Final answer:
The correct word to fill in the blank is 'assiduous,' which means showing great care and perseverance in one's efforts.
Step-by-step explanation:
The correct answer is a) assiduous. This word is used to describe someone who is diligent and conscientious in their efforts. The sentence would therefore read: 'He was just an average player when he first joined the team, but everyone admired his assiduous efforts to improve his game.' The word 'assiduous' implies that the player worked very hard and paid close attention to detail in order to improve. None of the other options would be appropriate in this context. 'Abstruse' means difficult to understand; 'austere' means severe in manner or appearance, and 'arbitrary' means based on random choice or personal whim.