I'm interested in organizing a 3x3 basketball tournament at my school or summer camp, but I find the rules for players incomplete: there are 4 players on the roster, eligible for playing (3 on court, 1 substitution), but no mention of "healthy scratches" to replace the roster for injury, and so forth. Any indication in this respect?
As with any sport, this is an organisational aspect outside of the rules, and usually left to the specific organiser's discretion.
The relevant governing body should put out regulations covering circumstances such as how players can be replaced between games in the event of injury. In the absence of a higher authority such as a regional or national association directing otherwise, this is down to what the tournament organisers can provide and will allow.
For example, FIBA's 'Internal Regulations Book 3 Players and Officials' section 129:
National Member Federations are entitled to register the following team delegation members on the Preliminary Team Delegation Roster:
a. Maximum of twenty-four players (24);
and section 135:
[Barring exceptions] the Final Team Delegation Roster shall be composed of a maximum of twenty-five persons (25) as follows:
a. Minimum ten (10) and maximum twelve (12) players out of the twenty-four (24) players [from the previous form]
suggesting that the limit is to only those players selected by the time the tournament starts.
One could look to FIBA's 'Official 3x3 Basketball Rules Official Interpretations' (indicated as the "Yellow version" 2019) section 4, example 4.4 for guidance on constructing an appropriate regulation for this case.
In a FIBA 3x3 Official Competition, Team A has fewer than 3 players on the court ready to play because of injuries, disqualifications etc. This happens:
- (a) Prior to the start of the game. ...
The obligation to be present a minimum of 3 players is valid only for the beginning of the game. In case (a), the game shall not start.
In contrast from a different sport for comparison, World Rugby regulations for the Rugby World Cup require "final" rosters of up to 31 players, but provide for injury-based replacements with a 48-hour no-play limitation. That is, a new player can be flown in as injury cover, but may not play for two days. This regulation is more appropriate in rugby due to the significant physical aspects of play and the need for highly specialised training in a few major roles to ensure safe play.