Below is the full definition of P/E. P/E measures 'the involvement of the skater physically, emotionally, and intellectually as they translate the intent of the music and choreography'.
IMO, because Akiko's routine is not choreographed to the music and Mao's is, it is very difficult for her to get a high score no matter what. I would say that Mao executed her movements to the music better than Akiko, has better carriage, better clarity of movement, and better variety and contrast compared to Akiko.
The only criteria that Akiko did better than Mao at NHK was 'projection'. Akiko definitely projected more energy that day compared to Mao. But that is only one out of the six criteria of P/E. In the other five criteria of P/E, Mao was better than Akiko, so it is no wonder that Mao scored better (7.96 to Akiko's 7.93).
If P/E was all about projection, then Akiko should have scored higher than Mao in P/E. But unfortunately for Akiko, in order to get a high score in P/E, you need choreography, and her routine doesn't have that. She basically skates from one element to another with great energy, but without paying too much attention to the nuance of the music.
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Performance/Execution
Definition: is the involvement of the skater/couple/teams physically, emotionally, and intellectually as they translate the intent of the music and choreography.
Execution: is the quality of movement and precision in delivery.
Criteria:
-Physical, emotional, and intellectual involvement
In all skating disciplines each skater must be physically committed, sincere in emotion, and equal in comprehension of the music and in execution of all movement.
-Carriage
Carriage is a trained inner strength of the body that makes possible ease of movement from the center of the body. Alignment is the fluid change from one movement to the next.
-Style and individuality/personality
Style is the distinctive use of line and movement as inspired by the music.
Individuality/personality is a combination of personal and artistic preferences that a skater/pair/couple brings to the concept, manner, and content of the program.
-Clarity of movement
Clarity is characterized by the refined lines of the body and limbs, as well as the precise execution of any movement.
-Variety and contrast
Varied use of tempo, rhythm, force, size, level, movement shapes, angles, and, body parts as well as the use of contrast.
-Projection
The skater radiates energy resulting in an invisible connection with the audience.