24 Responses to “Which Games Are the Most Important In a 7-Game Series?”

1. Neil Paine Says:
   June 8th, 2010 at 9:28 am

   This Finals is actually in a position where every game could have more importance than the previous game:

   *Series started 0-0 (chg = .160)
   *Lakers win, Game 2 is 1-0 home team (chg = .166)
   *Celtics win, Game 3 is 1-1 (chg = .193)

   If (and only if) the following pattern takes place, the importance will escalate with every game of the series:

   *Celtics win, Game 4 is 2-1 home team (chg = .204)
   *Lakers win, Game 5 is 2-2 (chg = .240)
   *Celtics win, Game 6 is 3-2 away team (chg = .300)
   *Lakers win, Game 7 is 3-3 (chg = .500)

   I'm not sure how often this happens historically, with the importance escalating every game, so I'll have to check that out at some point.

2. DSMok1 Says:
   June 8th, 2010 at 9:36 am

   Excellent work, Neil. Very useful information.

3. sidole Says:
   June 8th, 2010 at 10:24 am

   Celts will sweep home.Bye bye PJ.

4. David Fauber Says:
   June 8th, 2010 at 10:51 am

   Good stuff, I think the grids would be better if you pruned out the redundant "away" entries and just presented it from the perspective of the home team. (eg 3-1 at home is the same as 1-3 away, you're just showing the inverse of the probabilities)

5. Ben Says:
   June 8th, 2010 at 11:04 am

   Great Stuff. I agree with David Fauber's comment.

6. Mike G Says:
   June 8th, 2010 at 11:50 am

   Guess what: every game is of equal importance.
   They're also equally 'crucial'.

   And if you increase your chances from 15% to 30%, you haven't increased it 15%; you've increased it by 100%.

7. DSMok1 Says:
   June 8th, 2010 at 11:53 am

   That doesn't make sense, Mike. He's talking in terms of Series-Win-Probability. The games are not of equal value in terms of that. It's like a leverage index at the game level.

8. Bill Reynolds Says:
   June 8th, 2010 at 1:32 pm

   Under the 2-3-2 format, there have been 25 Finals played (1985-2009). Before this year, the first two games were split 10 times (in 1985, 1988, 1990, 1991, 1992, 1994, 1998, 2001, 2003, and 2004). In all ten of those series, the team that won game 3 went on to win the series. Remarkably, the road team won game three seven of the ten times -- 1988, 1990, 1991, 1992, 1994, 2001, and 2003.

   Suggests that tonight's game is very big indeed.

9. Jason J Says:
   June 8th, 2010 at 2:32 pm

   I’m not sure it is that surprising that the away team has won the majority of game 3s going into it tied 1 - 1. When you think about it, that’s the team with the better regular season record, the team that earned home court advantage in the first place.

   They are still the favorites in most instances (except when there’s some strange scenario like the 2008 champs playing hurt and lethargic through the second half of the season and then proving to be better than the two teams with the best records…), and you’ve got to imagine that by game 3 both teams have settled down some. Most of the surprises are gone, and the team that has proven itself to be better over the course of the season is likely to be better once all the early adjustments have been made. As a general rule.

10. Mike G Says:
    June 8th, 2010 at 3:45 pm

    Jason J is right. You could look at any of the games (1-7) and probably find the favored team has won 60-70% of them.

    DSMok1, I too was "talking in terms of Series-Win-Probability".
    Yesterday, it's a "crucial" game when you're down 3-0 or 3-1; today it's not "important".

    Both of these conflicting claims are equally weird.

    A team that's adjudged to have a 55% chance of winning a series cannot double their chances in one game. A team with a 15% chance can, though.

    If you're down 3-1 (or 3-0) and come back to win the series, I don't see how you could argue any of those last 3 (or 4) games was less important than any other.

    And if you don't win the series, that still doesn't make any win you got less important.
    Unless, in retrospect, the loser gained nothing by winning any games.

11. Neil Paine Says:
    June 8th, 2010 at 3:55 pm

    Mike, I referred to all elimination games as "crucial" the other day because I needed a way to define "crucial" games, and I felt like that should be a part of it. Then a commenter said, "actually, a game 4 when you're down 0-3 isn't very crucial because a win or a loss won't change the leading team's Series Win Probability that much. So I told that commenter I'd look at each game from a Series Win Probability perspective, and this post is what I found. He was right, in the sense that a Game 4 with the series 3-0 or 0-3 doesn't have the same "leverage" as a Game 4 with the score 2-1 or 1-2. If any of this is difficult to understand, I suggest you read up on the concept of Win Probability Added in baseball, come back, and re-read this post. Then hopefully you'll have a better grasp on the concept I'm working with here.

12. Mike G Says:
    June 8th, 2010 at 6:07 pm

    I do understand leverage. Suppose you have to move a large boulder out of the road. You have a lever and a fulcrum. The first leverage moves the boulder a couple of inches; then you move the fulcrum, and you're able to move the boulder a foot; then you move it again, lever it, and off the road it goes.

    Of course, if you can't ultimately move the rock off the road, the first successful leverages are useless, in retrospect. But if you succeed, it's clear that the first, small move of the rock was the most critical, because it allowed the next moves to proceed.

    You actually use more leverage to move an object a shorter distance.

    If you're down 3-1, winning the 5th game is the utmost necessity. It raises your chances of winning from .144 to .360 : That's 2.5 times as good. Your opponent's likelihood has dropped from .856 to .640 . From comfortable to iffy.

    When Orlando came back from 0-3 to make it 2-3, I read the Celtics were "desperate". What 2 unimportant games can do.

13. UB Says:
    June 9th, 2010 at 7:18 pm

    I believe I was the poster that asked about this a couple weeks ago (and, again, thanks for doing this, Neil - great stuff!). So allow me to chime in, Mike.

    The point is, yes, to come back down from 0-3 requires you to first win that 4th game. The Magic tried to do it, and got 2 of them back. But the funny thing is - that's all they got.

    Is there, at least within the context of THAT series, any difference between losing 0-4 and 2-4? The team is eliminated either way. The extra wins don't get stored up in some kind of special calculation for the next season, at least in direct form (insert arguments here about experience in playoff games, etc).

    In other words, with regards to Orlando's winning their series against the Celtics, the Magic victories in Games 4 and 5 were meaningless. They didn't matter, because the Magic lost anyway. And that's because coming back from 0-3 is extraordinarily unlikely. What the 'crucial' index is meant to show, is whether or not a game significantly impacts the overall likelihood of a team winning a series.

    Think of it in betting terms.

    When Boston is up 3-0, and a guy comes to you and offers you an even-odds bet (so, you bet a dollar to win a dollar) that the Celtics will win the series (so, if the Celtics win the series you lose the best), there's NO WAY you take that bet. When Boston is up 3-1, you still absolutely don't take the bet, though you might think about it for just a moment (the old "Hmm... Nahhhhhhhh."). When Boston is up 3-2, now you're considering it - you still probably don't, but at least now you're considering it for more than a moment ("You know, if Orlando shoots the lights out in Game 6..."). And if the Magic had gotten to 3-3 and he offered you the same bet, with Orlando playing at home, you'd be likely to actually take the bet.

    So that game 4 doesn't change your impression of the series very much (not very "crucial" to the outcome of the SERIES itself). Game 5 changes it more, but not THAT much more (after all, they're still down 2-3 and going to Boston). But game 6 makes a HUGE change in your belief in who's more likely to win the series, in that if the Magic win it now you believe they have a very good chance at going to the Finals.

    So a great performance in game 4 doesn't do much for the overall likely outcome of the series (remember, this whole discussion began with a conversation on individual player performance in 'crucial' games). If a player throws down a huge Game 4 when down 0-3, we tend not to crown him as being particularly clutch (though I've noticed we tend to rarely apply the 'clutch' moniker to big men not named Russell anyway). If that same monster game is played in Game 7, it's far more likely to reflect positively on his legacy.

    I will say, Neil, ironically I'm slightly revising my own position on the matter. At least with regards to media response (because we all know their takes ALWAYS reflect the actual reality), a star player who has an excellent game in any closeout game FOR his team tends to get significant accolades. Not that it makes that much of a difference in the actual series, but the reflection on that player tends to be pretty significant if he nails shut a series with a huge game, regardless of how far ahead in the series the team is.

14. Mike G Says:
    June 9th, 2010 at 10:04 pm

    "... the Magic victories in Games 4 and 5 were meaningless. They didn't matter, because the Magic lost anyway. And that's because coming back from 0-3 is extraordinarily unlikely."

    Maybe you should just say, any wins in a series you eventually lose are meaningless. After the fact.
    In 2006, Dallas' 2 wins against Miami proved to be meaningless, because they lost the series.

    In 1970, the Suns went up 3-1 on the Lakers. LA won a (meaningless?) game 5 and the next 2. Oh -- does that mean the Suns 3 wins were meaningless?

    In 1981, the Celts were down 3-1 to Philly. They won the next 3, by a total of 5 points.
    There not only was no meaningless game, there was not a meaningless possession!

    If you've turned a 0-3 deficit to 1-3, you are certainly in position to keep winning. It's been done. It doesn't really matter if you've gone W-L-L-W-L or L-L-L-W-W, a 2-3 deficit is still as close as a series can be after 5 games.

    Someday, a team will win a series after being down 0-3. Will that, after the fact, make all wins meaningful, back to the beginning of time?

    To win a series, you win four games. Each one has equal value. The betting odds have nothing at all to do with that.

15. Neil Paine Says:
    June 9th, 2010 at 11:04 pm

    So Mike, do you believe a home run hit when you're trailing 12-1 is as "clutch" as a walk-off HR in the bottom of the 9th in a 1-1 game?

16. Mike G Says:
    June 10th, 2010 at 6:10 am

    When you're down 12-1, you need 12 runs to win the game; each of those is equally valuable.
    If you started the rally, that led to the miracle comeback, then yes, you started something great. Everyone behind you, avoiding the final out, perpetuates it.

    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.

17. themojojedi Says:
    June 10th, 2010 at 7:53 am

    I love this stuff! Haven't really thought it through yet so I'm just spitballing some ideas about equal vs unequal importance of games:

    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?

18. Mike G Says:
    June 10th, 2010 at 9:41 am

    "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?"

    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.

19. Mike G Says:
    June 10th, 2010 at 10:43 am

    If a guy is 1-5 from the FT line, he's shooting .200 .
    Another guy is 4-5, shooting .800

    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?

20. Hk Says:
    June 10th, 2010 at 4:51 pm

    The argument that we need to try to "understand" the media's flawed perception, and overreaction, of players is ridiculous. We need to promote logic not contort our views to support some hack writer or sports analyst.

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

21. UB Says:
    June 10th, 2010 at 7:35 pm

    It's not an issue of understanding the media's perception, it's trying to better clarify it. Each playoff victory has the same value. But each playoff game does not contribute the same amount to the relative likelihood of a series victory. When a team is down 0-2 and returns home, a loss in that game is much more damaging than if the series is tied 2-2.

    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.

22. Hk Says:
    June 10th, 2010 at 11:36 pm

    What about the Magic Series this year? If they had split one of those "less" important games 1 or 2, that changes everything. Dwight Howard could have performed at the exact same level and taken his team to a 3-3 tie heading back to Orlando. Slight favorites instead of fishing.

    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.

23. Hank Says:
    June 13th, 2010 at 2:23 pm

    So who has the best game 7 stats in playoff history? (All rounds.)

24. paul Says:
    May 23rd, 2011 at 6:39 pm

    this is great!

    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.