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The phrase "a much higher score" is correct and usable in written English.
It can be used when comparing scores, typically in contexts such as tests, assessments, or competitions to indicate a significant increase in points.
Example: "After studying for weeks, she achieved a much higher score on her final exam compared to her previous attempts."
Alternatives: "a significantly better score" or "a considerably higher score."
Exact(9)
"We should have been leading by a much higher score in the first half," the Leverkusen coach, Roger Schmidt, said.
"It actually shows we can get a much higher score.
Undergraduates (majors and nonmajors) in phase II averaged a much higher score of 84.8.
Mean sequence coverage of 40% was obtained, which is a much higher score than that generally admitted 15-200% of protein coverage) (19).
Single peptide hits (SPHs) were also accepted but above a much higher score threshold and provided the protein sequence coverage was 2.5% or more, see hereafter.
Since the network genes are functionally coherent subsets of all differentially expressed genes, we expected them to gain a much higher score in specialized categories and possibly a lower score in broad categories.
Similar(51)
And they did it by trading goals with a much higher-scoring team.
Notably, we found Polyscan tends to assign homozygous indels with much higher score by investigating the raw sequencing data.
A much higher PEI score was obtained for a Croatian population of 5,527 patients ≥ 18 years of age: the mean enablement score was 6.6 (95% CI not provided) [ 9].
Terrorists, listed immediately above investigative journalists on the document, were given a much higher "capability" score of four out of five, but a lower "priority" of two.
A share leaking a small significant secret area has a much higher quality score than a share leaking a larger insignificant secret area.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com