MySQL-搜索并替换table1.field'；s contents与table2.otherfield的内容

我需要一个MySQL查询，它将执行以下操作：

我希望它引用teams.id，而不是players表第3列中的alpha团队名称

table: players

id         player_name           team
------------------------------------------
1          Sue Smith         Silly Chimps
2          Mike Olson        Black Cats
3          Tim Hood          Silly Chimps
4          Chris Row         Grease Monkeys
5          Fred Ware         Black Cats


table: teams

id              name
-------------------------------
1              Black Cats
2              Grease Monkeys
3              Silly Chimps

因此，在搜索和替换更新之后，players表将如下所示：

id         player_name           team
------------------------------------------
1          Sue Smith              3
2          Mike Olson             1
3          Tim Hood               3
4          Chris Row              2
5          Fred Ware              1

球队的桌子将保持不变。如果我能澄清什么，请告诉我

update players, teams set players.team = teams.id where players.team = teams.name