Allardyce nevertheless feels the 25-year-old represented a 'risk' as a signing. The West Ham boss was discussing the fact that the Hammers passed up the opportunity to sign Wilfried Bony, who has since gone on to become a prolific goalscorer at Swansea City.
As the 60-year-old says, though, Bony would have represented a risk - more so than Andy Carroll (although that is debatable).
Allardyce believes signing strikers who are unproven in the Premier League is something that may not always produce success but he is delighted that Sakho is proving a gamble worth taking.
"Admittedly, the £8m-£10m player represents a risk that you are going to have to take more often than in the past because there are far fewer top players around," Allardyce wrote in his weekly column for the London Evening Standard.
"Diafra Sakho, at a lot less than that sum, could prove to be a one-in-a- million signing. Likewise Enner Valencia and Cheikhou Kouyate have made bright, encouraging starts."
West Ham travel to Sunderland tomorrow afternoon and are without a win in four games in all competitions, although they remain only five points off third in the league.