Saturday, November 21, 2009

Series as Schedule Building Blocks - Part 1

Schedules are about teams playing games.  But typically for me individual games are not considering during much of the process.  For most of the way I only care about series rather than the individual games that compose series.

The fewer independent parts to have to manage and manipulate, the easier the process is.  That theme will be recurring.

A 3-game series of games on consecutive days is much easier to work with than 3 individual games.  The series packages the games together into a single unit, so that is what I use until the point where the individual games need to be put down on specific dates for the end product.  With mostly 3-game series and some 4-game series, then rather than 6 or 7 games per week I only have to manage 2 series.

In fact, exactly 2 series per week like that (as is typical for modern MLB as described previously) is how I prefer to work.  I get the number of games, but immediately shift to considering number of series, which hopefully is directly related to the length of the schedule.

The MLB schedule is 26 weeks, or 52 half-weeks.  One of those half-weeks is the All-Star Break, so there are 51 half-weeks for series, thus the aim would be 51 series.  For 162-games schedules like MLB I figure to try to match that.  How is that done with 3-game & 4-game series?  Here is the math, with X being the number of 3-game series and Y the number of 4-game series:

X + Y = 51 (total series)
3*X + 4*Y = 162 (total games)

Rearrange the first equation to solve for Y, then substitute that for Y in the second equation:

Y = 51 - X
3*X + 4*(51 - X) = 162

Solve the second equation for X, which allows for determination of Y also from the first total series equation:

3*X + 204 - 4*X = 162
X = 42
Y = 9

We could have figured that out a little less explicitly mathematically.  What if 162 games were all in 3-game series?  That would be 162/3=54 series.  That is 3 more half-weeks than the MLB template.  I fairly regularly end up making schedules with only 3-game series, but for 162 games that makes the season a week and a half longer.  To avoid that the games of the "extra" 3 series need to be absorbed by other series to make some 4-game series.  With 3 extra series of 3 games each, that is 9 series that need to be made into 4-game series.

Whatever the total number of games, if given the flexibility my first step is to translate that number of games to a workable number of series.  For 144 games, 46 series allows for about the same frequency of offdays.  For 120 games, 38 series is an obvious choice.

The next trick after that is slotting opponents home and away into those series.  That can be very tricky and lead to having to go back and start all over.  Consider the 51 series for a 162-game schedule.  That is an odd number meaning that the number of home and away series will not be equal, probably being 25 of one and 26 of the other.

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