An appropriate consensus standard for 23.2115 (take-off performance) is ASTM F3179 which has been revised twice since 2016 but that version is freely viewable at
https://www.astm.org/VIEW_ONLY/web/v...file=33n_8602N
There's a helpful GAMA
Part 23 Rule Rewrite Training Session on Youtube (
) on the overhaul of CS/Part-23 standards done 3 years ago. In the GAMA video, at about 23 min 30 sec, there's an NTSB/
GA-JSC chart categorising fatal GA accidents over the period 2008–2015. Eyeballing the chart it appears barely one per cent of are attributed to runway excursions "RE"—see ICAO taxonomy (pdf
link). The chart is available on the GA Joint Steering Committee site under GA Safety Performance on the documents page (
link). Similar statistics are reported for accidents in Europe, eg EASA GA-LOC-I fact sheet (
link, pdf
link).