But they haven't kept a clean sheet yet this season.
Kouyate blazed a huge chance over the top from Arnautovic's centre after the restart and Abdoulaye Doucoure almost punished the visitors' profligacy as he whipped a 20-yard strike just beyond the left-hand post.
"I watched him at Stoke and he was the type you'd never be keen to play against because of his power and strength". Had Andy Carroll concentrated more on hitting the target as opposed to hitting any opposition player with a flailing elbow, West Ham fans would have had a reason to temporarily suspend their justified chants against a board that has overseen this miserable descent.
Our two Central Defensive Midfielders this week are the Dynamic Duo of Cheikhou Kouyate and Pedro Obiang.
"I thought we gave the ball away too cheaply too many times and I expected us to do better".
Richarlison was allowed too much space in the penalty area and his low shot forced Joe Hart into a good save, with Kiko Femenia drilling the rebound, via a deflection, inches wide. Their reward came when Richarlison latched onto Hughes's pass in the 64th. The aforementioned comments on the Everton match were also in vain, the Merseysiders having further dented the morale of Silva's side in that last league outing before the international break.
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From Yakubu Aiyegbeni at Everton to Victor Anichebe at Sunderland, Moyes' teams seemed more fruitful with a strong presence up front. An early lead for the Reds quickly became two as Liverpool found much joy in attacking with pace down the flanks.
As the Hammers floundered in their attempts to muster a response, Carroll's frustration grew further and he was booked for an off-the-ball barge on Richarlison.
"Of course, we know what happened before, but it is time to change and think about what we are doing right now and that's what we are doing".
That could very well still happen but he's had a nightmare start. Forward Marko Arnautovic last night had an X-ray on a suspected thumb fracture sustained late in the game. "Every day is the same in our work". "I don't want to talk anything more about the situation - what I can control is my team and I will be at training for the next session on Monday".
Moyes knew his luck was not in when Manuel Lanzini's goalbound shot was cleared off the line by Christian Kabasele. The result was typical of the Hammers' season - another shambolic defensive display coupled with a lack of clinical finishing at the other end of the pitch.
The experienced players in the squad will also recognise the perils which face the club who are only a single point above the relegation zone now and this could easily see the classic first-match bounce of a manager's new career path.