A good half of College Football programs were de facto ineligible for the BCS Championship game before a single down is played. "Mid-Major" teams (those not in the oldest and largest conferences) cannot ascend high enough in the computer poll rankings because the teams they play are not good enough to satisfy the strength of schedule requirement. They cannot play elite teams because they must schedule the games years in advance, before the Mid-Major knows if their team will be any good that season. And then when they do play those elite teams and win, it almost always occurs at the beginning of the season, which poll voters have forgotten by the time they are ready to pick the Championship pairing. Utah, Hawaii, and Boise State have all gone undefeated in recent years without a realistic chance of playing for a National Title. The disparity has gotten so bad that it has spawned congressional hearings to investigate it. Whether this is Unwinnable by Mistake or Unwinnable by Design (keeping the big $ in the BCS) is a matter of intense debate.
The "By Design" theory got stronger in 2010: The first official BCS poll (the top two in the poll at the end of the season played for the championship) came out in late October. The top team was... Oklahoma, who was #3 in both human-voted polls. Oregon was #2 (1 in the human polls), Boise St. was #3 (#2). When Oklahoma lost the following week, that week's new BCS #1 was... Auburn - again, ranked #3 in the human polls.
Somewhat applies for College Basketball (men's and women's) as well. The major schools are able to recruit the best high school players, thus colleges named after states (or "X State") fill the annual March Madness tournament year after year (oh, and Duke). But sometimes colleges get lucky and pull off the inexplicable upset in the tournament, thwarting the conventional wisdom; and setting themselves up for a Curb Stomping in the Regional Rounds. On the other hand, if you're in a lesser Conference and had an excellent season (by your standards) but lose in the Conference Finals, then you get sent down to the National Invitational Tournament. Conversely, if your college finishes with a regular-season record barely above .500 and wins your conference tournament by surprise, expect a free trip to a random arena to lose by at least 10 points. Granted, players that focus primarily on sports pick their college based on which of the schools they are accepted to has the best record, but that merely creates a Vicious Cycle for (Regular) Students and Alumni of schools who are too young to be "in the loop".
Combat sports have judges to determine a winner if no one is knocked out, submitted, or otherwise not stopped by the referee/doctor. Rounds are almost always odd-numbered to prevent draws. While a judge usually technically has the right to rule a round a 10-10 round, it's highly rare and openly discouraged, so 99 percent of all rounds are judged for a winner gaining 10 points and the opponent 9 or less. In theory, this should almost always lead to a winner. However, with foul deductions and total domination in a round can lead to 10-8, 9-9, etc rounds, and the overall math of the final score may lead to a draw. This still requires at least two of the judges to come to the same score (or have one judge rule it for one fighter, one for the other and the third a draw). For the most part it the system works, but it does come up on occasion, and can be especially disappointing when it happens in championship fights.
During the tournament for the inaugral Flyweight championship in the Ultimate Fighting Championship, a tie-breaking winner take all fourth round was to be instituted in case of a draw, so as not to have to rematch and slow down the tournament. Unfortunately in one fight, the person counting up the scores made an error and the fight was announced for a winner when it was in fact a draw. The error wasn't found out until later when it was too late to do the fourth round, and the fight was officially ruled a draw, forcing the rematch they were actively looking to avoid with this rule.
One of the most infamous instances of this trope in Mixed Martial Arts was Fedor Emeileaneko's first "loss." In a tournament in the Japanese RINGS organization in the late 90s, future king of the MMA heavyweights Fedor received a fight-stopping cut from an illegal elbow from Japanese pro-wrestler T.K. Under normal rules, the fight should have been declared a no contest. However, due to the tournament, the RINGS officials decided their must be a winner to continue to the next bracket, and the fight was declared a loss for Fedor. Fedor would go on to otherwise be undefeated until 2010, leading many of his fans at the time to clamor and petition to have the blemish on his record removed. However, due to the Wild West nature of early MMA, there really was no one to petition this to. RINGS had since folded as an organization and Japan has no official sanctioning body for MMA. The closest would be the fight records of Sherdog.com, which is still used by many as the unofficial fight record database. Sherdog stood by the original ruling in the records, and every organization Fedor fought for recognized the loss in his stated record.