The Elo rating system is a method for calculating the relative skill levels of players in two-player games. The creator of the system, Arpad Elo, was a professor of physics at Marquette University who wanted an improved chess rating system. The Elo rating system has its roots in chess; however, this system and its derivatives are used for various other applications, including baseball and video gaming.

Inspired by the folks over at Baseball-Reference.com, we have taken the Elo rating system and applied it to the ranking of famous people who have made significant contributions to the field of Psychology and helped make it what it is today.
Our data pool consists of a selection of people from two biographical dictionaries of psychology: Zusne (1984)^{1} and Sheehy (1997)^{2}.

Every person has an initial rating of 1200 points.
These ratings are then updated by randomly selecting pairs of opponents and having them "compete."^{3}
As in the original Elo rating system, this adjustment is based on each person's Elo rating score.

We start by computing the win probabilities for each person (let's call them A and B):

```
P(A wins) = 1 / (1 + 10^((RB - RA) / β))
P(B wins) = 1 / (1 + 10^((RA - RB) / β))
where RA = Elo rating for A
RB = Elo rating for B
β = 200
```

After the winner has been selected, the ratings of the two players are adjusted. If A wins the match then the new ratings are:

```
RA_new = RA + K * P(B wins)
RB_new = RB - K * P(B wins)
where K = K-factor of 10
```

While if B wins the match then the new ratings are:

```
RA_new = RA - K * P(A wins)
RB_new = RB + K * P(A wins)
```

For example, suppose Sigmund Freud ("SF") has a rating of 1500 and Alfred Adler ("AA") has a rating of 1450. The win probabilities for each person are:

```
P(SF wins) = 1 / (1 + 10^((1450 - 1500) / 200)) = 0.64
P(AA wins) = 1 / (1 + 10^((1500 - 1450) / 200)) = 0.36
```

If SF wins then the new ratings are:

```
SF_new = 1500 + 10 * 0.36 = 1503
AA_new = 1450 - 10 * 0.36 = 1446
```

While if AA wins then the new ratings are:

```
SF_new = 1500 - 10 * 0.64 = 1493
AA_new = 1450 + 10 * 0.64 = 1456
```

This is a community-based project with the goal of rating the most influential people in the history of Psychology. In each matchup, you should choose the person who you believe made the greater impact to Psychology as a discipline. It is up to you to determine how much weight to give to each individual's listed contributions.

If you have any comments or questions, please send us some feedback.

^{1} Zusne, L. (1984). Biographical dictionary of psychology (rev. ed.). Westport, CT: Greenwood Press.

^{2} Sheehy, N., Chapman, A. J., & Conroy, W. A. (Eds.). (1997). Biographical dictionary of psychology (rev. ed.). New York: Routledge.

^{3} Opponents are not actually chosen at random.
Similar to Baseball-Reference.com, the first of person is randomly selected to begin the process.
Following that, a second person with a rating within 150 points of the first person is randomly selected to complete the pair.
This is done in order to prevent bizarre choices (e.g., Zick Rubin over William James) from distorting the ratings.