Update column in rows with variable for each row

I have a database and have added an additional column ‘team’ so it looks like this

date   |   forename   | surname   | team
-----------------------------------------
1/1/01 |   james      |  smith    | 
2/2/02 |   paul       |  jones    |
3/3/03 |   steven     |  bradley  |

I want to add an entry to the team column from each, chosen using the random package from a list of teams

import psycopg2
import random

dbconfig = {
    "dbname": "mydb",
    "host": "127.0.0.1",
    "user": "user",
    "password": "password",
    "port": 5432,
}

connection = psycopg2.connect(**dbconfig)
connection.autocommit = True

teams = ["liverpool", "chelsea", "arsenal"]
cursor = connection.cursor()

cursor.execute("select * from players")
players = cursor.fetchall()

for player in players:
    team = random.choice(teams)
    query = f""" update trades set team = '{team}' """

But when I do this it updates the team for every row rather than just the current one, so I get left with

date   |   forename   | surname   | team
-----------------------------------------
1/1/01 |   james      |  smith    | chelsea
2/2/02 |   paul       |  jones    | chelsea
3/3/03 |   steven     |  bradley  | chelsea

Can I update the rows one by one or in bulk using the random variable?

>Solution :

Include a WHERE clause that matches the specific row based on the date, forename, & surname. This way, each row will be updated individually with a random team from the teams list.

for player in players:
    team = random.choice(teams)
    query = f"UPDATE trades SET team = '{team}' WHERE date = '{player[0]}' AND forename = '{player[1]}' AND surname = '{player[2]}'"
    cursor.execute(query)