In major league baseball, a team can be said to be "two and a half
games out of first place" in its division. Where does the "half" come
from or what does it refer to?

Hello.

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
lost."
source: "Baseball Standings," hosted by udel.edu
http://www.cis.udel.edu/~breech/contest/problems/baseball-standings.html

For A & B, let's take a look at a real example from this morning's
sports page:

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
place."

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
games.

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."

search strategy: baseball "games behind" means
(plus my own knowledge as a baseball fan)

I hope this helps.  If any of this is unclear, please use the "request
clarification" feature to let me know.  Thanks.

---

Clarification of Answer by juggler-ga on 23 Jul 2003 21:50 PDT

Sorry for that typo in the first sentence:
"... same win/loss percentage."

---

Clarification of Answer by juggler-ga on 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.

Example:
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.

                   Games Behind
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
this calculation:

Games behind: 1/2 * (Team A games over .500  -  Team B games over
.500)
Games behind: 1/2 * ( 10 - 2 )
Games behind: 1/2 * ( 8 )
Games behind: 4

I am overwhenmed by the completeness of the response...answer given
both conceptually and mathemetically. I was also pleased with the
speed and amused that the researcher picked up in context ...and used
in the answer...that I am a Red Sox fan!  Many thanks, Juggler.

Thank you very much for the generous tip.  Best of luck to the Sox!
-juggler

I understand all of this...

But the question is.. how do you FIRSTLY know who is the first ranked
team ??? The one with an higher PCT ??? What about if a team have 5
games played and another 10 games played (could happen in some
little/fantasy league)..

Is a team with a 2-0 record higher ranked than a team with a 5-1 record?

Thanks

Philberg,

You really should have posted this as a new question, but what the heck...

Okay, you say:
Team A  2 wins, 0 losses (1.000)
Team B  5 wins, 1 loss   (.833)


Games Team B is behind Team A = (1/2) * ((WA - WB) + (LB - LA))
Games behind = (1/2) * (( 2 - 5 ) + (1 - 0))
Games behind = (1/2) * (-3 + 1)
Games behind = (1/2) * ( -2) 
Games behind = -1

So Team B is actually one game AHEAD of Team A.

On a percentage basis, Team A has the "better" record (1.000 versus
.833), but on a "games behind" basis Team B is leading by a game. 
Here's the standings for this fantasy league:

        W   L   PCT    GB
Team B  5   1   .833   -
Team A  2   0  1.000   1

Think about it this way...  If Team A wins its next game, it'll be
3-0.  If Team B loses its next game, it'll be 5-2.   As such, both
teams will be 3 games over .500, and, as such, "tied."

In that case, though, Team A would be listed first as its percentage
would be better:

        W   L   PCT    GB
Team A  3   0  1.000   -
Team B  5   2   .714   -

Ok,

And normally, baseball standings is ranked by GB or PCT ?

I'm looking at mlb.com and they're all even games so GB and PCT always fit.

For a fantasy league, should I sort by GB or PCT ?

Thanks for your quick answer, I appreciate.