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Overall Player of the Year: Angelique Kerber
At the end of 2015, if you said that she would win 2 Slams and become the year end number one, I would have thought you were crazy. She was more of a "remember that awesome match where she lost?" type of player. She still has a bunch of those matches, but she pulled through for two slams. Had she managed to win 2 of the gold medal, Wimbldeon, and the WTA finals, her season would have gone down as one of the best of all time, as it was, it was merely fantastic.
Men's Player of the Year: Novak Djokovic
His level may have dipped after the French Open, but he won more slams than anyone on the men's side, completed a career Grand Slam and held all 4 slams at the same time. I don't know if he'll bounce back to his previous level, but he's had a career that qualifies him as one of the all time greats.
Women's Player of the Year: Serena Williams
By her standards, winning 1 slam and reaching the final of 2 others may be a disappointment, but those are crazy standards. Anyone other than Kerber would gladly trade their year for hers. I have doubts that she'll ever get to number 1 again, because of her schedule, but she can still put the fear of Serena in any player.