## Who is the Center of the Hollywood Universe?

Hopefully, you've played around a bit with The Oracle of Bacon and discovered how few steps are necessary to link just about anybody who has ever been in a movie to Kevin Bacon, but could there be some actor or actress who is even closer to the center of the Hollywood universe? The answer turns out to be: yes.

By processing all of the 1,912,323 actors and actresses in TMDB, I discovered that there are currently 568 people who are better centers than Kevin Bacon! What does it mean for one person to be a "better" center than another? Consider the following breakdown of people by Bacon Number (as of March 21st, 2023):

Bacon Number# of people
0 1
1 2,054
2 207,491
3 640,094
4 239,305
5 30,551
6 4,662
7 800
8 163
9 28
10 4

That means that there is 1 person who can be linked in 0 steps (Bacon himself), 2,054 people who can be linked in 1 step, 207,491 people who can be linked in 2 steps, etc. So we can compute the average Bacon Number as follows:

$\begin{array}{c}\frac{0·1+1·2054+2·207491+3·640094+4·239305+5·30551+6·4662+7·800+8·163+9·28+10·4}{1+2054+207491+640094+239305+30551+4662+800+163+28+4}\\ =\frac{3482461}{1125153}\\ =3.095\end{array}$

So the average Bacon Number is about 3.095. We can compare that with the average Jackson Number for actor Samuel L. Jackson. The breakdown is as follows (as of March 21st, 2023):

Jackson Number# of people
0 1
1 5,174
2 305,534
3 638,458
4 151,481
5 20,391
6 3,355
7 581
8 150
9 24
10 4

By computing the average of these numbers we see that the average Jackson Number is about 2.902 making Jackson a better center than Bacon. This is not to denigrate Mr. Bacon, and it should be noted that being the 569th best center out of 1,912,323 people makes Bacon a better center than 99% of the people who have ever appeared in a feature film. A list of the 1,000 best centers in the Hollywood universe is available for your enjoyment.

Is there a "worst" center (or most obscure actor) in the Hollywood universe? Of course. I won't tell you the name of the person who produces the highest average number—won't you have more fun finding him/her yourself?—but his/her table looks like this (as of March 21st, 2023):

XXXXXX Number# of people
0 1
1 1
2 4
3 1
4 4
5 8
6 6
7 19
8 9
9 455
10 31,956
11 501,607
12 489,023
13 86,409
14 12,852
15 2,262
16 407
17 112
18 17

That's an average of 11.604!