Game Balance Standings Inconsistency

Spanish ~ Español - Inconsistencias en las Tablas de Posiciones

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:

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 - 2) ] /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 :

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.

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