Hey hope my reply did not come across as un-thougtful. It's more how you setup the question. There's no reason why someone with a "very compelling story" shouldn't get in with a 720 GMAT. The better question is perhaps, is your story truly compelling? Of course everyone thinks their story is compelling, but will the adcom think so? That is a better question. If the adcoms find your story compelling, I see no reason why you wouldn't get in. But enough with semantics-- How do you determine if your story is indeed compelling? Top business schools get thousands of applications every season from individuals with impressive work experience, great GPAs, and top GMAT scores. However, schools are looking for more from candidates than this alone. Top business schools are looking for demonstrated leadership potential, ingenuity, teamwork, and a passion for making a difference in the world. Particularly when writing your essays, and thereby presenting your story, the most important things are to be engaging, passionate, clear, and memorable, in order to stand out from the crowd. This is how to make your story compelling.
Specifically, pertaining to your essays, you should ask yourself:
Are these examples exemplary?
are they different from others in your field?
do they show leadership?
do they show teamwork?
do they exhibit thoughtfulness?
do they indicate decision making skills or acumen?
…make them think?
…stick in their brain?
…hook them in?
give the reader insight into
…how you think or make decisions?
…how you lead people?
…how you react under pressure?
…how you work on a team?
…how you breakdown a problem?
…how you respond to an emergency?
…what you enjoy doing?
…how you treat others?
…how you leverage an opportunity?
…how you are innovative?
…how mature you are?
do they exhibit
…propensity towards community involvement?
…tendency towards resilience?
...a good level of general knowledge?
…a clear understanding of core concepts of various issues?
…clarity of thought?
…consistency of performance?
…personality, attitude, and the way you react in tough situations?
Do they point to your
…thought process in terms of career planning?
…thought process in terms of decision making?
…diversity of opinion?
…ability to handle difficulty?
Do they demonstrate
…how you deal with success?
…how you deal with failure?
…how you deal with authority?
…how you lead when you're not in charge?
…how you handle conflict?
…how you felt about your situation, not just what you did?
If you can say ‘yes’ to at least a handful of these questions, you may be right that your story is compelling. Hope this helps!