There has been some discussion on the HST thread about the new service pattern including a link to a presentation given by Scotrail to TACTRAN (who are of course the Transport Partnership covering the Stirling council area).
https://www.tactran.gov.uk/cms-assets/2018 09 25 Item 5 ScotRail Presentation.pdf
This is a very interesting document and it makes clear that there are losers as well as winners:
There are also some numbers specifically about journeys from Polmont and Linlithgow to Larbert / Stirling / Dunblane.
The following journey pairs appear in the Top 10 for each station shown:
POLMONT - STIRLING Annual Journeys 37,930 Daily Journeys 120
STIRLING - LINLITHGOW Annual Journeys 26,783 Daily Journeys 85
LARBERT - LINLITHGOW Annual Journeys 7,370 Daily Journeys 23
BRIDGE OF ALLAN - LINLITHGOW Annual Journeys 3,342 Daily Journeys 11
So we can see there are people seeing a slower service as a result of the change.
Ultimately however we can see why the choice that has been made and the reasons that justify it when we see the cumulative impact on customers:
c5,000 daily journeys between Stirling area and Edinburgh are 10-15min faster. Impact on c300 journeys per day
16 times more people benefit from the faster journey times between Stirling and Edinburgh than lose out from extended journeys on the Linlithgow - Stirling corridor. Even if no-one uses the services from Stepps / Gartcosh / Cumbernauld to Edinburgh (unlikely) and even if there is no benefit for travellers from Falkirk Grahamston who have service frequency doubled to Edinburgh with 50% of those services running faster than before (again very unlikely) then it appears the decision is reasonable just based on those numbers.
It is unfortunate for Linlithgow - Stirling customers but I can see why this decision has been made for the greater good.