Today I heard a sentence like 「松本さんは クライムゲームを計【けい】 4回担当しました。」. I searched Google and found that there's also 「全」 but I can't find their usage explanation. How to use 「計」 and 「全」 before counters?
Apparently 計 is short for 合計 (total, sum) while 全 is for 全部 (all, everything).
So 計 should be used with numbers which result from adding something, e.g.
The total will be 30000 yen
While 全 is for cases when there is a complete set of something:
All 16 volumes (of a manga series)
In your example sentence, it seems that Matsumoto-san was involved in four crime games in total, but presumably there were other crime games without his/her involvement.