Every singles tennis match is bound by the same dimensions — played on a court 78 feet long by 27 feet across and a net 3.5 feet high at the posts, with rackets no more than 29 inches long and 12.5 inches across — yet each one is a laboratory for innovation, unrestrained by a risk-averse coach or the conflicting desires of teammates. Not every tennis player thinks or talks deeply and consciously about analytics, but each one is analyzing herself and her opponents, strategically and tactically, before a match, between points and before every shot.

Top-ranked players can afford coaches who analyze and dissect play instead of serving as glorified companions, hitting partners and lay sports psychologists — but even they can’t help players once they’re on court at Grand Slam tournaments.

Singles players make hundreds of decisions in each match, sometimes thousands, all alone on their side of the net. Hit a backhand or run around the ball to hit a forehand? Hit the ball with slice or topspin? Come to net or stay back? Go for placement, speed or spin on serve? Serve to your opponent’s forehand or backhand? Any one decision like these might involve an entire coaching staff in another sport, but tennis players not only do it alone, but under match conditions that evolve because of weather, injury or an opponent’s change in strategy.

In this way, the sport’s very format lends itself to invention and calculated risk-taking. Top stars play as many times in a season as an NBA or NHL team, and far more often than an NFL team. Unlike those team sports, though, they aren’t working toward a single championship. Each event is a fresh start, and the biggest events — the Grand Slams — come four times a year. This year there’s an extra target in the Olympic Games. Lose at a major tournament, and there’s another chance or two in the next few months.

The experimentation isn’t just born out of opportunity, but necessity. Every tennis player who isn’t ranked No. 1 gets chances to play as an underdog, as seen in this year’s Australian Open. Angelique Kerber is ranked sixth in the world, yet bookies gave her just a 19 percent chance of beating No. 16 Victoria Azarenka in the quarterfinals because Azarenka had won all six of their previous matches. (For the vast majority of matches — those that aren’t fixed — prematch odds are a decent indicator of players’ chances to win.) Maria Sharapova is ranked fifth in the world, yet she was given just a 22 percent chance of beating top-ranked Serena Williams in the quarterfinals — after all, she’d lost 17 matches in a row to the American. Even after losing a match in which she tried guessing where Williams would hit her first serves, Sharapova said she relished meeting her rival. “If I don’t have that chance then I don’t have the opportunity to try something different,” Sharapova said. She added, “She makes you go back to the drawing board, not just for me, but for many other players.”

Underdogs can try new things without much fear of failure, and sometimes those new methods can produce great upsets, such as Fernando Verdasco’s win over Rafael Nadal in the first round despite being given just an 11 percent chance before the match. Sometimes they almost produce great upsets, like when Gilles Simon (4 percent) extended Novak Djokovic to five sets in the fourth round. And sometimes they don’t even come close, like when Margarita Gasparyan (8 percent) won just three games in the fourth round against Williams. “I have a lot of double faults because I want to hit the ball more aggressive in the second serve, but I have mistakes,” Gasparyan said. Sometimes you swing big and you miss big. But that loss didn’t cost Gasparyan any money or ranking points, didn’t bring her any harsh questions from reporters, and didn’t get Gasparyan fired by her boss, because she has no boss.

Players who were big underdogs, or faced them, often use the word “aggressive” to describe their approach in trying to pull off a big upset — Kerber used it in one news conference to describe how Annika Beck had tried to beat her, and how she would in turn try to beat Azarenka. Sometimes aggression can describe underdogs’ in-match demeanor, like when Lukas Rosol unnerved Nadal with his posture while returning serve on his way to eliminating the two-time champion from Wimbledon in 2012. More often, though, “aggressive” describes underdogs’ style of play, such as Rosol’s and Verdasco’s. It means playing offense, not defense, and taking big risks on individual shots by hitting the ball hard, close to the lines and the top of the net. Any one shot is less likely to go in, but hitting a series of shots like that throughout a match can neutralize top players’ defensive skills and natural talents while giving underdogs their best chance to win. Tennis players have figured out something that still flummoxes multimillionaire decision-makers in other sports: The riskiest strategy is often what looks like the lowest-risk tactic, and even if aggressive shots misfire once or twice, hitting many of them will pay off down the line.

“Today I was just like trying to be as aggressive as possible, but also not like so crazy,” Verdasco said after ousting Nadal. “Sometimes if you do like what I did today, you put all the balls outside, it’s like, ‘This guy’s crazy. He just hit everything and he miss.’ But when they are coming in, you play unbelievable. The difference is just so little and can be so big.”

“I’m an aggressive player,” Sharapova said after her fourth-round win. “But there is a difference between making the wrong errors and making the right errors. I feel like, yeah, I made errors. I went sometimes for a little bit too much. But I think the difference is sometimes you’re making errors, but you feel like you’re doing the right thing. Ultimately when the time comes, you have to believe that those errors are just, you know, a few centimeters wide or long that they’re going to start going in.” Sharapova had to believe guessing Williams’s serve placements would give her a better chance to win. She didn’t, but she probably wouldn’t have anyway, and it might work in a future meeting.

Not every player, though, has the same strength and competitive advantages of Rosol, Verdasco and Sharapova. Part of what makes a tennis tournament a lab with many simultaneous experiments is the wide range of players’ physiques and skills. After Barbora Strycova’s effort to beat Azarenka in the fourth round fell short, Strycova — who is seven and a half inches shorter than Azarenka — was asked about her unusual style, which includes serving and volleying, a rarity in women’s tennis today. “I’m not big enough to play powerful tennis,” Strycova said.

Simon is 6-foot, weighs just 154 pounds and has earned more than $10 million with his mind and his defense, not his power. After he’d pushed Djokovic to the limit, Simon contrasted himself with Stan Wawrinka, the last man to oust Djokovic from a Slam. “I have to find my own way to do it,” Simon said. “Like I wish I could hit like Stan, but that’s far from being the case. … I just try to keep it simple, use my strengths, use his weaknesses, yeah, just try to work it out.”

Roger Federer was watching. When a reporter pointed to Djokovic’s 100 unforced errors against Simon — representing 57 percent of the points the Frenchman won — as a sign the world No. 1 played badly, Federer replied, “How much did you see Gilles Simon play? I’m just wondering, because I think people miss the point of him. He plays every match like that. He makes you miss. He makes you go for the lines and he runs down a lot of balls. A lot of points end in errors … he knows exactly what he’s doing out there, and it worked almost to the very end.”

Athletes of all sizes and skills can thrive in part because tennis’s structure rewards idiosyncratic game styles, whatever you may have heard about the stultifying sameness of today’s players. At the macro level, that may be true, but players who have an uncommon style are hard to prepare for when matchups are set only a day or two ahead of time, and when you could face any of hundreds of other players in a Grand Slam. Dustin Brown was 30 when he upset a 29-year-old Nadal last year at Wimbledon, yet the two had played just once before and Nadal looked utterly perplexed by Brown’s serve-and-volley, go-for-broke, rush-between-serves game. Williams doesn’t encounter many opponents like Roberta Vinci, whose slicing, net-charging game halted the world No. 1’s 33-match Grand Slam winning streak at the U.S. Open last year.

And a player’s style isn’t a fixed quantity but one that can change during a career. A player can change her serve, or her racket, or where she stands on returns, or how often she comes to net. Federer has gone from a serve-and-volley style on fast surfaces earlier in his career to a baseline game to a hybrid that includes net charges off short-hop returns. He found the right mix for one set against Djokovic in Thursday’s semifinal, but Djokovic’s own tactical countermoves won the day, clinching the decisive break with a searing return as Federer charged the net. Fellow semifinalist Milos Raonic, who beat Federer to win the Brisbane tournament earlier this month, has excelled this year by improving his net game. Sharapova has started switching her racket to her nondominant left hand to reach balls out wide. Sometimes players work on new tactics in practice, then unveil them in matches — and shelve or retool them if they don’t work out. The constant adjustments to counter new rivals and tactics push the best players to new heights — by our Elo measure, Djokovic is playing the best tennis the sport has ever seen.

The tennis lab is far from optimal. The sport’s stats are limited and hamstrung by its fragmented structure, which makes it hard for players — and for us — to quantify the success of new gambits. Many players and coaches don’t pay attention to the stats that are available. For every player who talks tactics in news conferences, there are three who say they just try to “play my game.”

But don’t just listen to what they say. Watch how they play. You might learn a thing or two about mixed strategy and when the biggest risk is not taking risks. The women’s and men’s singles finals start at 3:30 a.m. Eastern on Saturday and Sunday, respectively. That’s not too early for coaches in another sport who could stand to learn about the right time to take risks.

CORRECTION (Feb. 1, 10:50 a.m.): An earlier version of this article referred incorrectly to Rafael Nadal’s record at Wimbledon. Nadal was the runner-up at Wimbledon in 2011 to Novak Djokovic, and so was not the defending champion in 2012.