How many matches required to reach semifinal of the World Cup 2019?

There are 10 teams in world cup 2019. Each team has to face all the other teams once. So the total number of matches is ¹⁰C₂=45.

Lets Calculate

 (a) LEAST matches to be won to have a chance to reach in finals and (b) No of wins that guarantee the qualification for world cup 2019.

(a) For this, we have to assume that the Top 3 teams performed exceptionally well, winning as much as possible. So the last 7 teams compete for the 4th place. In such case, the top three teams win 9, 8 and 7 matches respectively or you can say 8,8 and 8. As there are 45 matches there should be 45 wins and 45 losses. (We are not going to consider Tie matches. It will result in further complications). In this case, the first 3 teams win 24 (9+8+7) of those matches. The remaining 21 wins can be divided equally giving 3 victories to each of the 7 teams. The one having highest NRR among them qualifies. Mathematically its possible to qualify with 3 wins but the probability of any such thing happening is ≈ 1/2³⁴. So I think we should be on the safe side to say that Minimum wins required for qualification is 4.

matches required to reach semifinal of the World Cup

(b) For this we have to assume that the bottom 5 teams lost as many matches as possible and the Top 5 teams played equally well (in terms of victories). The number of matches won by 6th, 7th, 8th, 9th and 10th team will be 4, 3, 2, 1 and 0respectively or you can say that altogether they won 10 matches. Now again there should be 45 victories. So the top 5 teams have those remaining 35 wins. Equally dividing the victories (for toughest competition), the teams win 7 matches each and the one with lowest NRR gets eliminated. Again, its mathematically possible but the chances are so less that we can say that 7 Victories guarantee a Qualification.

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Summarising- Minimum wins required is 4 but usually it won’t be enough for qualification unless the team is lucky. 5 wins will be enough unless the team is unlucky. Win 7 and you are surely in for the semis. (Luck here means the relative performance of other teams and their Net Run Rate).

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I think a comparison with current IPL format will be helpful. You can say that 7 wins in this World Cup are equivalent to 11 wins (out of 14) in IPL. Similary 6 wins equivalent to 10 or 9, 5 wins equivalent to 8, 4 wins equivalent to 6 or 7. 3 wins equivalent to 5.