[CORRECTION: I originally titled this Federer and the paradox of luck, but it's actually more correctly termed the paradox of skill, so I've amended the title of this post. It's a term I first read in Michael Mauboussin's The Success Equation: Untangling Skill and Luck in Business, Sports, and Investing, a book I highly recommend.]

I was curious about a moment in the Federer-Murray Australian Open semifinal when the commentators and cameras caught Federer saying something to Murray and giving him a brief menacing stare after a long rally at 6-5 in the fourth set.

Without microphones on court, the commentators weren't sure what he said or why, but they briefly showed Murray responding with a exaggerated nod and smirk. The commentators did detect and remark on that brief moment of tension, and given how rarely we see tennis antagonism manifest itself in a visible way on court, it stuck in my brain as curious mystery.

My buddy Ken sent me this article which clarifies the incident a bit.

Murray prevailed in 15-stroke rally with a forehand winner, with both players finishing the point near the net. But Federer, on the brink of defeat, appeared to have taken issue with a slight mid-rally [hesitation] by Murray, and shouted “you [expletive]-ing stopped!” across the net. Murray appeared at first surprised, then amused, twisting his face into an exaggeratedly satisfied smirk, laughing and nodding toward his player’s box.

Federer was known for being a hothead early in his career, but I never saw much of it firsthand. Since his ascension into tennis immortality, he's largely been seen as a very level-headed sportsman.

One thing I have noticed a few times that seems to bother Federer is that when he plays one of the other Big Four (Djokovic, Murray, Nadal), he is particularly sensitive to any points they win by luck. The article above mentions that BBC commentators had to apologize on air for audible obscenities from Federer during the semi against Murray.

Federer’s first clearly audible obscenity in his semifinal loss to Andy Murray came with Murray serving at 4-5, 15-30. Murray fired a body serve which Federer could just get his backhand in front of and sent him into mostly indistinguishable muttering, punctuated with a loud, hard expletive in the middle.

Federer’s second audible offense came with Murray serving at 3-4, 40-40, in the fourth set. Murray won a 17-shot rally, and Federer exclaimed that his opponent had been “lucky,” preceding that word with a choice adverb.

I suspect most of you are thinking of the same adverb I am, so if I don't write it out I hope you don't see it as "ducking" the question [rimshot].

But a more memorable example is that extraordinary forehand return Djokovic hit against Federer in the 2011 U.S. Open semifinal. Down match point and 5-3 in the fifth set, Djokovic crushed a sideline-grazing crosscourt winner off of a Federer first serve (you can see it at 8:12 of this video).

In the press conference after that match, which Federer eventually lost , he was unusually testy when asked about that Djokovic shot.

"It's awkward having to explain this loss," a tetchy Federer said, "because I feel like I should be doing the other press conference."

There followed a string of excuses and justifications which not only were barely sustainable given the evidence but seriously disrespected the winner.

Asked about the quite remarkable forehand winner Djokovic hit to save match point, Federer reckoned the Serb did not look at that point like someone "who believes much anymore in winning. To lose against someone like that, it's very disappointing, because you feel like he was mentally out of it already. Just gets the lucky shot at the end, and off you go."

Djokovic was honest enough to admit the shot was a gamble – but Federer was reluctant to give him credit even for that courage in a crisis, preferring to regard it as desperate.

"Confidence? Are you kidding me?" he said when it was put to him the cross-court forehand off his first serve – described by John McEnroe as "one of the all-time great shots" – was either a function of luck or confidence.

"I mean, please. Some players grow up and play like that – being down 5-2 in the third, and they all just start slapping shots. I never played that way. I believe hard work's going to pay off, because early on maybe I didn't always work at my hardest. For me, this is very hard to understand. How can you play a shot like that on match point? Maybe he's been doing it for 20 years, so for him it was very normal. You've got to ask him."

Translated, Federer hates that tennis might be decided in any way by luck rather than skill. It makes sense, that someone who might be the most skilled tennis player of all time might be disgusted that luck plays any part in outcomes of majors.

It will be fascinating to see if Federer alters his game in any way this next year or two given his age and the competition from his three chief rivals. I suspect deep down Federer has always believed he is more skilled than any of his opponents, and that might explain one of his chief weaknesses, an unwillingness to be more aggressive on service returns. If you believe you are better than your opponent in every aspect of the game, it's sufficient to put the ball back in play on the return because you believe you'll win the subsequent point more often than not.

But the paradox of skill is that the more evenly matched opponents are in skill, the more of a role luck plays in determining the final outcome. As beautiful as Federer's game remains (in a sense, the continued aesthetic beauty of his shots makes it hard to measure his decline), in today's power baseline game, his rivals are a close match to him in both movement and groundstrokes. You can make a strong case that one or more of them are superior to him in areas like serve, return, footspeed, and the backhand.

Given that he no longer has that discernible skills gap to his chief rivals, a healthier acceptance of the role of luck might shift his strategy in ways that help him capture that next major. For example, it wouldn't hurt him to be more aggressive on return, to take some chances to go for the big winner and shorten some points. Can someone who is still so good and who can still recall with vivid detail the time when he had no rival be self-aware enough to change?