While I'm not sure how much the modern methods are amendable to napkin math as stated in the article a lot more methods use simulation which if you can code are

While I'm not sure how much the modern methods are amendable to napkin math as stated in the article a lot more methods use simulation which if you can code are pretty straightforward to get working. Jake Vanderplas's presentation https://speakerdeck.com/jakevdp/statistics-for-hackers https://speakerdeck.com/jakevdp/statistics-for-hackers can give you some concrete ideas of how far you can get with just a random number generator.