Mathematical Elimination

Most websites that carry the Major League standings these days have a column with an elimination number.  Looking at this number from the point of view of the first place team, it can also be called the "magic number."  This is the number of games the first place team wins plus the losses of the team in question that will total the elimination number.

But there's a factor missing in "mathematical elimination" that I wish would appear in the elimination number.  I will explain.

Scenario #1:  Suppose Team A is in first place, two games ahead of Team B with three games left to play.  Team A's magic number (which is the same as Team B's "elimination number") would be two.  Team B can win the division if they win their three games and Team A loses its three.  Or the could tie and Team B could win a playoff game.  That's simple. 

Scenario #2:  Now suppose Teams A and B are tied for first place, and Team C is two back with three to play.  Team C has an elimination number of two, but both Team A and Team B have magic numbers of four against each other.  Well, in this case it is less likely, but if Team C wins all its games and both Team A and Team B lose their games, Team C still will win the division.  In this scenario, Team C still has a chance.

Scenario #3:  Well, there's a potential catch to scenario #2.  What if Team A plays Team B the last three games of the year?  Even though Team C is only two back with three to play, because one of the teams, A or B, necessarily will win at least two of three against the other, Team C has already been mathematically eliminated!  Their "elimination number" is still two, but it's impossible for them to win.  They were already eliminated at least from the previous game played.  Elimination numbers don't take into consideration the number of games played between multiple teams in front of that given team.  And if there are more than two teams ahead of the given team, it becomes even more complex.  In short, the problem is that guaranteed future wins are not counted in the elimination number.

A real life example came from 1989.  With a month left in the season, the Giants were 5 games up on the Padres.  A short news clip noted that the woeful Braves were mathematically eliminated the previous day.  The assumption was that the Braves could have won all their remaining games, the Giants would lose all their games, and the Padres would lose all games but at most five.  A three-way tie would result and the Braves could win a tie-breaker.  But upon looking at the schedule, I saw that the Giants and Padres still had six games against each other to play.  How could the Giants lose all six and the Padres win five at most?  Only if both teams lost the same game, which couldn't happen.  So I figured out that the Braves were actually eliminated the day before that.

How can the real elimination number be calculated?

Interleague Rivalry Matchups for 2013

In my last post, I said I would publish a list of interleague rivalries, those interleague matchups that will (or probably will) occur every year, regardless of which divisions play each other.  These rivalries in 2013 will consist of a home-and-away four game series, two games in each city, in the last week of May.  Here is a list of all rivalries, with American League team listed first.  The first five rivalries will be the five pairs of teams that play in the same metro area, followed by the rivalries that play in the same state, followed by all the rest.  Then some notes.

New York Yankees / New York Mets
Los Angeles Angels / Los Angeles Dodgers
Chicago White Sox / Chicago Cubs
Oakland A's / San Francisco Giants
Baltimore Orioles / Washington Nationals

Tampa Bay Rays / Miami Marlins
Cleveland Indians / Cincinnati Reds
Kansas City Royals / St. Louis Cardinals

Seattle Mariners / San Diego Padres
Boston Red Sox / Philadelphia Phillies
Toronto Blue Jays / Atlanta Braves
Minnesota Twins / Milwaukee Brewers
Detroit Tigers / Pittsburgh Pirates
Texas Rangers / Arizona Diamondbacks
Houston Astros / Colorado Rockies

Notes: The Texas Rangers and Houston Astros were longtime interleague rivals, both being from Texas, but now the new realignment has moved them into the same division. Each of them has a new National League rival.  The groups that don't have a natural rivalry built-in seem a bit forced, but what else can baseball do?  I'm not sure long lasting rivalries will be created between these teams, but you never know.  Detroit and Pittsburgh are only a few hundred miles apart, and the Twins/Brewers pairing might be helped by the already existing Vikings/Packers rivalry from the NFL.  Not to mention college football.  Toronto and Atlanta played against each other in the World Series, and Seattle and San Diego share an ocean.  Boston and Philly are large east coast cities that could make a good rivalry.  The last two sets I have no hope for.

The 2013 Season Schedule

The new 2013 season schedule is out!  I've checked it out (for all 30 teams to some small degree) to see how it deals with the new realignment.  The Houston Astros will be moving from the NL Central to the AL West next year, and each league will have 15 teams, and each division in baseball will have 5 teams.

I believe in an unbalanced, yet symmetrical, schedule.  Baseball history was full of such a thing until 1977 when the American League expanded from 12 to 14 teams.  Well, the new schedule has a number of surprises, some seem good, others not so.

I believe in an unbalanced schedule simply because if you have divisions and a balanced schedule, the divisions are meaningless.  You simply need to play more games against teams in your own division.  Otherwise, just have one league and x number of playoff teams.

I believe in a symmetrical schedule simply because it fosters a level playing field for all teams.  If the schedule is asymmetrical, there will be built-in bias for some teams.

Okay, enough of that.  Let's get to the schedule.  The schedule is unbalanced, and slightly asymmetrical.  The schedule retains the traditional 162 games for each team.  It seems that each team plays the other teams in its own division a total of 19 times each.  Ten in one park, nine in the other.  Nineteen games times four other teams equals 76 division games.  Each team plays the other ten non-division teams in its own league either 6 times (against four of the teams) or 7 times (against six of the teams) for a total of 66 out-of-division league games. 

Interleague features for the very first time that each team in a division plays each team in the other league's matching division, and only that division.  (Except for "rivalry" matchups which I will get to next.)  Each team in a division plays the teams in the other division a mix of games: three games each against four of the five teams, then two separate two-game series - home and away - (for a total of four games) against the fifth team.  This totals 16 interleague games against the selected division to be played that year.  In addition, because each league has an odd number of teams, every series during the year will see at least one interleague matchup, including opening day and the last series of the season.

Finally, the "rivalry" interleague games.  For the first time ever, every team in baseball has a rivalry team in the other league.  This is because the number of teams in each league are the same.  I will provide a separate post listing those rival matches.  Here's the cool thing about the rivalry matchups.  All rivalry series in baseball will be played simultaneously.  The last week of May, starting with Memorial Day, will see a four game series (M, Tu, W and Th) between each rivalry.  But, it will be a four game home-and-away series!  The first two games on Monday and Tuesday will be in the park of one team, and the second two games will be in the park of the other team!  This means that the metro areas that share two teams (and thus are rival teams) will play four games completely within the metro area.  I will develop this, again, in a subsequent post.  Also, I noticed a scheduled day-night double header during one of the rivalry series.  I'll tell which teams at a later time.

So, each team it seems will play 76 division games, 66 inter-division games, 16 interleague divisional matchup games, and four interleague rivalry games, for a total of 162 games.  As strange as some of the things are in this schedule, the relative symmetry compared to schedules past is far preferable to there being an interleague matchup each day of the season, as an example.