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Daily Box Score 9/9: Magic Numbers


As I mentioned yesterday, this year's playoff races do not look like they will be close. Although the Rangers helped their cause significantly last night, they still have less than a one-in-three shot at the playoffs. The next lowest team (predictably, the Red Sox) are at 81.8%.

Entering tonight's games, there's a sizable gulf between the ins and the outs. All this means is that it's a perfect time to look at playoff races, because we can be so dispassionate.

Table of Contents

Judging The Wild Card
Scheduling for the Playoffs
Magic Number, Reconceived
Discussion Question of the Day


Judging The Wild Card

This is the 16th season of the wild card system, which means pretty soon it'll be asking to borrow the car and thinking about college.

SI's Ted Keith thinks it's worth reflecting yet again on the benefits of the system:

Three previous seasons (1998, 1999, 2007) have needed a one-game wild-card playoff to determine the last playoff spot, but three other times (2001, 2005, 2006) teams have finished tied for first in the division and not needed a playoff because a tiebreaker gave one team the division title and the other the wild card.

Now in its 16th season, the wild card may wind up playing a more vital role this year than ever before.

This season certainly doesn't present the sort of divisional drama we have seen in years past. But is the wild card everything it's made out to be? 

BDD's Jeff Lubbers, at least, isn't so impressed. He argues:

Following games of September 8 the closest wild card race is 2 games (American League) while the closest divisional race is 3.5 games (N.L West).

Of course, part of the reason that the divisional races are less than intriguing is that once again they are overshadowed by the wild card race. Take, for example, the N.L. West. While a 3.5 game lead with 22 games to play (as the Dodgers currently hold over the Rockies) is a healthy lead in early September, it is anything but insurmountable. However, the "race" between the two teams has lost its luster as both teams will likely qualify for the playoffs. What would be more exciting than the two teams facing off the last weekend of the season in Los Angeles with the Dodgers holding a one game lead while only one team will make the playoffs? Not much. However, with both teams making the playoffs the series becomes virtually meaningless. Both managers will worry more about getting their playoff rotations in order than winning games.

The Dodgers have a 99.5% chance at the playoffs, while the Rockies aren't far behind at 86.2%. The Rockies do stand just three games ahead of the Giants, but runs are harder to come by in San Francisco than birthers. Absent a spike in offense, the Giants stand to be left playing October golf in neat, two-hour-affair fashion, one game at a time.

If that's the case, then I think Lubbers is right. But there is the real possibility here that, like the 2007 AL East/Wild Card (which he cites approvingly against the wild card), this NL West race could end up being like a game of musical chairs, with two spots and three teams. As long as the second and third place teams remain closely clustered (or better yet, if all three do), this will be an exciting race. 

Now, you might argue that a race for the second spot in a division isn't as exciting as a race for first place. In fact, I'm sympathetic to this argument. But as it stands, the Wild Card race is tighter than the divisional race, and that has to be accounted for.

Scheduling for the Playoffs

Of course, if we're talking about all the excitement the Wild Card provides, the big divisional races must have been all but decided. And the one division that was predicted to be closest at the beginning of the year simply hasn't been.

The AL East standings show the Yankees nine games ahead of the Red Sox and 17.5 games ahead of the Rays. The class of the AL have a 99.6% chance of making the playoffs. With their magic number at 15 (see at right), at least some Yankee fans are looking to the playoff schedule:

Because the team with the best record in the league can pick which Division Series schedule to play, the Yankees, nursing a 6.5-game lead in that race over the Angels, will probably get the luxury of that choice. [...]

The Yankees’ choice comes down to one of days off. Take a look at the Division Series schedules. If the Yanks opt for the A series, they play five games in eight days and could bring back their games 1 and 2 starters in games 4 and 5. If they opt for the B series, they play five games in seven days and would either bring back their game 1 starter on three days’ rest or use a fourth starter.

Yes, you read that right. The Yankees record is 6.5 games better than that of the Angels, the next best in the AL. You can find the Division Series schedules here. As that site explains:

The Club with the best record in the American League will have the right to decide whether it will play in the seven-day or eight-day Division Series (i.e., whether it will start its Division Series on Wednesday, Oct. 7 or Thursday, Oct. 8). The A.L. Club with the best record will make its selection no later than one hour following the completion of any game that finalizes which club will have the best record in the Championship Season or finalizes the matchups in the Division Series, whichever is later.

Ben Kabak (the author of the River Avenue Blues post) argues the choice will come down to Joba Chaberlain's performance. The fact that the Yankees have the luxury of gaming the choice this far out has to be seen as an additional advantage, doesn't it?

Magic Number, Reconceived

The best time to change a metric is when no one is relying upon it. And the one formerly-ubiquitous September stat that has been oft-absent for much of this year is the magic number. Magic number is traditionally defined as the sum of wins by the first place team and losses by the trailing team that would result in mathematical elimination. 

Or, put mathematically:

If we let g = number of games in season, then the magic number (M#) can be calculated as:

M# = g + 1 - W - oL

where "o" denotes opponent. 

But Walk Like a Sabermetrician isn't satisfied with plain-Jane magic number:

Of course, there's a big difference between having a M# of 5 with 10 games to play and having a M# of 5 with 20 games to play. We could look at what I will call Magic Percentage (M%)--the percentage of game outcomes that must go a team's way in order for them to clinch. In this case, game outcomes include both the team in question's games and the games of their opponents.

Ah, the old rate stat vs. counting stat argument. But it is interesting to note that the traditional magic number and the suggested magic percentage give different bits of information. For example:

Suppose that the race between the Alphas and the Bravos is shaping up like this, with ten games left for each team:



The Alphas' M# is 9. Again, that means that a combination of nine Alpha wins and Bravo losses will clinch the division. Since each team has ten games left, there are twenty total game outcomes outstanding, and 45% of them (9/20) must go the Alphas' way. Therefore, their M% is 45%.

You can find full magic percentages for this year's races at link, so I encourage you to visit the site.

Discussion Question of the Day

Let's pose two questions raised in today's Box Score:

  1. Is this year evidence of the Wild Card's greatness or its weakness?
  2. What do you make of magic percentage? Is it worthwhile? Is magic number?