About the Hall of Stats

They say, “It’s the Hall of Fame, not the Hall of Stats.”

But what if it were?

The Hall of Stats shows us what the Hall of Fame would look like if we removed all 242 inductees and replaced them with the top 242 eligible players in history, according to a mathematical formula.

The Formula Back to Top

The Hall of Stats is populated by Hall Rating, a mathematical formula based on the Baseball-Reference versions of Wins Above Average (WAA) and Wins Above Replacement (WAR). WAA combines all aspects of a player’s game—hitting, pitching, baserunning, fielding, positional value, and more—and estimates how many more wins that player was worth than an average player. WAR takes that a step further and estimates how many more wins the player is worth than a replacement player. (I wrote an article with more detail about Wins Above Average vs. Wins Above Replacement.)

The precursor to the Hall of Stats was called the Hall of wWAR. wWAR stands for “weighted Wins Above Replacement”, which basically means the formula starts with WAR and applies a series of weights. wWAR is still a big part of the Hall of Stats, but it now has a completely different formula.

wWAR = adjWAR + (1.8*adjWAA)

Before I go into what adjWAR and adjWAA are (and where the 1.8 comes from), I want to explain what Hall Rating is.

Hall Rating

Hall Rating is simply wWAR expressed in a more intuitive way (you’ll see Hall Rating displayed on the Hall of Stats, but not wWAR). The Hall of Stats borderline for induction is represented by a Hall Rating of 100. This is similar to how 100 represents league average in OPS+ or wRC+.

With a Hall Rating of 399, you could say that Babe Ruth’s career was worth about four Hall of Fame careers. Meanwhile, Eppa Rixey essentially sits on the Hall of Stats borderline with a Hall Rating of 101. Hall of Famer Lou Brock is not included in the Hall of Stats because his Hall Rating is just 72.

adjWAR (Adjusted Wins Above Replacement)

adjWAR attempts to capture the value of the player above a replacement player. It starts with a player’s WAR and undergoes a series of adjustments:

adjWAA (Adjusted Wins Above Average)

While adjWAR measures total career value, adjWAA aims to measure peak value. It begins with Wins Above Average and also undergoes some adjustments:

The 1.8

The Hall of Stats equally weighs a player’s career value (adjWAR) and peak value (adjWAA). These numbers, however, are on different scales. adjWAA is multiplied by 1.8 to adjust for this. To get 1.8, I collected all Hall of Fame inductees and divided their total adjWAR by their total adjWAA.

More About Baseball-Reference’s WAR

If you are interested in what exactly goes into Baseball-Reference’s implementation of WAR, they have written about the calculations in incredible detail.

Known Limitations

Similarity Scores Back to Top

Baseball-Reference uses Bill James’ similarity scores on their player pages. While Baseball-Reference and Bill James are both wonderful, I don’t think their similarity scores are all that useful.

What James’ scores show is that two players’ raw numbers were similar. Here’s an excerpt from the point system used to identify a pair of "similar" batters:

  • One point for each difference of 2 home runs.
  • One point for each difference of .001 in batting average.

The issue here is that these numbers are not adjusted for era, park, or anything else. A .300 batting average with 8 home runs in the deadball era made you a star. A player with those same numbers in the steroid era actually may have been a below average player, depending on his position.

Speaking of position, here is part of James’ positional adjustment:

  • 240 - Catcher
  • 168 - Shortstop
  • 132 - Second Base

The 240-point adjustment is applied to all players who primarily caught, regardless of the player’s time spent behind the plate or at other positions.

How We Do It

The Hall of Stats similarity scores are calculated with one thing in mind: value. We don’t care how many home runs a player hit or what his batting average was. We care how many runs above average his total offensive game was. Similarly, we don’t care what his primary position was. We care about the run value of the time he spent at each of his positions.

Our similarity scores are calculated using:

The closer a pair’s score gets to zero, the more similar the players are. Because most of the inputs are centered around league average, the better a player gets, the harder it is for him to have closely similar players. For example:

(Note: Similarity scores are currently available for all players with 1500+ plate appearances or 500+ innings pitched.)

Special thanks to Tim Vaughan (@MechanicalTim) for giving us a crash course in how to calculate similarity scores.

More About the Project Back to Top

The Team Back to Top

Adam Darowski

Jeffrey Chupp

Michael Berkowitz

The Tech Back to Top

The site is built with Ruby on Rails, Haml, Sass, jQuery, and CoffeeScript.

Open Source

The Hall of Stats is open sourced and available on GitHub.

Data Downloads

I’ve received multiple requests to make my data available. The following files are available as a CSV: