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October 6, 2011

The BP Wayback Machine

Is the Best of Five the Worst of Series?

by Mike Carminati

While looking toward the future with our comprehensive slate of current content, we'd also like to recognize our rich past by drawing upon our extensive (and mostly free) online archive of work dating back to 1997. In an effort to highlight the best of what's gone before, we'll be bringing you a weekly blast from BP's past, introducing or re-introducing you to some of the most informative and entertaining authors who have passed through our virtual halls. If you have fond recollections of a BP piece that you'd like to nominate for re-exposure to a wider audiencesend us your suggestion.

As we prepare for the three remaining Division Series to be decided, revisit Mike Carminati's case for switching to a longer series format, which originally ran on November 2, 2006.

 

I can't write five words but that I change seven.
-Dorothy "Don't Call Me Dave" Parker

Even though they comprise just a quarter of the playoff teams each year, we have not had a World Series without a wild card since 2001. Since the wild-card experiment began in 1994 there have been seven World Series out of 12 with at least one wild card, and one with two (2002, San Francisco and Anaheim). Wild-card teams have won four of the 12 World Series.

The odds that a given wild card would win a Series are one out of four. The odds that at least one World Series team got in via the wild card are seven out of sixteen and that both were wild cards is one out of sixteen. All of these numbers have been exceeded, and when you consider that the wild card cannot have the home-field advantage in either of the first two rounds, the results are even more improbable.

It makes one wonder if there is something inherently wrong in the playoff system that favors the wild card. Then again, the Cardinals had the 13th-best record in baseball this year. In fact, the last season in which the two best teams per league met in the World Series was 1999 (Yankees vs. Braves), and the only other in the wild-card era was in the strike-shortened 1996 season (Braves vs. Indians). So maybe the system does not help just wild cards, but underdogs in general.

The prime suspect is the five-game Division Series. It seems that the shorter series make it easier for apparently inferior teams, like wild cards, to reach the next round. Remember that baseball used the best-of-five for the League Championship Series for many years until it was expanded to its present best-of-seven format in 1985.

Major League Baseball is reportedly investigating changes to the Division Series format, though fewer home games to the underdog is the present direction, not expanding the series. This even though there will be three more open dates during the playoffs starting next year.

You may recall that the original format for the wild card called for the underdog to host the first two games while the team with home-field advantage hosted games three through five, if necessary (i.e., 2-3). Under the current system the underdog is home for just games three and four (i.e., 2-2-1). There were only two series that went the full five games under the old system and both of those were won by the teams with home-field advantage (1995 Seattle over New York; 1997 Cleveland over New York). Also, the format used for the old best-of-five LCS round (1969-84) matched the old division series format (2-3).

But a number of questions remain about the five-game series: Do they somehow favor the underdog? Do they favor the inferior team? These are two separate questions given that wild-card teams with superior records are often the lower-seeded team. Does losing either Game One or Two at home doom that team to failure? Are they inherently inferior series?

What I found strongly indicates that eliminating the wild card and moving to four divisions would be a much fairer way of crowning a champion.

First, let's stake out the territory. How deep has each type of series gone in the past? (Note, data through the 2006 LCS round) Below are the data for all five-, seven- and nine-game series:

	Best Of    # G     # Series        %
5         3        32             38%
5         4        26             31%
5         5        26             31%
7         4        23             17%
7         5        33             24%
7         6        36             26%
7         7        47             34%
9         7        1              25%
9         8        3              75%

Note that for seven-game series, just 17% are four-game sweeps, the lowest total, while twice as many series (34%) end up going the full seven games. However, for five-game series, the three-game sweep is the most popular result (38%). Just 31% go to the full five games.

What would happen to those series if we truncated them to five games? I looked at the results for all seven- and nine-game series had they been stopped when one team won three instead of four games. Now, I understand that the results (or at least the strategies) would probably have been somewhat different in some cases had they been a best-of-five, but I do believe it illustrates a point. In the table below the games won and lost for the team that won the series are represented as if it were played as a five-game series:

	G Won    G Lost   #Series     %
0        3        1         0.70%
1        3        10        6.99%
2        3        17        11.89%
3        0        28        19.58%
3        1        50        34.97%
3        2        37        25.87%

In total, about one in five (19.58%, the sum of the first three rows above) seven-game series would have a different result if they were truncated to a best-of-five. In four out of five series, the victor would have been the same whether a best-of-five or best-of-seven were played.

However, you will note that the same number of games that changed hands resulted in sweeps in either format (19.58%). Of course, four-game sweeps would translate into three-games sweeps if truncated. What we are interested in are those games that had a possibility of changing hands. We need to break down the list above by actual situation:

	Actual W    Actual L        G Won        G Lost        #Series
4             0               3            0             23
4             1               3            0             3
4             1               3            1             30
4             2               3            0             2
4             2               3            1             15
4             2               3            2             19
4             3               0            3             1
4             3               1            3             9
4             3               2            3             16
4             3               3            1             4
4             3               3            2             17
5             2               3            2             1
5             3               1            3             1
5             3               2            3             1
5             3               3            1             1

There were 50 series in which the loser won three games (out of 143 total series). Of those, 28 would have had a different result of truncated to a best-of-five. That's far from conclusive, but it does support some of the issues we raised about five-game series.

So is there something about the game number itself? Do the better teams win games late in a series, whereas mediocre ones can sneak in a win or two early? Let's look at the winning percentage for the series winner per game num:

	Best Of    Game Num Won    Lost       PCT
5          1        56     28        .667
5          2        64     20        .762
5          3        65     19        .774
5          4        41     11        .788
5          5        26     0         1.000
7          1        85     54        .612
7          2        94     45        .676
7          3        91     48        .655
7          4        98     41        .705
7          5        79     37        .681
7          6        62     21        .747
7          7        47     0         1.000
9          1        2      2         .500
9          2        2      2         .500
9          3        1      3         .250
9          4        3      1         .750
9          5        3      1         .750
9          6        3      1         .750
9          7        3      1         .750
9          8        3      0         1.000
Overall    1        143    84        .630
Overall    2        160    67        .705
Overall    3        157    70        .692
Overall    4        142    53        .728
Overall    5        108    38        .740
Overall    6        65     22        .747
Overall    7        50     1         .980
Overall    8        3      0         1.000

You will note that it's impossible for a series winner to lose the fifth game in a best-of-five or the seventh game in a best-of-seven.

Besides that, you see that the winner in a five-game series gets better as the series wears on. However, in a seven-game series, there is more of an ebb and flow. The best winning percentages are in order, Game Seven (obviously), Six, Four, Five, Two, Three, One.

This seems to imply that Game One matters the least when the series is complete. I wonder, if we break down the Game One scenarios, whether that will remain true.

First, let's look at the series results overall based on whether the series winner was home or away for that game and whether they won or lost the game:

	Series Winner H/A        G Won     G Lost   # Series Won   %
A                        0        1         46             41%
A                        1        0         66             59%
H                        0        1         38             32%
H                        1        0         79             68%

Teams that started on the road were slightly more likely to win the series if the won game one (66 to 46) while teams that started at home were about twice as likely to win a series if the won game.

Let's break that down by series length:

	Winner H/A    Best Of   G Won   G Lost    # Series Won    %
A             5         0        1        16             35%
A             5         1        0        30             65%
A             7         0        1        30             46%
A             7         1        0        35             54%
A             9         1        0        1              100%
H             5         0        1        12             32%
H             5         1        0        26             68%
H             7         0        1        24             32%
H             7         1        0        52             68%
H             9         0        1        2              67%
H             9         1        0        1              33%

You will notice that while teams home start at home are equally likely to win a series if they win as opposed to lose whether the series is five or seven games (both are exactly 68% to 32%). However, a team that wins game one on the road in a five-game series is much more likely to win their series than his counterpart in a seven-game series (65% to 54%).

We can break this down further for five-game series given that their format changed in 1998 from a 2-3 to a 2-2-1 format:

	Winner H/A    Best Of  G Won    G Lost   # Series Won   Format
A (Favorite)  5        0        1        9              2-3
A (Favorite)  5        1        0        17             2-3
A (Underdog)  5        0        1        7              2-2-1
A (Underdog)  5        1        0        13             2-2-1
H (Underdog)  5        0        1        5              2-3
H (Underdog)  5        1        0        17             2-3
H (Favorite)  5        0        1        7              2-2-1
H (Favorite)  5        1        0        9              2-2-1

If this is getting more confusing the further we delve into the data, here is a summary based on home teams in all of the scenarios:

	Situation                           Series W  Series L  %
0-1 H                               38        66        37%
1-0 H                               79        46        63%
5G 0-1 H                            12        30        29%
5G 1-0 H                            26        16        62%
7G 0-1 H                            24        35        41%
7G 1-0 H                            52        30        63%
5G 0-1 H, 2-3 format (Underdog)     5         17        23%
5G 1-0 H, 2-3 format (Underdog)     17         9        65%
5G 0-1 H, 2-2-1 format (Favorite)   7         13        35%
5G 1-0 H, 2-2-1 format (Favorite)   9          7        56%
5G Overall Underdog                 22        26        46%
5G Overall Favorite                 16        20        44%

What we find is that a team that starts a five-game series at home and loses is at a severe disadvantage. Under the old format, a home team (the underdog) losing Game One won the series just 23% of the time. Under the current format a home team (favorite) losing Game One won just 35% of the time.

However--and I think this is the kicker--when the underdog won Game One at home under the old format (2-3) they won the series 65% of the time, but under the current format (2-2-1) the favored team after winning Game One wins the series just 56% of the time. This is doubly perplexing when you consider that an underdog under the old format had just one more home game (Game Two) no matter how deep the series went but the favorite under the current system could potentially have two more home games (Games Two and Five).

Apparently, the advantage of winning Game One at home under the current format is not outweighed by the disadvantage of losing Game One. Under the old system, the result of Game One had a great deal to do with the result of the series, which seems to favor the underdog who hosted Game One. However, you can see above that the underdog under the old format had a 22-26 record.

Therefore, the old format (two at home for the lower seed followed by three at home for the higher seed) actually favors the favored team more than the current 2-2-1 format.

Before I say that for sure, let's look at the numbers through Game Two. Here is the summary table for results through the first two games of a series:

	Situation                              Series W  Series L   %
5G 0-2 H                               1         20        5%
5G 1-1 H                               14        20        41%
5G 2-0 H                               23        6         79%
7G 0-2 H                               3         19        14%
7G 1-1 H                               43        20        68%
7G 2-0 H                               34        19        64%
5G 0-2 H, 2-3 format (Underdog)        0         14        0%
5G 1-1 H, 2-3 format (Underdog)        7         8         47%
5G 2-0 H, 2-3 format (Underdog)        15        4         79%
5G 0-2 H, 2-2-1 format (Favorite)      1         6         14%
5G 1-1 H, 2-2-1 format (Favorite)      7         12        37%
5G 2-0 H, 2-2-1 format (Favorite)      8         2         80%

This confirms what we saw for Game One. In a five-game series, losing at least one of the first two games at home puts a team at a disadvantage (14-20 for a 1-1 start). However, winning one of the two first games at home puts the team in a favorable position (43-20, 68%). If we break it down by five-game format, teams that split the first two games at home have lost the series more often under the new format than the old (37% won vs. 47%).

Next, I would like to look at what I call "brink" games to compare among the series lengths. A brink game is the game that gets a team to the brink of winning. After a brink game, all games are elimination games. A team might not win the series after a brink game, but the other team is always one game away from losing the series.

Below is a list by best-of type of the average brink game number, the percentage that represents of a full series, the average wins for the trailing team as of the brink game, and the ratio of wins for the trailing and leading teams as of the brink game.

	Best Of   Avg Brink G    % of Full  Avg Loser W   Ratio Loser:Winner Ws
5         2.40           48%        0.40          20%
7         4.19           60%        1.19          40%
9         6.25           69%        2.25          56%

For example from above, at the point that the first team reaches two wins in a best-of-five, the trailing team had just 0.4 wins on average.

You will notice that on average five-game series reach the brink game before the series is half over (48%) while the other series needed at least 60% of a series, on average to drive their opponent to "the brink." As of the brink game, the trailing team had just 20% of the wins of the leading team in a five-game series while they had double that in a seven-game series.

So what does this mean as the series progresses? Here are the average results in the game after a brink game (or the first elimination game):

	Brink G   Best Of  Won   Lost     PCT
2         5        39    11       .780
3         5        26    8        .765
3         7        22    5        .815
4         7        41    18       .695
5         7        35    18       .660
5         9        0     1        .000
6         9        1     0        1.000
7         9        2     0        1.000

Overall   5        65    19       .774
Overall   7        98    41       .705
Overall   9        3     1        .750

Once a team is driven to the brink of elimination, the odds of them regaining control of the series are very remote. However, teams trailing in a seven-game series appear to have a better chance than in a best-of-five, especially as the brink game gets later in the series.

Two games after the brink game, the results look like this:

	BrinkG   BestOf   Won       Lost     PCT
2        5        15        3        .833
3        5        16        0        1.000
3        7        4         2        .667
4        7        24        3        .889
5        7        33        1        .971
5        9        0         1        .000

Overall  5        31        3        .912
Overall  7        61        6        .910
Overall  9        0         1        .000

Very few teams survive two games with their backs to the wall no matter the length of the series. However, given that the brink game in a best-of-seven is generally later, the leads to a longer series overall.

The seven-game series seems preferable from the "brink" game perspective, but are the individual games better; that is, more competitive?

The average margin of victory for all playoff games with the average winning and losing runs:

	BestOf   MoV     Winning Runs      Losing Runs
Overall  3.19     5.52             2.33
5        3.35     5.77             2.42
7        3.12     5.44             2.32
9        3.29     4.84             1.55

Yes, the average margin of victory is about a quarter of a run higher in five-game series than seven-game series (3.35 to 3.12).

However, you may notice that the best-of-five did not exist before to division play. What if we run the numbers just since 1969, the year that divisional play started:

	BestOf     MoV          Winning R      Losing R
5          3.35         5.77           2.42
7          3.07         5.62           2.55

The average margin of victory actually gets a farther apart.

What if we just look at the playoffs since the wild card was instituted in 1994?:

	BestOf     MoV          Winning R      Losing R
5          3.41         6.09           2.68
7          3.19         5.77           2.58

Well, they go down a bit from the overall average, but the margin of victory in games that are part of five-game series are still more than in a seven-game series.

So five-game series are less competitive than seven-game series by looking at the series as a whole or by looking at the individual games in the series.

Finally, I wanted to look at a very simple test, do the better teams win in one type of series or another? By better, I mean the team that had a better record in the regular season.

However, this gets a bit problematic. If two teams face each other in a playoff and one was just a game or two better than the other, can we say for certain one is better? This gets more tricky when the teams are in different divisions or more so with different leagues. Then there's an unbalanced schedule and idiosyncratic interleague schedules.

I decided to look mainly at teams that were significantly different from each other. To do this, I took all series and found the standard deviation for differences of their winning percentages. The average difference in winning percentage was .043 with a standard deviation of .0329.

Using these data, I classified some playoffs as having one team that was significantly better. In these series, the better team won 61% of the playoffs, which is slightly better than the series in which neither team is significantly better than the other. In those series, the better team won 58% of the time:

	Si. Diff?  Wnr Better?  # of Rounds  % Won  WC Winners  WC Losers  % WC
N          N            61           58%    11          4        73%
N          Y            45           42%    4           4        50%
Y          N            47           39%    7           3        70%
Y          Y            73           61%    2           7        22%
                                            24         18        57%

However, I also looked at just the data for wild card teams. For those series, the marginally better teams won 73% of the time, but the significantly better teams lose a great deal more often.

If we break these data down by length of series, it gets even more interesting:

	Best Of  Si.     Winner   Rounds  % Won  WC Winners WC Lsrs  % WC
         Diff    Better?
5        N       N        32      73%    9          3        75%
5        N       Y        12      27%    1          1        50%
5        Y       N        10      25%    3          2        60%
5        Y       Y        30      75%    1          4        20%
7        N       N        28      47%    3          1        75%
7        N       Y        31      53%    4          3        57%
7        Y       N        38      48%    4          1        80%
7        Y       Y        42      53%    1          4        20%
9        N       N        1       33%    0          0        0%
9        N       Y        2       67%    0          0        0%
9        Y       Y        1       100%   0          0        0%
                          227            26        19        58%

For seven-game series, better teams, whether significantly better or not, win slightly more often than they lose (53% of the time). However, the best-of-five is a differently story. In five-game series, if one team is significantly better, they win a great deal of the time (though most pre-date the wild card). However, if a team is slightly better, they lose about three-quarters of the time. Now, as I described earlier, it is very difficult to say if one team is truly better in these cases, but they still should not be losing three-quarters of the time.

For the wildcard data, that I have included on the right, the wild cards seem to defy the odds throughout, winning more often when the team is worse no matter the length of the series or how great the difference is between the two teams.

Where does this leave us? It appears the solution is to expand the first round to seven games and to eliminate the wild card by expanding to four divisions. This would require the majors to expand by two teams. Given that there will be three extra off-days during next year's playoffs, expanding to seven games should not be difficult.

If the first round cannot be expanded, the old format (2-3) should be instituted. It actually favors the team with home-field advantage.

Some may say that there isn't enough data to say for certain that these changes must be instituted. But if we want the regular season to have meaning and the playoff system to make some semblance of sense, some change should be instituted. Even Major League Baseball cannot deny it after this incomprehensible postseason. The low television ratings for the World Series may be impetus enough for them to finally act.

Mike Carminati is the author of Mike's Baseball Rants. You can reach Mike by clicking here.

4 comments have been left for this article.

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