Substitutions change the lineup spot, not just the player.

How to track a substitution

1. Identify the rule set for the game, because re-entry and courtesy-runner rules vary by level.
2. Check whether the ball is dead and whether the manager has reported the change to the plate umpire.
3. Record which player left the game and which batting-order spot the substitute now occupies.
4. If several defensive players enter at once, confirm each new fielding position and batting-order spot before play resumes.
5. For a pitcher, also check any minimum-batter, first-batter, injury, mound-visit, or pitch-count rule that may limit the change.
6. If a removed player tries to return, apply the competition's re-entry rule if it has one; otherwise remove the illegal player from the game.

A substitute replaces a player in one lineup spot

A substitution is the legal replacement of one player by another. The incoming player does not create a new batting spot. That player inherits the replaced player's place in the batting order and then plays whatever legal defensive position, baserunning role, or batting role the manager assigns.

That is why baseball substitutions affect more than the player on the field. A pinch-hitter, pinch-runner, defensive replacement, or relief pitcher can change who is eligible to bat later, who has left the game, and whether a team has enough bench players for future moves.

Most substitutions happen during a dead ball

Under professional-style rules, a player may be substituted at any time while the ball is dead. The manager should notify the plate umpire immediately and state the substitute's batting-order spot. The umpire then announces the substitution or causes it to be announced.

If a substitute is not announced, the move can still become effective by action: for example, when a batter takes a place in the box, a runner takes another runner's base, a pitcher takes the rubber, or a fielder reaches the replaced fielder's position and play begins. Plays involving an unannounced substitute still count.

Professional-style substitutions are permanent

In MLB and other professional-style rule sets, a player who has been removed from the game may not re-enter in any capacity. A starter who is pinch-hit for is done. A runner who is replaced by a pinch-runner is done. A fielder who leaves for a defensive replacement is done.

The removed player may usually remain on the bench if team rules allow, but that player is no longer eligible to bat, run, field, pitch, or act as a courtesy runner. If the player improperly appears in the game again, the umpire removes that player when the problem is noticed.

Amateur rulebooks may be different

Many youth, school, tournament, and recreational competitions modify the professional rule because participation, pitcher protection, roster size, and safety are different at those levels. A common version allows a starting player to leave and re-enter once, but only in that player's original batting-order spot. Some leagues also use free defensive substitution, extra hitters, courtesy runners, or mandatory-play rules.

Those details are not universal. Before assuming a player can return, check who is eligible for re-entry, how many times re-entry is allowed, whether substitutes can re-enter after being removed, whether pitchers have separate restrictions, and whether the batting order must stay fixed.

Pinch-hitters and pinch-runners become substitutes

A pinch-hitter enters to bat for another player. A pinch-runner enters to run for a player who reached base. In professional-style rules, either move removes the original player from the game immediately. The pinch player now owns that lineup spot unless another legal substitute later replaces them.

A common misunderstanding is that a pinch-runner is temporary unless the defense changes. That is not true under MLB-style rules. Once the pinch-runner is used, the original runner cannot come back later in the game.

Pitching changes have extra limits

A pitching change is both a substitution issue and a pitching-rule issue. A relief pitcher who enters the game takes the appropriate lineup spot under the substitution rules, but the pitcher may also have to satisfy a minimum-batter rule, a first-batter requirement to start an inning, or a local pitch-count restriction before being removed.

A pitcher can sometimes move to another defensive position without leaving the game, depending on the rule set. That is a defensive-position change, not re-entry. Once the pitcher has been substituted out of the game entirely, the normal no re-entry rule applies unless the competition has a special re-entry rule.

Multiple changes must be made clearly

A double switch or multi-player defensive change can alter more than one batting-order spot. The manager must make the batting-order assignments clear to the umpire before the substitutes take their places. If the manager does not immediately give the required information, professional-style rules give the plate umpire authority to assign the substitutes' batting-order spots.

This matters because the batting order controls who is due up later. A confused double switch can lead to a batting-out-of-order problem if the team sends the wrong player to the plate.

How umpires enforce an illegal return

When a removed player illegally re-enters in a game with no re-entry rule, the umpire directs the manager to remove that player. If the mistake is caught before play starts with the illegal player involved, the proper substitute can usually enter. If play has already started, the play generally stands, but the illegal player is removed and the manager may face discipline if the umpire judges the re-entry was knowing.

In games with a re-entry rule, the umpire applies that rule first. The question is not simply whether the player has appeared before; it is whether the player is eligible to return under that competition's conditions and whether the player is returning to the correct batting-order spot.

Misunderstandings to avoid

• "A starter can always come back" is wrong under MLB-style rules. Re-entry exists only if that competition's rulebook creates it.
• "A pinch-runner is just temporary" is wrong in professional-style baseball. The pinch-runner replaces the original runner in the game.
• "The substitute can bat anywhere" is wrong. The substitute takes the replaced player's batting-order spot unless a legal multi-player substitution changes the assignments.
• "An unannounced substitute makes the play invalid" is usually wrong. If the substitute legally enters by action, plays involving that player count.
• "A pitcher moving to first base has left the game" is incomplete. A defensive-position change is not the same as being substituted out.
• "Every youth league uses the same re-entry rule" is wrong. Youth, school, travel, and tournament rules can differ sharply.

What changes the ruling

• Pinch-hitter bats for the shortstop: the pinch-hitter now occupies the shortstop's batting-order spot. In MLB-style rules, the original shortstop is out of the game.
• Pinch-runner enters for the catcher: the catcher has been replaced. Any later return depends on whether the competition has a specific re-entry or courtesy-runner rule.
• Starter leaves and later returns in a youth game: this may be legal only if the local re-entry rule allows that starter to return, usually in the same batting-order spot.
• Reliever enters but has not met the required batter minimum: the manager may be unable to remove that pitcher yet unless an injury or rulebook exception applies.
• Removed player takes the field by mistake: the umpire removes that player once discovered. Plays that already happened are not automatically erased under professional-style rules.

Source material

• MLB Official Baseball Rules: Rule 5.10
• MLB Official Information
• MLB Three-Batter Minimum Glossary
• MLB Designated Hitter Rule Glossary
• Little League Rules, Regulations, and Policies