West Ham flirted with relegation during the 2013-14 campaign before eventually recovering to finish 13th.
Part of the problem at Upton Park was the team's troubles in the final third, with the club scoring just 40 goals last term.
This season has seen a marked improvement on that front, though, with the club riding high in fourth having scored 26 goals in 15 top-flight matches.
And manager Allardyce is thrilled with the way the team is converting their chances.
"What we've got this year is that we're taking our chances more," he said ahead of Saturday's visit to Sunderland.
"You play in the best way you can with the team you've got and we've never been short of creating chances."
Allardyce is expecting a tough encounter at the Stadium of Light against a Sunderland side that have had their own problems in front of goal this term, with only Burnley and Aston Villa scoring fewer than their tally of 13.
"Sunderland is a difficult place to go," he added. "[Sunderland head coach] Gus Poyet has probably struggled for goals and that would have got them more wins than the draws."
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