Robbery (and this is an aggrevated robbery) is a Crime involving Moral Turpitude)
Petty Offenses clause does NOT apply (due to possible sentence and actual time served)
ESTA will NOT pick this up, as ESTA does not search on these criteria. ESTA is used to prevent Terrorists, previous VISA abusees, Wanted people etc from travelling.
The information on ESTA is used alongside the US-VISIT system. US-VISIT is the fingerprint/photo process backend. This system links to NCIC (National Crime Information Center) which contains details on the UK conviction (but not seemingly the memorandum of conviction). This system will alert U.S. Customs and Border Protection Agency there is a problem, and he will be refused admission.
NCIC and all VWP share this information freely. Data Protection rules do NOT apply.
There is lots of documentation out there regarding this
For example
INA: ACT 212 - GENERAL CLASSES OF ALIENS INELIGIBLE TO RECEIVE VISAS AND INELIGIBLE FOR ADMISSION; WAIVERS OF INADMISSIBILLITY Sec. 212. [8 U.S.C. 1182]
District of Columbia Official Code (to check US sentencing guidelines)
End of the day, even with a Visa, the Border Protection Agency can deny you enyrt.