I just finished Ian Mortimer's 1415: Henry V's Year of Glory, and it seems that many noblemen asked for x amount of masses to be sung in their names or the names of others, usually at a specific church. I had a few questions, however, when Henry V himself asked for literally thousands (possibly into the tens of thousands - I can't remember) of masses to be sung after his death. Did a mass sung in someone's name differ from any other mass, or would all masses in England "count" towards the total? Was anyone in charge of ensuring that these masses actually happened? And did Henry V - or any noble who wanted masses sung, really - actually expect that the number of masses they requested would be sung, or was it, for lack of a better term, the thought that counted?
This is an interesting question. I'm not sure how "precise" the counts were for several thousand masses. I do know that when a king, archbishop, pope, or someone extremely important died, messengers would be sent around the kingdom, diocese, or continent with news of the death and instructions for how long the bells should be smothered and how many/for what length of time masses were to be sung for the deceased.
In a large geographic area, it would seem to be difficult to keep track of how many churches, very far apart from one another, were conducting these masses. However, it may well be that the ecclesiastical network was well-connected enough to keep track of these things, or that at the central cathedral or other religious body, they computed estimations of how many were being sung in how many places and for how long. In contrast, in a place like a monastery (say, if an abbot or monk died) it would be much easier to keep track of how many masses were actually being sung in the name of the deceased, because all of the masses were taking place in the same place.
The number of masses a person requested in their will was often based on how important they were, but also how afraid they were of purgatory and how many sins they believed themselves to have committed. Remember that masses and prayers said for a person's soul were believed to ease and shorten a person's time in purgatory and journey to Heaven, and priests often told parishioners that their sins could be forgiven through the donation of money, property, or the purchase of indulgences. A similar principle would have applied to the allotment of postmortem masses. They were symbolic of a person's power and importance, but also genuinely believed to have a lasting impact on the person's spiritual life after death.
I can't say for sure that 4,500 masses as opposed to 5,000 would have been perceived as a massive discrepancy in terms of the efficacy of the masses and the carrying out of the will, but the masses were by no means only a symbolic gesture that wasn't expected to be carried out to the fullest extent possible.
A nobleman didn't just request x number of masses, he left money to establish a Chantry, a sort of trust to pay priests to say those masses. If he was especially wealthy he might pay for a Chantry chapel in his local church or cathedral, or maybe just an altar. So essentially the priests were under contract to say those masses- and there would have been legal penalties for not doing so.
Here's an example of a Chantry deed from 14th century England.