Any compiled data on how close these mathematical/theoretical calculations come to predicting the actual results over time?

The human factor (motivated/de-motivated by the series status) might account for some variations from these predicted results.

I'm only discussing individual legacy, it shouldn't be taken into consideration. That's a team stat based on favorable situations outside of skill.

This isn't saying the players should just -give up- when down 0-3 or 1-3. It's saying that when a team is down 0-3 and wins game 4, they're still not very likely to win the series. Because of that, a high-level performance when a team is down 0-3 is not as 'important' as a high-level performance when a team is down 2-3.

A team can win the 1st game and still lose the series, right? But a team that wins a game 7 must win the series, correct? So game 7 is more 'crucial' than game 1 - can we accept this premise? What the data above suggests is that, in addition to that concept, there's a scale for ALL the other games which affects the likelihood of a team's winning a series.

Each playoff game is equally important, I'm with Mike G on this one.

If the .200 shooter makes one, his FT% rises to .333 : an increase of .133
The .800 shooter making one rises to .833 -- up .033

Was the first one 4 times as important or crucial?

Good question. The closest we have in the real world, perhaps, is the series that stands 3-0 . Each game thereafter either prolongs the series or ends it.

In either scenario (relying on simulation for Themojojedi's proposal) I cannot fathom an argument that any remaining game has more importance than another. Nor does it make a bit of sense that a team down 3-2 has no chance, simply because they were once down 3-0.

Is this an argument between marginally equal importance of games versus conditionally unequal importance (given results of preceding games)?

Are there scenarios where these two concepts are both true and scenarios where they aren't?

If two teams are exactly evenly matched is home-court advantage the only driver of the unequal importance of games?

If we get to a Game 7 tied 3-3 are each of the first 6 games now viewed as equally important regardless of whether the series started 3-0 or whether it was 2-2 after 4? Is Game 7 now the only game that is important?

If Stern ruled that the two teams had to play all 7 games regardless of when the series was won, would we agree that all games after one team wins 4 are meaningless/without importance?

Does the fact that games are played in sequence rather than simultaneously create unequal importance due to the potential to eliminate the existence of (important) games later in the series?

If in Stern-world II all 7 Games were "played" simultaneously rather than played sequentially would we all agree that each game's outcome is equally important?

If we simultaneously "play" all 7 games and then randomly sample the game-by-game results (without replacement) until we have a series result does the importance of each game change because of the order that they were sampled?

If we integrate/simulate over all possible samples/drawings are the games now viewed as equally important again?

Then in retrospect, your homer that made it 12-2 must have rattled the opposition, got their pitcher out of the game, begun a series of unlikely events leading to a 12-run 9th inning. Maybe the winning run is just a bases-loaded walk, with no particular hero.

Basketball uses the same math.

If you're down 20 at the half, your coach might say you just need to get it to single digits going into the 4th. Then you're 'back in the game'. Overcoming great odds for the next 24 minutes, every play might be 'clutch'.

If anyone actually involved with the game should believe this --

"... 1-3 games ... aren't really "crucial" at all -- you're basically going to lose the series anyway, no matter whether you win or lose the game..."

-- then we'd have been deprived of some mighty dramatic sequences in the history of the sport.

The year after Boston's comeback from 1-3 vs Philly (1981), the same thing almost happened next year: Sixers up 3-1, they dropped the next 2. In game 7, at Philly, many fans assumed they'd repeat the previous year's collapse; there were actually empty seats, and this was a game with about 4 Hall of Famers per team.

Assumptions are crazy. One game is one game.