The rabbit hole of my birthday

Today is my birthday.  And I began to wonder if my birthday has evenly fallen on each day of the week...

If leap years didn't exist, your birthday would march through the week one day each year and given knowledge of which day of the week you were born, you could figure out which day of the week your birthday is on.

For example (yes, this lady is going to reveal her age!), born on a Friday and today is birthday #58.  So 58 mod 7 is 2;  Friday + 2 = Sunday!  

That's interesting, by the non-leap year calculation, I should have celebrated my birthday on 9 Saturdays, 9 Sundays, 8 Mondays, 8 Tuesdays, 8 Wednesdays, 8 Thursdays and 8 Fridays.

<sarcastic news flash>  Leap Years do exist and 2000 was a leap year (divisible by 400)

My birthday falls before Leap Day (2/29) so my birthday has been affected by leap days 14 times. (next year, it will be 15).

My early morning paper journal entry was doodling to figure out how many times my birthday has occurred on each day of the week.  It's the same. (but it wasn't always).

As the day progressed, I kept trying to figure out if you could mathematically determine the answer to my original question (what is the distribution of days on which the birthday has occurred)...

After dinner, I sat down to my work computer and whipped up a little program on the dev server to accept input of a birth date and an age.  The results displayed are the number of times your birthday has occurred on each day of the week (as well as the number of times it would have occurred if leap days didn't exist) as well as the number of times leap days have affected your birthday.

It's just a little bit of code.  I tested myself for a few years before and after this year. 

Conclusions for a birthday that occurs before Leap Day and in birth year that is a leap year plus 2:

• Given that the number of leap years I've celebrated is a multiple of 7, the distribution of days will be the same. 
• Also in the year where the number of leap days I've been alive is 1 before a multiple of 7 (e.g. my 54th birthday in 2020), the distribution of days is the same.
• That's a total of 5 years that it aligns. (ages 54 - 58)

I  tested two others.  After leap day in leap year+2  and leap year +1 (significant people in my life)

For a birthday (born in a year that is leap +2) occuring after Leap Day (e.g. March - December) 

•  Given that the number of leap years celebrated is a multiple of 7, the distribution of days will be the same. 
• Or in the year where the number of leap days the person has been alive is 1 before a multiple of 7 (e.g. 53rd birthday in 2019), the distribution of days is the same.
• That's a total of 5 years that it aligns. (ages 53 - 57)

For a birthday (born in a year that is leap +1) occuring after Leap Day...

• Given that the number of leap years celebrated is a multiple of 7, the distribution of days will be the same. 
• Or in the year where the number of leap days the person has  been alive is 1 before a multiple of 7 (e.g. 54th birthday in 2019), the distribution of days is the same.
•  That's a total of 5 years that it aligns. (ages 54 - 58)

 I'm still no closer to any mathematical solutions for this but it's been a fun rabbit hole in which to go exploring.  I have realized that your birth year relative to a leap year does affect the outcome.  It's getting late so this exploration will have to continue another day  (seems like a good task for those days where nothing else is going right)