But Pulis remains far from satisfied with his squad depth, as he expressed his desperate need to secure further reinforcements before the transfer window shuts on August 31. I think we've seen an improvement all across the club in recent seasons and we must continue.
"We need to get some players in and quickly", he told Sky Sports after the match.
"They've got to be players that improve us".
"The squad is just not strong enough". The next few weeks are really vital.
He added: "Jay's been fantastic during pre-season".
"Ahmed Hegazi looks like a really, really good buy".
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One of their 15 draws came last season but was at Turf Moor, which also witnessed 10 of their 11 league wins for the season. At the other end, Peter Crouch has six Premier League goals against the Toffees including one last season.
The Argentina worldwide went close again early in the second period with a header into the side-netting as the Baggies continued to pose a threat from dead balls.
Bournemouth have now conceded goals from set-pieces on three successive visits to The Hawthorns, and only West Brom's poor finishing prevented a heavier defeat, with Rodriguez twice curling the ball beyond the near post.
The Baggies chairman said: "We are continuing a transition from one ownership to another and it is absolutely essential that this process is accompanied by stability within the club". We gave away a needless free-kick, and against West Brom that is a risky thing.
Finishing 10th last season, West Brom hovered between mid-table and as high as 7th spot, with an unlikely shot at European football on the agenda at one point in the campaign.
Rodriguez was preferred to Salomon Rondon in attack for the hosts and he nearly marked his bow with a goal in the ninth minute, Asmir Begovic saving smartly from the striker's snap-shot. I thought we were ready. "There is obviously stuff for us to work on".