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Staffordshire's Lord's dreams came to an end in a tense finish at Leek when Oxfordshire progressed into a semi-final home tie against Berkshire with just three balls to spare.
The finish came as an anti-climax as Oxfordshire, who had been set a target of 200, were awarded the winning runs courtesy of a waist high no-ball bowled by David Edward.
Bowling the last over and trying to deny the visitors the required four runs, the Longton seamer sent down two dot balls to start the over well but then conceded two runs from his third delivery before the wayward ball and conceding the two runs the visitors needed to complete the win.
Having earlier been asked to bat, Staffordshire opened their innings briskly as Peter Wilshaw struck five boundaries in taking Ryan Newhook's opening over for 21.
However it proved a prelude to a dramatic collapse as Brian Sims, George Cairns and Sam Seadon departed without troubling the scorer to leave Staffordshire in deep trouble at 24 for three after four overs.
When Harvey himself fell to a catch at the wicket by his opposite number Ian Hawtin Staffordshire were 59 for four, with four of their top order batsmen managing 15 runs between them.
A partnership of 64 between opener Wilshaw and Mo Sheikh put the Staffordshire innings back on track, but both fell to injudicious shots when well set.
Sheikh failed to take advantage of a life on 34 when his ill-timed attempted sweep gave former England Under-19 off spinner Paul McMahon his first wicket, and Wilshaw then played round a ball from the same bowler to depart for a well made 60 from 85 balls.
Wilshaw, whose knock included ten boundaries, was the sixth wicket to fall at 141 and it was left to wicket keeper Paul Goodwin to marshal the tail before he was the last player dismissed, run out for 43, with one ball of the fifty overs left.
Opener Jamie Hewitt was to prove Oxfordshire's cornerstone as they paced their run chase intelligently, although the outcome could have proved much different when at 74 for three the game Harvey failed to cling on to a catch at slip from Charlie Knightley.
The experienced batsman, making his first appearance of the season for the county, added 87 for the fourth wicket before being run out courtesy of Wilshaw's direct hit for an excellent 74.
When Knightley departed 11 runs later for 36, Staffordshire were back in the game but a spilled catch by Sims, running in from the cover boundary, proved costly as Jack Brooks took full advantage and smashed a six and a four later in the over to put Oxfordshire within sight of victory.
Craig Barker then conceded three singles from the penultimate over before the visitor's reached the finishing line with three balls to spare from Edward’s final over.
Although Staffordshire took the visitors to the wire before bowing out of the competition, captain Richard Harvey conceded they had failed to make the most of their opportunity.
"It's so frustrating. If we had posted a total of around 230 - which was well within our capabilities - we would have had a winning score. At the end of the day it is our own fault,” he said.
“It is our fault we were four down with just 15 overs gone, and that we recovered well only to lose wickets at bad times. I dropped a catch at a crucial time and then we dropped another near the end which cost us vital runs. The fact we came so close despite these errors is why it is so frustrating."
He continued, "Out batting was inconsistent throughout. We got off to a shocker and then rebuilt only to let it slip. 200 wasn't enough and the bowlers did well to get us so close."
Staffordshire chairman Nick Archer concluded: "We finished 20 or 30 runs short. We are inconsistent and that has cost us."
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