INDIAN WELLS, CALIF.—“I understand my game pretty well,” Alexandr Dolgopolov said after his upset win over Rafael Nadal on Monday. That’s not an answer you hear every day from a tennis player, mainly because not many pros, especially ones who have been ranked No. 13 in the world, are asked if they know what they're doing out there.

But that's the question that was put to the 25-year-old Dolgopolov. With him, though, it's not necessarily an insult. The Ukrainian, who is one of the sport's all-time originals, admits that he has had only two coaches in his career—his father, Oleksandr, and Jack Reader of Australia—because it’s not easy to find people who can figure out how to work with him. Dolgopolov only kept Reader around, “because he wasn’t really pushing me or trying to change a lot in my game.”

“Some people have their view on tennis," Dolgo said this week of his experience with coaches, "and they try to make [the player] play the way they want. But for me, I don’t think that’s the best decision.”

It’s not hard to see why. Watching Dolgopolov reminds me of the way a young Ilie Nastase, another all-time original, described his approach to the game: “I want to play tennis inside-out.”

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Dog Days

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Dolgopolov plays tennis inside-out. He carves his two-handed backhand with reverse sidespin. He floats to the ball casually, yet when he gets there, he can rocket it as hard as anyone. His drop shot is often his most consistent weapon. He has more variety with his two-handed backhand than most players do with their one-handers. He has never seen a routine ground stroke he couldn’t spice up with a leap or a buggy-whip or a follow-through across his head. And while Jim Courier compared Dolgo’s whiplash service motion to a Jack in the Box today, it’s always made me think of Jim Carrey's spastic dance in the old Roxbury SNL skits. Either way, Dolgo uses it to generate an amazing amount of pace.

Dolgopolov’s mother was a gymnast, though from the way he travels around the court in leaps and bounds, I would have guessed he had a ballet dancer in the family. Even between points, he walks with a spring in his step, as if his feet are lighter than the rest of ours. As with all natural athletes, though, his ease of movement masks the frenetic work that makes it happen. Today Dolgopolov signed two of his sneakers and threw them into the crowd, because, as he said, “It was better than throwing them in the litter box.” He burns a hole in his shoes every match he plays.

On Thursday, Dolgopolov added another counterintuitive piece to his puzzle. Faced with the prospect of having to return Milos “Missile" Raonic’s serve, which may be the most lethal in the game, Dolgopolov did what all true originals would do: He moved toward it.

“I tried to come forward on it,” Dolgopolov said. “I tried to get into his head, that I would anticipate it. I was quite fast on my return today. I’m quite pleased how I anticipated on his serve and have seen the toss of the ball.”

Quite fast indeed. The crucial point of the match came at 3-3 in the second set, with Raonic facing a break point. The Canadian had led 3-1; now he was in danger of losing a third straight game, and, unbelievably for him, a second straight service game. At break point Raonic went back to what qualifies as “old reliable” for him: A 141-M.P.H. bomb. Except that this bomb exploded on him. Dolgo rifled a backhand return, and then another backhand down the line for the break. He held out from the there for a 6-3, 6-4 win.

According to Raonic, Dolgopolov succeeded in getting in his head with his return right away.

“First serve of the match, 141,” Raonic said, “[he] returns deep. 30-all in the first game, 145 into the body; returns it even harder than I served it on him. He made me think more than most people can on my service games.”

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Dolgopolov is having a good month, playing his most consistent tennis since he reached No. 13 in January 2012. Three weeks ago he made the final in Rio on clay, beating Fabio Fognini and David Ferrer before losing to Nadal; two weeks ago he made the semis on hard courts in Acapulco. So far at Indian Wells, he has beaten the No. 1 player in the world for the first time and reached his first semifinal at a Masters event.

It would be tempting to draw a line between the troubles in Dolgopolov's native Ukraine, which began in earnest late last year, and his sudden success. He says he’s certainly aware of what’s happening there, and he made sure that one of his signed shoes went to a couple who were holding up a Ukrainian flag in the second row. After the match, Dolgopolov said that he’s “not a politician,” and he can only play tennis, but he’s happy if he has “put a smile on people’s faces” back home for a few minutes.

Dolgopolov credits his surge to something simpler: He was healthy enough to get a solid, month-long training block in at the end of 2013. The good form has followed. Asked how he beat Nadal, Dolgopolov answered in his usual matter-of-fact way, like a surfer from the Black Sea.

“I’ve played quite good for a few weeks,” he shrugged. “I’m healthy, in good form, so why not?”

There’s been a lot of talk recently about players being inspired to make breakthroughs by Stan Wawrinka’s Australian Open title. More than anyone, I’d like to see Dolgopolov, with his inside-out grace, and his backstory as a Ukrainian, continue to make strides. He can be frustrating, but he never seems to hit a shot or play a point exactly the same way twice. A prodigy and the son of a tennis pro who suffered an early case of burnout, it’s nice to see him enjoying the sport again.

I’ve liked Dolgopolov’s game since seeing him as a junior at the Orange Bowl in 2005. He was all about the drop shot then, and I wrote that he might be the next Fabrice Santoro. At the start of this year, Dolgopolov talked about hiring Santoro as his coach, but they never got past the talking stage. The Magician is probably one of the few people who could have understood the Dog.

On the one hand, I would have loved to see what those two came up with together—in some ways, Dolgo as Baby Santoro was more of a pure genius than he is today. On the other hand, as far as his results go, staying away from the Magic Man is probably the best thing that happened to Dolgopolov all year. He understands himself, and that’s enough.