The answer is 0.. That's right 0 in theory if the pitcher is on the mound and licks his fingers the umpire can call a ball. So if the pitcher does this 4 times the batter walks. So in theory if the pitcher walks 3 batters and picks off 3 batters there will be three outs and no pitches were thrown. Walk 4 batters in an inning and score 1 run the pick off the other 3 and you win with 0 pitches thrown. Again in theory of course...
We have to define what we mean by a "regular game" first.
I'm going to base my answer on a "regular game" being a nine-inning game in which a winner is declared.
Let's say the home team wins 1-0, which means nobody has to pitch the bottom of the ninth inning.
In this case, the answer is 1.
In order for the run to score at least one pitch must be thrown. Let's say a home run by our home team.
I liked what the guy said about a ball being called for a pitcher touching his mouth. However, baseball rules say that after being warned not to do that, if he does it again, he's ejected. So it's impossible for a pitcher to just keep doing that until a run scores. You'd have to go through your whole pitching staff in one inning just to get a run to score.
Intentional walks also count as four pitches, even though they're not really pitches, but just tossing the ball to the catcher.
I don't see how a run can score without a single pitch being thrown. If someone can show me differently, I'm all ears.
Now, the matter of the outs being made. In nearly every way a batter can make an out, at least one pitch must be thrown, except:
6.06 (b) A batter is out for illegal action when-He steps from one batter's box to the other while the pitcher is in position ready to pitch.
So, if every batter, except for our guy who hits the home run, breaks this rule before a single pitch is thrown to him, no other pitches need to be thrown.
The answer is 1.
You essentially answered your own question on how someone can score without a pitch being throw. Do exactly what you said, then 2 outs in bottom of 9th, pitcher (s) continue to go to their mouth, until it is 4 balls and batter gets 1st. Wild pick-off throw to 1st base, runner comes around to score winning run -- home team wins 1-0, no pitches thrown --- it would never happen, but neither would any of these other scenarios listed
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