Pecker is a key witness in the case against the former US president, who is accused of falsifying business records to cover up hush-money payment
In fact, it was almost disingenuous to label it as a 'battle' for survival, so meek were the performances of Norwich City, Aston Villa, Bournemouth, Watford and West Ham.
Until West Ham finally displayed the necessary resolve required when attempting to beat the dreaded drop, the grand sum of points accrued in the 15 games played by the bottom five since the resumption of the season was three.
It makes grim reading. Bottom club Norwich have lost all three, scoring none and conceding eight. Bournemouth, now 19th, have lost all three, scoring once and conceding seven.
Aston Villa, in 18th, picked up two points from their four games while Watford, the only team to beat Liverpool this season, appear to have fallen back to their early-season form, also picking up one point from nine.
Shortly before West Ham kicked off against Chelsea, Norwich were hammered 4-0 at Arsenal and, more shockingly, Bournemouth were demolished 4-1 at home by Newcastle - a result that suggests Eddie Howe's south coasters are sinking fast.
Which is why substitute Andriy Yarmolenko's 89th-minute breakaway winner for West Ham felt so massive.
The roars of joy inside the empty London Stadium from West Ham's players, coaching crew and assorted security staff could have been heard right up their Thames Estuary heartland.
In the context of a relegation 'battle' more akin to lemmings headings for the cliffedge, West Ham's win felt like nine points rather than three. It moved them up to 16th place with 30 points, three above Villa.
Manager Davis Moyes was quick to point out that one win was not enough, although his suggestion that his side might need three more victories might be overly cautious.
They go to mid-table Newcastle on Sunday with a chance to establish a safety cushion. While adrift Norwich's home game against sixth-from-bottom Brighton and Hove Albion on Saturday offers perhaps a last chance to kickstart a late escape bid, the fixtures look grim for the others.
Villa are at record-seeking Liverpool, Bournemouth are at Manchester United and Watford, one point above the trapdoor, go to a chastened Chelsea side.
This is the first Premier League survival scrap played out in empty stadiums - perhaps a mitigating factor in the lack of spark displayed by those near the bottom. Vociferous home support when the stakes are high can make a difference.
"It's very easy from the outside to think (the players are not giving all), especially with the manner of the games at the moment. With the lack of a crowd impacting perceived efforts, I think," Howe said after defeat by Newcastle.
"I can see close at hand what it means to the players, how much they are hurting."
The suffering shows no sign of easing though with Bournemouth's last six games including clashes with Tottenham Hotspur, Leicester City, Manchester City and Everton.
Pecker is a key witness in the case against the former US president, who is accused of falsifying business records to cover up hush-money payment
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