Granted, they want to finish their season on a high; there would be no greater fillip going into the winter than to sign off here in style against the champions.
But the visitors can at least rest easy that the threat of relegation has finally been averted.
Up until last Friday, when they beat Warwickshire in a tense game at Headingley, there was a very real danger of them dropping into Division Two.
Although the pressure is off in a wider sense, this was a day that summed up why Essex are the champions and why Yorkshire have suffered a difficult campaign.
Replying to Essex’s first innings score of 227 on day one, Yorkshire had hopes of going beyond it and establishing a useful lead.
Instead, they were bowled out for 111, their lowest completed first innings total of the season, as Essex’s powerful bowling line-up worked its way through Yorkshire’s brittle batting.
Essex followed up with 134-2 in their second innings to establish an advantage of 250 that some might feel is already sufficient.
After the murky weather on day one, hazy sunshine greeted the players for the start of day two. Overhead conditions were as good for batting as they are likely to be at 10.30am in late September, but after a solid start in which Yorkshire experienced few alarms, their problems began with the total on 23 in the 11th over with another failure for Kraigg Brathwaite.
The West Indian tried to turn a ball from Jamie Porter to leg that perhaps shaped away from him at the last moment and knocked out his off stump, Brathwaite’s score of four following innings of 18 and 17 on debut against Warwickshire.
Porter, the 24-year-old pace bowler, and Simon Harmer, the 28-year-old South African off-spinner, have been the standout bowlers in county cricket this season, but Adam Lyth showed that he is no respecter of reputations when he welcomed Harmer into the attack by sweeping his first ball for four and launching his second delivery high into the River End.
With his fifth ball, Harmer hit back when he had Alex Lees caught behind from a nicely flighted off-break, and Lyth’s fluent contribution was curtailed in its prime when he fell for the top score of 35, pushing forward at Neil Wagner, the New Zealand left-armer.
Yorkshire slipped to 54-4 when Wagner trapped Jack Leaning lbw and to 74-5 when Andrew Hodd drove a Wagner full toss firmly back at the bowler, who inadvertently deflected the ball on to the stumps with Gary Ballance stranded.
With Tim Bresnan dropped for this game and pace bowler Matthew Fisher batting at No 7, Yorkshire’s tail had an unusually long look to it, despite Fisher having helped Yorkshire to victory with the bat against Warwickshire, along with Steve Patterson.
Yorkshire’s sixth wicket fell to the final ball before lunch when Hodd was trapped lbw by a Wagner yorker that might have been slanting down leg-side.
The last four wickets went down in the space of five overs shortly after lunch. Patterson was pinned lbw on the back foot by Porter; Jack Brooks was caught behind trying to cut a wide delivery from Harmer; Fisher had his off stump knocked back by Porter, having battled hard for almost 90 minutes, and Karl Carver was caught behind trying to leave a Harmer off break.
Only Lyth, Ballance and Hodd reached double figures as Yorkshire fell two runs short of their previous lowest completed first innings total this season – 113 against Essex at Scarborough.
Indeed, Yorkshire’s three lowest completed Championship scores this summer have all come against Essex, who also ejected them for 150 in the second innings at North Marine Road.
Trailing by 116, Yorkshire made early inroads into Essex’s second innings here.
With the fourth ball of the third over, Brooks trapped Varun Chopra lbw with a full-length delivery and, with the sixth ball, he pinned Ravi Bopara to leave the home side 6-2.
At the River End, Brooks’s new-ball partner, Ben Coad, was extremely unlucky as he went past the outside edge several times, his opening spell of 6-3-5-0 a testament to his accuracy.
At tea, Essex had recovered to 24-2 from 17 overs, 140 ahead, and they turned the screw in the final session with the ruthlessness of champions.
Nick Browne (53) and Dan Lawrence (75) were not separated during the final session, taking their stand to 128 before bad light ended play with eight overs left.