Deaf,
You bring up an interesting point. I have made an observation (in my almost 50 years of living) and use it often to amaze people.
We, generally, give significance to such things (as you pointed out above) based on relationships WE FORM about the various incidents. For example, you pointed out so many 13s, yet how many legs did the racer have? How many legs did each dog have? What is the total of 13 dogs' legs? How many miles did he travel?
Often, when playing cards with a group I will make a bold announcement. I say, "The next card will be <blank>*!" I then turn over the top card. Statistically, I have (about) a one-in-thirteen chance. But, when I am correct the crowd is amazed and tell the story for weeks after. If I am wrong (12 out of 13 times) it is quickly forgotten.
This is the principle that fuels (so called) Psychics and those who profess to "Talk to the dead".
Try the little card stunt the next chance you get. You may even amaze YOURSELF!!
*[<blank> can be any card that strikes your fancy. It should be a card you are NOT holding in your hand and has not been played]