Athletes and coaches should not think in terms of how a player handles "stress." This is because "stress" is a common consequence of unrelated causes. Here are some examples.
Competition Stress. This kind of stress motivates competitive people, who thrive on opportunities to win against an opponent. Michael Jordan, for example, was described as an uncommonly competitive person. In contrast, conflict avoidant people are de-motivated by competitive stress.
Stress of Anticipated Failure. This kind of stress de-motivates athletes who lack self-confidence. These athletes hold back effort when their thoughts wander to the outcome of a contest. They are wildly inconsistent. Former Chicago Bear quarterback Rex Grossman, for example, played like a champ in one game and like a minor leaguer in the next. At least before his recent marital problems, Tiger Woods was an example of a self-confident (and thus consistent) player.
Stress of Anticipated Injury. This kind of stress de-motivates timid athletes. It is evident in, say, a little league game where a batter is afraid of being hit by the ball. At the professional level, timidity is uncommon. The professional teams that have taken the Reiss Motivational Profile questionnaire, for example, score low for anxiety sensitivity, which means they tend to be less fearful than the general public. For the most part, top level athletes tend to be brave people.
Stress of Unpreparedness. This kind of stress de-motivates organized athletes but motivates spontaneous athletes. Peyton Manning is an example of a football player who prepares very carefully and, thus, would be expected to experience stress if he had to play a game without his usual preparation.
The "Reiss Sports Motivation Profile" is a standardized questionnaire that assesses what motivates any athlete and, thus, what the athlete would be experienced as stressful. This unique tool is used at the Olympic, major league, minor league, NCAA Divisions I and III, and high school and middle school level with world class and nationally eminent athletes. It cannot be used with children.
In conclusion, it is not valid to consider how an athlete reacts to "stress." "Stress" is just a common consequence of different motives, and it is the antecedent motive, not the consequent stress, that predicts performance. An athlete might be de-motivated by the stress of losing (even quit before the game is over) but motivated by the stress of competition. Another athlete could be de-motivated by the stress of poor preparation, while the same stress could motivate a different athlete, and yet neither athlete reacts much to the stress of being in a dnagerous situation.
