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The top 4 get into qualification rounds.
1) The minimum number of points that can help to qualify based on other teams' performances is 16:
There are 9 teams contesting this year (2012). League matches are of double round robin format. So, total number of matches before qualifying rounds = 2 * 9c2 = 72.
Total number of points = 2 * 72 = 144 (as each match is awarded 2 points in total)
The least no. of points happens in the situation when all teams score equal points and the top 4 with better run rates qualify:
This equals arithmetic mean = total points / 9 = 144 /9 = 16
i.e. Teams that score under 16 certainly do not qualify for top 4 spot, although converse need not be true
2) The minimum number of points that can certainly qualify a team is 25 (or 24 with better run rate):
Proof: Mathematically, this is the arithmetic mean of the maximum points that top 5 teams can score.
This can be evaluated by calculating total maximum points that top 5 can score against bottom 4 PLUS total they can score against each other.. and then dividing the total equally between the 5.
Max total score against bottom 4
= 2 * matches against bottom 4 (home & away)
= 2 * (5 * 4 * 2)
= 80
Max score between themselves (the top 5)
= 2 * matches between themselves (home & away)
= 2 * 5c2 * 2
= 40
Total = 80 + 40 = 120 points
(Alternately, this can also be arrived at by the shortcut:
Overall total points - least possible points that can be scored by bottom 4
= 144 - 2 * (4c2 * 2)
= 120)
Hence the arithmetic mean = 120 / 5
= 24
This mean means that no team with atleast 24 points will stand 5th (excluding the run rates)
Thus, any team that scores 25 points (or 24 with better run rate) certainly qualifies for the top 4 spot, although converse need not be true.
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