About the Hall of Stats

The Hall of Stats was conceived because the Hall of Fame voting process has become a political nightmare. A massive backlog of worthy candidates is piling up—some because of association with PEDs (or simply suspicion), but some because voters just don’t realize how good they were. There seems to be a false perception of what the Hall of Fame actually is. It’s not all Babe Ruth, Christy Mathewson, Ty Cobb, and Honus Wagner. For every Walter Johnson in the Hall of Fame there’s a Jesse Haines. For every Hank Aaron there’s a Tommy McCarthy.

Should each player better than Haines and McCarthy get in? No. But a player shouldn’t have to be Babe Ruth—or even Bert Blyleven—to get into Cooperstown.

The Hall of Stats uses a formula called Hall Rating to rank every player in baseball history. Hall Rating combines the value of a player’s peak and longevity into a single number that represents the quality of that player’s Hall of Fame case. It’s not perfect, but there’s a lot to be said for rating all players in history according to the same objective criteria.

There are 211 players in the Hall of Fame based on their MLB careers. According to the Hall of Stats, Blyleven ranks #33 among eligible players. He should have breezed into the Hall, but instead it took fourteen tries. Curt Schilling ranks #45. Jeff Bagwell ranks #52. Kenny Lofton—who received less than 5% of the vote—ranks #93. There’s no reason to keep these players out of the Hall of Fame… if you look at things objectively.

That’s what the Hall of Stats does. It ignores anything that happened off the field—PEDs, lifetime bans, MVP awards, etc. The Hall of Stats takes the current number of players in Cooperstown (211), kicks everybody out, and re-populates itself with the top 211 players according to Hall Rating. What you get is an objective Hall free of politics, grandstanding, and double jeopardy.

Hall Rating is based on Wins Above Replacement (WAR) and Wins Above Average (WAA) from Baseball-Reference. A series of adjustments are made to deal with shorter 19th century schedules, greater 19th century pitching workloads, the grueling act of catching, and more. The adjusted WAR component represents longevity while the adjusted WAA component represents peak. They are combined and indexed to 100 so the Hall of Stats borderline is represented by a Hall Rating of 100.

Babe Ruth has a Hall Rating of 395. Blyleven’s is 188. Lofton’s is a robust 131 while Hall of Famer McCarthy’s is merely 28. Of the 211 players in the Hall of Fame, 69 (just about one third) are removed from the Hall of Stats.

The Hall of Stats aims to show how run- and win-value statistics can be used to measure a player’s Hall of Fame case. It evolves to reflect the best data currently available (players can be added and removed, meaning this Hall doesn’t cling to its mistakes). The Hall of Stats also visualizes what a “default Hall” would look like if it were populated simply by the numbers. Should numbers be the only arbiter of who gets into Cooperstown? Certainly not. The Hall of Stats is merely meant to serve as a conversation starter. That objective starting point is one thing that’s sorely lacking in the Hall of Fame voting process today.

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 + (1.79*adjWAA)

Before I go into what adjWAR and adjWAA are (and where the 1.79 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 395, you could say that Babe Ruth’s career was worth about four Hall of Fame careers. Meanwhile, Billy Pierce essentially sits on the Hall of Stats borderline with a Hall Rating of 100. Hall of Famer Lou Brock is not included in the Hall of Stats becuase his Hall Rating is just 71.

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 1.79

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 1.79 to adjust for this.

To get 1.79 (actually 1.7866009711), 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

Note that each of these bios was written by Adam so he could gush about some of his favorite people.

Adam Darowski

Ever since introducing the Hall of wWAR in March of 2011, Adam Darowski has been obsessed with the idea of the Hall of Stats. A front-end designer by day for HubSpot, he researches, writes, designs, and codes about baseball in his spare time (and for such sites as High Heat Stats and Beyond the Box Score). Adam lives in Massachusetts with his wife and three young children. He tweets about baseball at @baseballtwit and everything else at @adarowski. He also runs the Hall of Stats Twitter account at @hallofstats.

Jeffrey Chupp

A former co-worker of Adam’s at PatientsLikeMe, Jeffrey is currently a Rails developer for Terrible Labs. Adam and Jeffrey previously collaborated on the Red Sox Hall of wWAR, a Baseball Hack Day project. Jeffrey is simply the Babe Ruth of Rails developers. There is nobody better. You can follow Jeffrey on Twitter at @semanticart.

Michael Berkowitz

If Jeffrey is the Babe Ruth of Rails developers, then Michael is the Mike Trout. Also a former co-worker of Adam’s at PatientsLikeMe, Michael currently works at Careport Health. In addition to being a software engineer, he is a singer/songwriter and linguist. You can follow Michael on Twitter at @hal678.

The Tech Back to Top

Adam developed the concept of the Hall of Stats, researched, crunched numbers, designed, and styled. Jeffrey took Adam’s designs and numbers and actually built the site (while helping Adam learn to be a little more self-sufficient along the way). Jeffrey also handled most of the initial Javascript duties. Michael originally took on special projects like player search, similarity scores, and season stats. Since the original launch, he has built most of the new features like positional pages, player rankings, and franchise pages and charts.

The site is built with Ruby on Rails, Haml, Sass, jQuery, CoffeeScript, and D3 (for charting).

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:

Thank You Back to Top

Thank You to my three favorite baseball Seans—Sean Forman (@sean_forman) of Baseball Reference, Sean Smith for originally creating this WAR framework, and Sean Lahman (@seanlahman) for his work on the Lahman Baseball Database. Also, thank you to Dan McCloskey (@_LeftField) and Sky Kalkman (@Sky_Kalkman) for letting me bounce ideas off them along the way. Thank you to the brilliant readers of High Heat Stats and Beyond the Box Score for providing wonderful feedback ever since I introduced wWAR. Finally, a huge thank you to Jeffrey and Michael (and Tim!) for helping me build the site of my dreams.