Crossword Genius

Self-seeking crank first caught leaving for game (10)

Ross

I believe the answer is:

egocentric

I'm a little stuck... Click here to teach me more about this clue!

'self-seeking' is the definition.
(I've seen this before)

'crank first caught leaving for game' is the wordplay.
I cannot quite see how this works, but
'first' could be 'i' (I in Roman numerals eg Elizabeth I) and 'i' is found in the answer.
'caught' could be 'c' (cricket abbreviation) and 'c' is present in the answer.
'game' could be 'go' (go is a board game) and 'go' is found within the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for egocentric that I've seen before include "Self-centred person with little regard for others" , "Selfish" , "Self-interested" , "Self-seeking" , "Not thinking of others" .)

I've seen this clue in The Times.
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