LONDON: Even if Pakistan beat Bangladesh at Lord's on Friday, they face a near-impossible task to qualify for the World Cup semi-finals.
The top four at the end of the 10-team round-robin phase advance to the knockouts.
Victory would draw Pakistan level on 11 points with fourth-placed New Zealand.
If two sides are level on points at the end of the group stage, the team with more wins goes through.
But a Pakistan success would mean both they and New Zealand had won five of their nine pool matches.
The next tie-breaker is net run-rate and New Zealand have a huge advantage at +0.175 compared with Pakistan's -0.792, which is in part a consequence of Pakistan's heavy defeat by the West Indies in their opening match, when they were skittled out for just 105.
Pakistan now need to surpass the record winning margin by runs in a one-day international of 290 if they are to overtake New Zealand.
But if Bangladesh win the toss and bat first, the 1992 champions' slim hopes of a semi-final spot will evaporate even before a ball is bowled.
That is because net run-rate can only be boosted by so much if a team is chasing a target, and in Pakistan's case it would not be enough for them to top New Zealand.
The Maths
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Here is what Pakistan, whose highest total at the World Cup so far is the 348-8 they made in a shock win over England, need to do:
If Pakistan score 350, they must win by 311 runs.
If Pakistan score 400, they must win by 316 runs.
If Pakistan score 450, they must win by 321 runs.
Is run-rate rule fair?
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An International Cricket Council spokesman defended the use of net run-rate in major tournaments, telling AFP: "Net run-rate is the second determining factor for league stage standings, with the number of wins the first criteria.
"Over nine games, with each team playing one another, net run-rate provides the fairest reflection of performance across the entire tournament in the event of both sides recording equal match results.
"All competing sides were consulted at length and agreed the playing conditions before the start of the tournament.
"Historically, net run-rate has been the accepted determining criteria for one-day league cricket."
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