Heading into tonight’s action, the Cardinals have opened up an eight-game lead over the Cubs. Their magic number stands at 31. Without taking anything for granted, when might they clinch the Central Division title? If you’re interested in speculatively buying a ticket to see the clinching game, let’s figure it out.

For the season, the Cardinals have won games at a .571 clip. Another way to look at winning percentage is to say that for every game, the team accrues about .57 of a win. Ceteris parabus, over a period of, say 10 games, they usually have won 5.7 games (over 100 games, 57 wins). On the other hand, the Cubs, the next-closest rival in the Central, lose at a rate of .49; that is, for every 10 games, they’ll have 4.9 losses.

In case you’re not familiar with the idea of the magic number, Wikipedia defines it thusly:

A magic number is a number used to indicate how close a front-running team is to clinching a season title. It represents the total of additional wins by the front-running team or additional losses by the rival team after which it is mathematically impossible for the rival team to capture the title in the remaining games. This assumes that each game results in a win or a loss, but not a tie.

So if we project the number of Cardinal wins and Cub losses at some point in the future that will accrue to 31 (today’s magic number), we’ll know the celebration date. We’re actually going to use the teams’ Pythagorean Win% instead of actual, since it tends to factor out some luck. The Cardinals’ PyW% is slightly worse than their acutal (.556, .571 actual), while the Cubs’ is slightly better (.525, .508 actual).

In the following chart, W is the number of accrued wins for the Cardinals at the end of the day; L is the accrued losses for the Cubs.

Interestingly enought, the teams’ head-to-head series occurs in the middle of the countdown. Obviously, the teams can’t accrue part of a win (or loss) in each of those games, but since this exercise assumes a constant rate of either winning or losing, we’ve treated the games as any others.

At any rate, if you want to witness the clincher, it looks like you’ll have to take a trip to Colorado. And for all of you optimists out there who would prefer to use the teams’ actual winning percentages, the big day would still occur at Colorado — just the night before.

This entry was posted by Pip on Tuesday, August 25th, 2009 at 4:30 pm and is filed under analysis. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.