The Oracle of Bacon

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 2,289,228 actors and actresses in TMDB, I discovered that there are currently 565 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 April 2nd, 2024):

Bacon Number	# of people
0	1
1	2,172
2	235,220
3	734,816
4	279,180
5	36,406
6	5,573
7	1,128
8	355
9	114
10	28
11	15
12	2

That means that there is 1 person who can be linked in 0 steps (Bacon himself), 2,172 people who can be linked in 1 step, 235,220 people who can be linked in 2 steps, etc. So we can compute the average Bacon Number as follows:

$\begin{matrix} \frac{0 \cdot 1 + 1 \cdot 2172 + 2 \cdot 235220 + 3 \cdot 734816 + 4 \cdot 279180 + 5 \cdot 36406 + 6 \cdot 5573 + 7 \cdot 1128 + 8 \cdot 355 + 9 \cdot 114 + 10 \cdot 28 + 11 \cdot 15 + 12 \cdot 2}{1 + 2172 + 235220 + 734816 + 279180 + 36406 + 5573 + 1128 + 355 + 114 + 28 + 15 + 2} \\ = \frac{4021479}{1295010} \\ = 3.105 \end{matrix}$

So the average Bacon Number is about 3.105. We can compare that with the average Jackson Number for actor Samuel L. Jackson. The breakdown is as follows (as of April 2nd, 2024):

Jackson Number	# of people
0	1
1	5,544
2	349,119
3	735,290
4	176,660
5	23,440
6	3,800
7	786
8	242
9	79
10	32
11	15
12	2

By computing the average of these numbers we see that the average Jackson Number is about 2.907 making Jackson a better center than Bacon. This is not to denigrate Mr. Bacon, and it should be noted that being the 566th best center out of 2,289,228 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 April 2nd, 2024):

XXXXXX Number	# of people
0	1
1	2
2	11
3	3
4	25
5	12
6	5
7	2
8	15
9	15
10	169
11	9,940
12	222,327
13	807,868
14	220,304
15	28,205
16	4,663
17	1,023
18	279
19	104
20	37

That's an average of 13.041!