Pompey must surpass their Great Escape tally and eclipse League Two title form if they are to meet Kenny Jackett’s points challenge.
Following defeat at Charlton on Saturday, the Blues have 10 remaining matches to earn automatic promotion to the Championship.
It represents a massive ask for the former League One leaders, who presently stand eight points adrift of the top two.
Boss Jackett, however, is refusing to abandon ambition.
In the aftermath of The Valley loss, he set Pompey a target of up to nine wins from 10 games. Effectively 27 points.
A stiff task is made even more improbable considering the Blues have taken eight points from the previous 10 fixtures during a wretched post-new year lull.
Still, that tough undertaking kicks off against Walsall tomorrow night, with victory over the 16th-placed side essential.
Coincidentally, it is 13 years to the day since Pedro Mendes netted a last-gasp triumph over Manchester City.
Now etched in Fratton folklore, that moment secured a dramatic 2-1 win to inspire what became known as the Great Escape.
Harry Redknapp’s side headed into the fixture without victory from their previous eight Premier League matches.
They subsequently totalled a remarkable 20 points from a possible 27 to avoid top-flight relegation with a game to spare, clinched at Wigan.
Jackett’s demand for 27 points would need to considerably exceed that return from the 2005-06 campaign.
More recently, Paul Cook’s team captured the 2016-17 League Two title amid stunning scenes.
A sensational end-of-season run consisted of 10 victories from 12 matches, culminating in a last-day 6-1 triumph over Cheltenham to seize the crown.
Broken down to the final 10 league fixtures, that period yielded 25 points from a possible 30 for Cook’s men.
Once again, that form would need to be surpassed in the present day to meet Jackett’s objective.
Certainly modern Pompey history has proven the remarkable can occur in late season.
Perhaps the size of the points challenge is overestimated, not taking into account Luton, Barnsley and Sunderland potentially enduring sudden blips.
Nonetheless, Pompey will have to produce something stunning to succeed from this juncture.