Surviving false shots is not necessarily luck. Skill also contributes! Being good enough to still deflect the ball to a safe area or being able to avoid edging it or getting into a position where lbw should not be given should not be put down to just luck.
As you carefully define in the very first paragraph, I think you use "luck" here to refer to the entire set of circumstances where the outcome cannot be determined by some action, only the probability of some outcome(s) shifted one way or another. This is not an unreasonable definition, if a little different from the intuitive understanding of the term most people have - in common use, I think the term's meaning is understood to be closer to situations where the outcome is unknowable (true random being the perfect embodiment) than simply not easy to determine.
It is obviously the case that the probability of the two outcomes of a false shot are not 0.5. If it were, one would not expect a batter to survive 20+ false shots on *average* - that is a probability of less than 10^-6 if each false shot had a 0.5 probability and was independent of the others (which is a reasonable assumption). So, obviously, such a batter, it would seem, is, on average, significantly reducing the probability of one outcome. You have pointed this out clearly as well.
More importantly though, the huge variation in false shot survival rate - 1 to 40+ - suggests that other confounding factor(s) than simply the base skill of the batter induce the extraordinary variation. They always (mostly) possess that skill, and always deploy (to be reasonably expected), yet end up causing hugely varying outcomes. It is perfectly reasonable to call all of this "luck" as we don't know what those confounding factors are, but the data would seem to suggest there is a elephant or elephants in the room, waiting to be teased out. When there is that much variation, usually some big, presently unknown but knowable, causative factors are in play.
Super analysis. Can you please share the false shot percentages, balls per dismissal for Sachin and a Rahul Dravid in test cricket?
Surviving false shots is not necessarily luck. Skill also contributes! Being good enough to still deflect the ball to a safe area or being able to avoid edging it or getting into a position where lbw should not be given should not be put down to just luck.
As you carefully define in the very first paragraph, I think you use "luck" here to refer to the entire set of circumstances where the outcome cannot be determined by some action, only the probability of some outcome(s) shifted one way or another. This is not an unreasonable definition, if a little different from the intuitive understanding of the term most people have - in common use, I think the term's meaning is understood to be closer to situations where the outcome is unknowable (true random being the perfect embodiment) than simply not easy to determine.
It is obviously the case that the probability of the two outcomes of a false shot are not 0.5. If it were, one would not expect a batter to survive 20+ false shots on *average* - that is a probability of less than 10^-6 if each false shot had a 0.5 probability and was independent of the others (which is a reasonable assumption). So, obviously, such a batter, it would seem, is, on average, significantly reducing the probability of one outcome. You have pointed this out clearly as well.
More importantly though, the huge variation in false shot survival rate - 1 to 40+ - suggests that other confounding factor(s) than simply the base skill of the batter induce the extraordinary variation. They always (mostly) possess that skill, and always deploy (to be reasonably expected), yet end up causing hugely varying outcomes. It is perfectly reasonable to call all of this "luck" as we don't know what those confounding factors are, but the data would seem to suggest there is a elephant or elephants in the room, waiting to be teased out. When there is that much variation, usually some big, presently unknown but knowable, causative factors are in play.
The definition is specific to cricket. In cricket, no single player determines the outcome a delivery.