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Game Balance Standings: Inconsistency

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Uploaded: 04/01/06

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Author Topic: * Game Balance Standings: Inconsistency
post_ball

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* Game Balance Standings: Inconsistency


This topic is resumed: see below.


"GB:  9 1/2"
What that's means ?




How can a team be 1/2 game behind ?

volger

eBA Stats Team
Jr. Member
*****
Posts: 19





It is an American system of Game Balance Standings used when there are played very much games a week and sometimes at a certain day, not all the teams have the same number of games played.
Pretend that TEAM A is playing against TEAM B the first day the season started. Pretend that TEAM C are not playing that day. If TEAM A win, the TEAM C would be a half game BACK because they have not played a game yet. If TEAM C win their play, then they are tied, and so on at every round.



In certain sports GB have the meaning of Games Back: it represents the number of games each Team would have had to win, instead of lost, in order to be tied with Team situated in the first place.
At the NBA "GB" is applied under the meaning of "Game Balance" enforcing an assortment of both definitions.
"GB" is here "Game Balance" and more definitions and discussions you can found at The eBA Global Basketball Directory.

 Smiley  John Volger - eBA Stats Team - The Basketball Statistics Analysis

louis_c

eBA Stats Team
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Posts: 12



This message RESUME the topic


Every time the season begins to move forward and we open the work of our Basketball Statistics Creative Analysis seems an appropriate time to take a look at a curious inconsistency that sometimes appears in team standings. Teams are generally ranked on the basis of both winning percentage and "games behind" the leader. Due to the great number of games played we'll use example from the baseball league standings:

EAST ............W .....L.....Pct. ...GB
New York ......92...  59.. .609... --
Boston .........88...  63.. .583..... 4
Toronto  .......74...  77.. .490... 18
Baltimore  .....74...  78.. .487... 18 1/2
Tampa Bay  ...71...  80.. .470... 21

There's no inconsistency here between the ranking according to percentage and the ranking according to games behind, and that's typical. Once in a while, however, the team with the higher winning percentage may be at least one-half a game behind in the standings. Let us analyze the mathematics and identify the conditions necessary for such an event. Team 1 is said to be "k games behind" Team 2 when one-half the difference between the number of wins by each team plus one-half the difference in the number of losses by each team is equal to k: [(w2 - w1) + (l1 - l2)]/2. In effect, the "games behind statistic  represents the number of games that Team 1 would have had to win, instead of lost, in order to be tied with Team 2.
Our second example is a real-life standings example of the type of inconsistency in rankings that can arise :


Team.................L.. ..Pct.... GB
Chicago...........  14  ..9..  .609....  1/2
Cleveland.........  18  12..  .600.... --
Minnesota........  14  14..  .500..  2 1/2
Detroit.............. 12  20..  .375..  6 1/2

Such an inconsistency is most likely to occur when one team has played substantially fewer games than the other.  The inconsistency can also come up later in the season' statistics, especially when two teams have relatively high winning percentages.




The following table shows the winning percentage of Team 2, and how many more games Team 2 must have played than Team 1 for the inconsistency to arise, illustrates why.

Winning percentage...............Critical number of games
............... .510.......................................  51
............... .530.......................................  17
............... .550.......................................  11
............... .570.........................................  9
............... .590.........................................  7
............... .610.........................................  7
............... .630.........................................  5
............... .650.........................................  5
............... .670.........................................  3

Two teams with extremely high winning percentages is also more common at the beginning in the season. If Team 2 has a winning percentage of exactly .500, the inconsistency can't arise because Team 1 could only be at least half a game behind Team 2 if its winning percentage was less than .500. Similarly, the inconsistency cannot come up when Team 1 has a winning percentage of exactly .500. Basketball is not the only sport in which teams are ranked according to winning percentage and games behind. The same anomaly could occur in football, baseball, and hockey team standings.

This summary resumes this topic and will be completed at "The Game" chapter of the eBA Basketball Statistics Analysis System.  Another Basketball game topics you'll find at the Basketball Game Discussions section of our eBA Stats.com site.

   Smiley   Louis C. Sierra -  eBA Stats Team - Basketball Statistics Analysis

 

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