Substituion while the game is active

Is ice hockey the only team game in which substitution is allowed while the “ball” is in play.

And yes I know the probably apocryphal story about King Kelly coming off the bench to catch the foul ball.

Lacrosse allows live substitutions, I believe. Not sure about Field Hockey.

NASCAR allows driver changes while the race is under the green flag. The replacement driver get no credit for what it accomplished from that point. In 2007 during an Busch series race at the Milwaukee Mile, Aric Almirola qualified a car for Denny Hamlin. Hamlin was in Pocono qualifying for a cup series race. Due to weather at Pocono, qualifying was delayed a few hours. This meant Hamlin didn’t make it to Milwaukee in time to start the race so Almirola started race. Hamlin arrived at Milwaukee after 100 of the 250 laps. Despite Almirola dominating the race up to that point, Hamlin was put in the car. Almirola was upset about the change and left the track immediately after being replaced. Despite losing 2 laps during the driver change, Hamlin drove the car to the win. The victory lane celebration was surreal, Hamlin got the glory but win, money, trophy and accolades went to Almirola. Almirola never accepted the trophy, today it is a warehouse full of Joe Gibbs racing memorabilia.

Hockey is the best known, but there are a lot of other minor sports that allow live substitution, including beach soccer, futsal, indoor soccer, handball, field hockey/floor hockey/roller hockey/broomball/underwater hockey, lacrosse, Australian rules football, and other even more minor sports. Water polo generally allows substitutions only during stoppages, but live substitution is allowed during Olympic competition.

Calvinball does if you want it to.

It can also be a team game if you want it to.

Yes, but as I recall each rule can be used in only one game.