Crossword Genius

Fail badly to restrain player — it's shown by this! (9)

Ross

I believe the answer is:

factorial

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'shown by this' is the definition.
The definition suggests a singular noun which matches the answer.

'fail badly to restrain player' is the wordplay.
'badly' indicates anagramming the letters (letters in the wrong order).
'to restrain' indicates putting letters inside.
'player' becomes 'actor' (synonyms).
'fail' is an anagram of 'fial'.
'fial' enclosing 'actor' is 'FACTORIAL'.

'it's' is the link.

Can you help me to learn more?

(Another definition for factorial that I've seen is " !".)

I've seen this clue in The Times.
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