Extreme rainfall - Lawn drainage holes

To help with drainage on the lawn with the ever increasing rainfalls.
I want to drill some holes with a auger bit upto approx 30cm depth and fill with either small pebbles topped with compost/soil.

Would a 8cm dia auger bit be ok from
your experiences. ?

 

I not sure but i found this any help?
YouTube

How to IMPROVE A CLAY lawn by drilling holes with an auger bit

 

My concern would be that you'd create a series of sumps where the water would accumulate in wet weather and not really improve the rest of the lawn.
You could put in proper land drains to take the water to a soak away at the low point of the garden. Either just trench and put drains in or strip the lawn completely put drains in and then put in improved soil and relay the lawn.
My personal approach would be to put paths in between a series of slightly raised beds and plant these up with a variety of bubs, perennials and shrubs.