In baseball standings, we say that Team A is "a game behind" Team B if
Team A needs to win a game and Team B needs to lose a game in order
for the two teams to have the same won/loss percentage.
Here's a more detailed explanation:
"In the Great American Pastime of baseball, standings are determined
according to how many games you are behind of another team. The
standings between 2 teams (A, and B) are determined as follows: A gets
one half game ahead of B for every win A has that B does not.
Likewise, A get one half game behind B for every loss that A has that
B does not. Stated a little more mathematically, the number of games
that B is behind is (1/2) * ((WA - WB) + (LB - LA)), where WA is the
number of games A has won, LA is the number of games A has lost, WB is
the number of games B has won, and LB is the number of games B has
source: "Baseball Standings," hosted by udel.edu
For A & B, let's take a look at a real example from this morning's
A. New York Yankees: 61 wins, 37 losses
B. Boston Red Sox: 59 wins, 40 losses
Again, the formula is (1/2) * ((WA - WB) + (LB - LA)), so:
Games behind = (1/2) * ((61-59) + (40-37))
Games behind = (1/2) * ( 2 + 3)
Games behind = (1/2) * 5
Games behind = 2.5
Thus, the Red Sox are said to be "two and a half games out of first
The mathematical reason for the "half game" is the fact that the Red
Sox have played one more game than the Yankees. The Red Sox have
played 99 total games while the Yankees have only played 98 total
As I first mentioned, Team A is a "game behind" Team B if Team A needs
to win a game and Team B needs to lose a game in order for the two
teams to have the same won/loss percentage, but what happens when Team
A plays a game but Team B doesn't (because of rain, scheduling, etc.)?
Well, let's take a look. Suppose that the Red Sox and Yankees had
both only played 98 games. Imagine that the Yankees are still 61-37,
but the Red Sox are 58-40.
Games behind = (1/2) * ((61-58) + (40-37))
Games behind = (1/2) * ( 3 + 3)
Games behind = (1/2) * 6
Games behind = 3
That is, if the Red Sox were to win three straight games and the
Yankees were to lose three straight games, the two teams would have
the same record (i.e., 61-40).
But what happened here was that the Red Sox played an extra game and
won, so they're not three games behind any more, but are they now "two
games behind"? No, because the Yankees would have to lose their 99th
game for that to happen. As a result, the Red Sox are stuck at "two
and a half games behind."
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(plus my own knowledge as a baseball fan)
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Clarification of Answer by
24 Jul 2003 11:05 PDT
Just a few more notes...
In a situation in which Team A has played 2 more games than Team B,
it's possible for Team A to be zero games behind.
Team A: 101 wins, 51 losses (152 total games)
Team B: 100 wins, 50 losses (150 total games)
Games behind = (1/2) * ((101-100) + (50-51))
Games behind = (1/2) * ( 1 + -1)
Games behind = (1/2) * ( 0 )
Games behind = 0
In this situation, Team A and Team B would be "tied" for first place,
but Team B would be listed first because 100/150 is a higher
percentage than 101/151.
Team B 100-50 .667 -
Team A 101-51 .664 -
Another way of looking at this is to consider the concept of "games
over .500." To say that a team is "five games over .500" means that
the team has won five more games than it has lost (e.g., 75 wins, 70
losses). If two teams are the same number of games over .500, then
they will be "tied." Again, though, the team with the higher winning
percentage will be listed first.
You can use the "games over .500" statistic to calculate "games
behind." For example, if Team A is "10 games over .500" (e.g., 80-70)
while Team B is "2 games over .500" (e.g., 76-74), you can simply use
Games behind: 1/2 * (Team A games over .500 - Team B games over
Games behind: 1/2 * ( 10 - 2 )
Games behind: 1/2 * ( 8 )
Games behind: 4