A girl participates in an athletic competition to show that girls can be as good as it as the boys are. She then makes good by a) outplaying/equaling her male counterparts in an athletic competition, or b) joining another team, and winning a game for her team. Sometimes this happens in retaliation to being called "just a girl". Nine times out of ten, the girl is treated as a hero (with the "being carried on the other athletes' shoulders" treatment) upon winning the game.
Note that this may require pulling a Sweet Polly Oliver.
This is frequently an instance of a Jackie Robinson Story. The Spear Counterpart is the Billy Elliot Plot in that they both subvert gender norms, but whereas that trope centers on the same-sex parent's disapproval, the parents' input in this case is not as vital, and they tend to range from supportive to neutral.
Sub-trope of Passionate Sports Girl. Compare Mars and Venus Gender Contrast.
This is the outcome in the film Little Giants. Becky's dad was pissed that she wasn't chosen for the town's football team because she was girl and so he started his own team and challenged the official team.
In Brave, princess Merida holds an archery tournament between three clans to see who is worthy of having her hand in marriage. All but one succeeds in hitting the bullseye, but Merida isn't impressed. She hits all three bullseyes easily, including splitting the arrow that hit the bullseye down the middle. Hilarity Ensuesand reality between her and Queen Elinor; Merida broke tradition, embarrased the three clans, and almost provoked a civil war because she didn't chose a husband.
It seemed like almost every sitcom in the 70s-80s had to have one of these episodes where not only did the female cast outperform the guys at everything, but turning every male in the show into a massive chauvinist whether they were in previous episodes or not.
Small Wonder, where Joanie, Harriet and Vickie go camping with the guys and prove superior in pitching tents, fishing and cooking - even at the end, it rains on the guys' camp and not the ladies who are five feet away.
This was actually a recurring theme in the show. Any time the boys and girls had a contest, the girls would win.
M*A*S*H had a bowling episode in which Margaret Houlihan tried for half the episode to tell Potter she would be a valuable asset to the team, but female team members were so far from his thoughts that when she said she wanted to help, he assigned her the task of seducing the major player for the opposition. Of course, once she ends up on the team proper, she pulls her weight, and the 4077th wins the bet.
Degrassi Junior High, "The Great Race." The girls' swim team challenges the boys' soccer team to a swimming match. The boys secretly know the girls' team is better, but they think they can win — because the girls' star swimmer is morbidly afraid of letting boys see her in a bathing suit and because they allow champion swimmer Snake to join the team, even though he's awful at soccer.
Lizzie McGuire features an episode where Lizzie turns out to be really good at flag football, and gets recruited to Ethan's team. She quits because she's treated as "just one of the guys" by Ethan but then learns that girls can be athletic and girly.
Dee in It's Always Sunny in Philadelphia took part in the football try outs in one episode just to prove that she was more athletic than Mac and Dennis who were also competing. Despite the fact that she had a "spine made of glass", she managed to make it the farthest than any of the other guys, but only because they were completely out of shape.
Subverted in the end of the episode, when she injures her foot just kicking the football.
In the Renford Rejects Robin is turned down for the school football team purely because she is a girl and the PE teacher Basil Stoker thinks it is a man's game. In the first season finale Robin is instrumental in helping the Rejects stay in the league by winning their last game of the season against the school team, the Razors.
In the Wishbone episode, "Bone Of Arc" Samantha joins the boys' soccer team and her team mates love her for it.
In the Degrassi episode, "Fight The Power" a few girls really look up to Jane for joining the football team. At the same time, she ends up being violently bullied by the rest of the team, the cheer leaders, and even the principal.
The second season of Jossys Giants introduced the players' girlfriends, many of whom were footballers themselves and who at one point beat a boy's team.
The first episode of Life With Boys is all about Tess's quest to join the wrestling team.
Briefly played with in an episode of Malcolm in the Middle: Reese joined in a wrestling team and had to fight a girl.
Patricia from House of Anubis. She is not only a former female jock, but is also proven to be feared by all the other students in the house whenever she gets mad.
The Fabulous Moolah became the first woman to wrestle at Madison Square Garden, which had previously outlawed women's wrestling.
Both Madusa Miceli and Jacqueline Moore won the Cruiserweight Championship, the former in WCW and the latter in WWE. Jacqueline also won her second Women's Championship from a man (don't ask).
Chyna became the first woman to hold the Intercontinental Championship. She would go on to hold it three times (the second one was a co-champ thing with Chris Jericho).
In Dragon Quest IV, Alena is the princess and expected by her father to act like a princess. She, on the other hand, wants to be an adventurer and prove that she can do more than look pretty in a dress. So, she instead breaks out of the castle, travels across the country, and roundly proves that she is more than capable of kicking ass and taking names by winning the battle tournament in Endor.
Quite a few eps of Rocket Power, with Reggie Rocket as the girl. For instance, "Major Scrummage", where she scores the winning points in a game of rugby. Justified, since she's the oldest by two years and the only one who has reached puberty.
Phineas And Ferb has an Olympics-type match between...well, Buford, the bully, who press-gangs Baljeet, and Isabella, who gets Candace to help her. The girls win.
Of course the girls and boys would have tied, if Buford hadn't cheated at the end.
Buford seems to retain an unwillingness to back down against girls in other episodes, too, such as "Let's Take a Quiz" and "Brain Drain." We never find out who wins the former, while Isabella beats him again in the latter.
"Lisa On Ice": Lisa becomes the star goalie of a hockey team, leading to the inevitable showdown with Bart, who plays for another team, although Bart is actually in conflict with Lisa due to Homer's favoritism rather than actual chauvinism. They eventually realize their relationship is more important and make peace without deciding a winner.
"Bart Star" subverts this: Lisa boldly declares her intent to join her brother Bart on his football team, but becomes reluctant when coach Ned Flanders welcomes her with open arms, mentioning the three other girls on the team, who are also welcoming. Lisa tries to salvage her mold-breaking intentions by decrying the footballs for being made of animal parts, but learns that they're synthetic, with the profits donated to charity. Unable to cope with not being on the moral high(er) road, she runs off sobbing.
Parodied in the South Park episode "Cartman's Silly Hate Crime 2000," where we're supposed to root for the boys in the sled race while it's the girls who act snotty and superior. Though their secret weapon (Cartman's massive extra weight) gets arrested for a hate crime, they wind up winning in the end, and the most annoying girl is implied to be eaten by a bear. Yay!
Subversion: Clone High, "Shot in the Dark", where "John Dark" turns out to be the Joan of Arc clone in a cap and mustache. She hits a free-throw to score the school's first point against their competition and win a bet principal Scudworth had made against their rival's principal... and then the team treats the Abe Lincoln clone as a hero (on the grounds that his stirring speech convinced all in attendance to let her shoot in the first place), leaving Joan feeling completely betrayed.
In Gormiti The Lords Of Nature Return, Toby's boasting about being better at judo are summarily shot down by Jessica beating him by one point at the school tournament. She was quite smug about it, too...
Anne Chan gets several little moments like this, usually in response to Alan or Tom claiming she can't surf, climb trees or follow a crook as well as them because she's a girl. They're both miniature crowning moments of awesome and Played for Laughs at the same time.
Subverted in an episode of What's New, Scooby-Doo? where the culprit turns out be a girl who was sabotaging the skateboarding tournament. She claims she was rejected because she's a girl (even though there is another girl there), but it turns out she was rejected because she genuinely sucks.
The Grim Adventures Of Billy And Mandy: Billy wouldn't allow Mandy in his baseball team because she's a girl. Trying to teach him a lesson, she disguised herself as a boy named "Manfred" by donning a baseball cap. That'll prove to Billy girls can play sports as soon as he sees through her Clark Kenting. (That means never)
Sometimes, the girl or her team doesn't quite pull off a win, but the girl has still proven herself anyway:
In Captain Tsubasa, softball player from Okinawa Maki Akamine helps Kojiro Hyuga develop new training techniques. However, when it's time for her big softball game, she loses, and Hyuga gives her her spirits back with a hug under the rain. Maki doesn't give up, continues training, and later she's chosen for the national softball team.
The end result in the book There's a Girl in My Hammerlock.
IF you feel like being generous. The main girl ONLY wins when the opponent forfeits because shes a girl, she never wins in a straight up match, the best she can hope for is not sucking. The only reason she actually participates is because the only other one in her weight group is even worse than her and the other one was withdrawn by his father who was insulted by her participating.
Claire Sawyer (Future Lawyer): You can't be denied because you're a boy. You can, however, be denied because you stink.
Done once in Zoey 101 and actually Subverted on the second occasion. The very first episode feature a girls vs boys Basketball game in which the girls lose by only one basket. By the end of the game however, the entire school was cheering the girls on. In one of the rare instances where Zoey didn't come out on top, she joins the male's wrestling team. The coach uses takes advantage of this trope because no guy on the opposing would wrestler her because they'd either be seen as a jerk for beating up a girl or look like a wimp for losing to one. Everyone except a Jerk Jock, who proceeds to wipe the floor with Zoey.
Chyna was the first woman to enter the Royal Rumble and compete in the King of the Ring tournament. She didn't win either of them but it was still pretty groundbreaking.
Beth Phoenix also entered the Royal Rumble and eliminated the Great Khali but was quickly eliminated by CM Punk. It was still very impressive.
Women in WWE who have competed in competitive intergender matches (which weren't squashes) aside from the two mentioned above: Molly Holly, Trish Stratus, Lita, Ivory, Jacqueline Moore, Victoria and Mickie James.
Molly Holly once knocked out The Hurricane with a frying pan.
Lita played a sort of Sister Bear role when her boyfriend Matt Hardy was battling The Undertaker at the 2002 Royal Rumble. She crashed the Rumble Match and she and Matt double-teamed the "Deadman." They didn't get very far, but it was still pretty Badass.
Mickie James humiliated Santino Marella by pinning him clean in a match in early 2009 (when Marella was in his "male chauvinist" phase).
In TNA there's also been Awesome Kong, ODB and Hamada.
Not sports but definitely a physical competition: in the Soul Calibur game series, Seung Mina's entire motivation for seeking the Soul Edge is to find it before her father's star pupil Hwang can. She hopes this will prove she's as valuable in a fight as any guy. (According to the official storyline, neither of them ever get close. In Hwang's SC 2 ending, though, Mina still gets a not-so-small reward by saving his life after his battle with Infernoand having Hwang openly thank her and acknowledge her strength.)
In Madden 12, McDonalds contest winner Hope Bromley appears in the free agent pool, the series' first female player. She's ranked 65 overallnote Higher than former #1 overall pick JaMarcus Russell.
Doug: the school baseball team rejects Patty from the school team just for being a girl, she forms her own team, with some other rejects and girls. In a game against the school team, Doug represents the game winning run for Patty's team after finally getting a hit... But what do you know, Roger makes the game winning catch from her at-bat and wins for the school. Patty then decides to turn down the school coach's offer to let her join the school team.
The Proud Family, the one where Penny plays on the school football team, single-handedly turns the homecoming game from a blowout loss into a game they have a chance to win... and drops the ball on the final play.
Inverted and parodied mercilessly on Futurama, with Leela proving to be the worst Blernsball player in history. Then it's played straight when another female player beats Leela. She is hailed for being the first woman in the sport to be good at it.
Leela's Arcturan Kung-Fu master insists he would automatically win in a fight against Leela because "Girls lack the will of the warrior."
Downplayed on Avatar The Last Airbender, with Katara's battle with Pakku. She proved herself to be exceptionally talented, but an untrained teenager wasn't going to beat the best Waterbending master in the world. However, it changes his mind about women fighting and she earns his respect. This is aided a bit when he learns he could have been her grandfather, but for his sexist attitudes.
In the Adventures of the Gummi Bears episode, "Girls Knight Out," Princess Calla joins a competition in disguise in a contest of who would be her Royal Protector to prevent being shackled with one, which includes a surprise challenge by her own father in disguise. Eventually, after winning, she comes clean to her father the King and he notes that he was deeply impressed by her fighting skills and publicly announced that she needed no bodyguard after all.
That was more about remain able to meet the Gummies without exposing them to whoever became her bodyguard.
In Hurricanes episode "Deep Cover", several players from the Hispaniola Hurricanes suffered injuries that prevented them from joining their uninjured teammates in a soccer game against the Garkos Gorgons. The Hispanola Hurricanes' owner, Amanda Carey, decided to join them but had to pull a Sweet Polly Oliver because the World Soccer League had a rule against girls being part of the team. The only chauvinist character in the story was Hurricanes Coach Jock Stone. The Hurricanes won 3-2, Jock learned a lesson, but Amanda was too honest to accept a victory like that and told the truth to the League, despite knowing the Gorgons would be declared winners.