Baseball

 

Take Me Out To The Ball Game

Katie Casey was baseball mad,
Had the fever and had it bad.
Just to root for the home town crew,
Ev’ry sou Katie blew.
On a Saturday her young beau
Called to see if she’d like to go
To see a show, but Miss Kate said “No,
I’ll tell you what you can do

 

Take me out to the ball game,

Take me out with the crowd;

Just buy me some peanuts and Cracker Jack,

I don’t care if I never get back.

Let me root, root, root for the home team,

If they don’t win, it’s a shame.

For it’s one, two, three strikes, you’re out,

At the old ball game. 

Next time you sing the chorus, remember the verse!

The American League regular baseball season is 162 games, at least since 1961.  That is what the asterix after Roger Maris’ regular season home run record was all about. The National League increased its season to 162 games in 1962.

An average season since the mid-1960s is  81 wins and 81 losses, a .500 record.  For the standings to be normally distributed, no team can win more than 162 games or lose more than 162 games.  Thus the record has to be such that 81 minus standard deviation/3 ≥0.  That means that the standard deviation of a 162-game season is 81 divided by 3 ≤ 0 or less than 27 games.  The variance is the square of the standard deviation or less than 729.  The team with the best regular season record, before the bias of the playoffs, was 100% the DOMINATE team, but each game was randomly decided, no fixes, so that the CERTAINTY of its being best team is: 68% with a record of 108 and 54; 95% with a record of 135 and 27; and over 99% with a record of 162 and 0.

However, since the introduction of the championship, division, and wildcard playoff series, the league regular season champions might be sitting their best players once the team has clinched a spot in the playoffs, and is no longer trying to win every game at the end of the season. Thus, the playoffs can determine the most DOMINATE team in those playoffs, but the CERTAINTY that this is also the best team can no longer be established.  The regular season is only a means to determine the seeding for the playoffs.

Each playoff series can determine a dominate team for that series, but can not also determine that the DOMINATE team in each series is the BEST team.  In a 3-game series, a team that wins 2 games is dominate but it could have been expected to have a 3-0 or a 2-1 record if all three games had been played.  But the CERTAINTY of the dominate team being the best team is only 34% (it is 88% for a 3-0 record but that is only 12% of the possible outcomes!)   In a 5-game series, a team that wins 3 games can be expected to have a 5-0, 4-1, or 3-2 record.  The winning team has a certainty of being the best team of 38%.   In a seven-game series, a team that wins 4 games can be expected to have a 7-0, 6-1, 5-2, or a 4-3 record.  This is a certainty of 40%.  However, the winner of the wild card or division round was not necessary the higher seed, so if the lower seed wins its certainty should be reduced by being in the previous round. 

The playoffs determine the most DOMINATE team in each series with an odd number of games, but they do not determine the best team with CERTAINTY.  It is the record of the losing team that does that. If the series is stopped after a majority of the wins have been achieved  (e.g. four games in a seven-game series), there is no way to determine what the record would have been in the games which were not played.

That is why the playoffs might be more exciting, but they are not, can not, be certain. If we wanted to be certain, we would have to play ALL of the games. In other words, Play Ball!