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The phrase "a much better performance" is correct and can be used in written English.
It is typically used to describe something that has improved significantly in quality or ability. Example: The team's new coach has helped them achieve a much better performance this season, leading them to win their first championship in years.
Exact(60)
He told the examiners that Countrywide's stock grew "25,000 percent over 25 years - a much better performance than Warren Buffett at Berkshire Hathaway.
"But over all, it was a much better performance.
That was a much better performance than the market has had most of this year.
In Britain, HSBC is up about 13 percent, a much better performance than was shown by other large European banks.
Very undeserved but a much better performance than against Leicester," he said of the 4-1 win last week.
The cell with Pt/CNTs showed a much better performance than with Pt/CB at high current densities.
An IIR filter can provide a much better performance than the FIR filter having the same number of coefficients.
The result shows that the newly optimized air-cleaner has a much better performance of noise elimination when engine operating.
and a detailed age estimation (e.g. 17, 23 years old, etc)., provide a much better performance than other methods.
Tonight there were a lot of good things over a sustained period of time and it's a much better performance level.
We lost quite easily at Spotland, 3-0, and then put up a much better performance at Norwich, who were in the second division.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com