on who serves first.
You can find out more information here:http://www.janmagnus.nl/misc/wimbledon.pdf
However, you may have to pay to get the complete set of research. http://www.pinnaclesports.com/en/betting-articles/sport/live-tennis-betting-strategy summarizes that only "...48.2% of sets in the men’s singles are won by the player serving first. In the WTA? Just 50.1%".