1. A method for determining eviction of store cache entries based on store pressure, the method comprising: determining, by one or more computer processors, a count value for one or more new store cache entry allocations; determining, by one or more computer processors, whether a new store cache entry allocation limit is exceeded; responsive to determining the new store cache entry allocation limit is exceeded, determining, by one or more computer processors, an allocation value for one or more existing store cache entries indicating an allocation class for each of the one or more existing store cache entries, wherein determining includes incrementing the allocation value of each of the one or more existing store cache entries by a value of one, beginning at an allocation value of zero and ending at a predetermined maximum allocation value, wherein incrementing occurs when allocation of one or more new store cache entries exceeds a programmable new store cache entry allocation limit, and counting a number of times each of one or more existing store cache entries has been incremented; determining, by one or more computer processors, based, at least in part, on the allocation value for the one or more existing store cache entries, at least one allocation class for eviction; determining, by one or more computer processors, an eviction request setting for evicting the one or more existing store cache entries; wherein determining an eviction request setting includes combining, by one or more computer processors, the at least one allocation class selected for eviction and one or more eviction set reasons, wherein the one or more eviction set reasons includes initiating eviction when a bandwidth limited path further down a cache hierarchy becomes free; and initiating, by the one or more computer processors, eviction for the one or more existing store cache entries belonging to the at least one allocation class selected for eviction, based, at least in part, on when the one of the one or more eviction set reasons is satisfied.