@AbuHajaar
She explains why she stopped running.
She had evaluated his magic and physical capabilities as below average earlier, yet if he was coming up that meant he had defeated Romantica which she had evaluated as strong and was moving at a high enough speed to catch up to her. This meant that a person with a power she couldn't evaluate was about to reach her from behind, so in order to prevent an attack she had to face him. This was the correct decision.
The mistake she made was during the fight. Once she had understood that he had an analysis skill and could turn another's magic against them, that that was how he had defeated Romantica despite being weak, and that her attack had brought him to a standstill, she should have realized that all she needed to do was cross the finish line because he didn't have the means to truly stop her. However, since she isn't the type to back down from a fight, as she is strong, she also forgot what the winning condition was in this competition and continued attacking and assuming that he was trying to attack her. At the end, she drew her sword because she thought he was moving towards her to attack and wanted to defend.
Honestly, her loss was due to a small mistake and things happened so quickly that it was a reasonable mistake to make.
Of course, we can also think of other things.
I think she had an opportunity to connect the dots concerning his ability. She knew he had poor mana and physical abilities, yet defeated someone with strong magic. There's probably nothing besides analysis magic that could explain that. But to be fair, most people, even geniuses, do not thoroughly think things through, especially when you consider she was making a split second decision.
She also didn't use any tactics during the fight. She went all in by summoning tons of magic arrows circles, then only used part of them. A question we can raise is: why didn't she continue running and summon a single magic arrow to attack him? It is probably because it is difficult to move, concentrate to activate the magic at the same time and aim at an opponent she isn't looking at.
I'd say the biggest mistake she made was at the start, when she told him he wasn't worth her putting any time in attacking him. If she had attacked him there and then, she would have learned what he could do and would have had plenty of time to evaluate her options and then reach the finish line. But it's not like her decision to aim for the goal and ignore her opponents was inhenrently wrong, and you know what they say about hindsight.
Really, the MC just surpassed expectations with unexpected high tier analysis magic and his smart use of the little magic he had. His creative use of magic is one thing but his analysis magic is noted as something that he shouldn't be capable of. It was mentioned that analysis magic is based on knowledge of runes - where did he acquire it? Then there's the speed of his analysis, which was compared to a tier 6 rank. The MC has a highly specialized stat build which appears weak.