One way to hold this word: picture a number going up on a board, and then ask who is standing next to it. Two different people can be. One made the number move — she put the ball in, or she answered the questions right. The other wrote the number down so that it counts. English gives both of them the same name, because -er only says "the one involved in scoring"; it does not say which side of the number they stand on. The sentence around the word tells you which: points belong to a scorer who plays, a sheet and a pen belong to a scorer who records.
From the word’s history
Wiktionary derives scorer from score + -er, tracing the ending back through Middle English -ere to Old English -ere, the ending that names the one who does something.
Wiktionary 記錄 scorer 是 score 加 -er，並把這個字尾一路追到中古英語 -ere、古英語 -ere，也就是「做這件事的人」。這正好解釋了為什麼一個字能同時是得分的人和記分的人——字尾只說「有份」，沒說是哪一種份。
Wiktionary, "scorer"
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