I have an ancestor Caroline Ellen Brown (also mentioned in this question: How might a "nurse-child" have been placed with their carers?) for whom the marriage and birth records are elusive. The three documents I have found that document an age suggest a birth year of 1828/1829 (Feb 1871 death and burial aged 42 according to her husband) or 1825/1826 (April 1861 census aged 35 according to the staff at Guys Hospital). Her maiden name comes from the birth certificate of her second child Stanley in May 1861.
As she was born prior to 1837, the GRO birth indices are of no use in finding her birth. The 1861 census gives a place of birth of Middlesex, City of London but I'm not relying on this as the provider of the information was likely the institution rather than herself or somebody who knew her. Her marriage ought to be findable via the GRO indices, but I've no strong candidate yet.
Her first known child Agnes was born in Hitchin, Hertfordshire in 1859; and Ellen died and was buried in Cheshunt, Hertfordshire in 1871. Her husband was born in Kidderminster, Worcestershire; and the family lived also in Kent and London. After her death, her husband moved to Aston, Worcestershire, re-married and then moved to Lichfield in Staffordshire where he died in 1904. So there isn't even a strong geographical clue to where I should be looking.
In an ideal world, every parish register in England would be online and I could locate every candidate record for her birth (assuming she was baptised). Unfortunately, we live in a less-than-ideal world...
But there is (for example) a Caroline Ellen Augusta Brown baptised in Sawbridgeworth, Hertfordshire on 20th May 1827 (according to findmypast.co.uk). Could be... but how likely?
Is there a technique I can apply (maybe based on name frequency in the approximate period of her birth — say 1820 - 1830) that will tell me how common her combination of names was? If it was very common, then finding this record means absolutely zilch, as there could be hundreds of similar records I can't see because they're not online yet. If, on the other hand, the combination is uncommon, this record warrants further investigation.
So, is there a possible statistical approach here? And if so, what datasets would it depend upon?