Hall of Stats

When the Hall of Fame ballot comes out each year, the debates start. Columnists compare today’s players to those of a “better time” and lament about the weakening of the Hall of Fame’s purity. The thing is, that “purity” doesn’t actually exist.

For every Babe Ruth, Ty Cobb, Cy Young, and Walter Johnson in the Hall of Fame there’s a Tommy McCarthy, Lloyd Waner, Jesse Haines, and Rube Marquard.

There’s a huge gap between Babe Ruth and Tommy McCarthy. How do you determine what “Hall-worthy” really is then? If you enshrine every player better than McCarthy, your Hall of Fame will have a population of 1,478. If you hold everyone to the same standards as Babe Ruth—or even Tony Gwynn—you won’t be adding Hall of Famers very often.

And what fun is a Hall of Fame if you never let anyone in?

Let’s make an example out of Alan Trammell. He’s currently struggling to get into the Hall of Fame and will likely be passed over by the BBWAA. Does he compare to Hall of Fame shortstops Honus Wagner and Cal Ripken? No, he doesn’t. But does he have to? Is he clearly better than Rabbit Maranville, Phil Rizzuto, and Travis Jackson? Yes. How about Joe Tinker, Joe Sewell, and Dave Bancroft? Yes, yes, and yes. All six are in the Hall of Fame. Alan Trammell was better than all of them.

To determine whether or not Trammell should be a Hall of Famer, we now have to consider both how much worse he is than the elite players at his position and how much better he is than some players already inducted.

It’s an absolute mess. The only way to fix it is to kick everyone out and start from scratch. So that’s what I did.

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

But what if it was?

The Hall of Stats removes everyone from the Hall of Fame and re-populates it based on a mathematical formula.

You decide which Hall is better…

The Formula Back to Top

The Hall of Stats is populated by 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 + (1.69*adjWAA)

Before I go into what adjWAR and adjWAA are (and where the 1.69 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 402, 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 101. 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:

• Position player WAR is adjusted for schedule length. In this case, a hitter gets more credit for a 3.0 WAR season during a 80-game schedule than he does for a 3.0 WAR season in a 162-game season.
  • This same adjustment is not given for pitchers, since shorter schedules allowed pitchers to be used more often. The exception is strike- or war-shortened years (where both pitchers and hitters are given an adjustment for how long the schedule would have been).
  • It is important to note that this adjustment is made based on the schedule length and not the number of games the player appeared in. A player who appeared in 120 games of a 162-game schedule does not receive any extra credit.
  • Players are not given 100% of the credit for games they did not play. Instead, they are awarded the average of their actual WAR and their projected WAR. This keeps us from over-adjusting for 19th century players.
• Catchers receive a generous positional adjustment from WAR. But this adjustment only rewards them for time actually spent on the field. Catchers play fewer games in a season and have shorter careers. Therefore, catchers are given an extra 20% boost by adjWAR. Without this adjustment, there would be very few catchers in the Hall of Stats. And that just wouldn’t be right.
• Relievers are similar to catchers in that they get a boost from WAR (via the leverage index), but it is not nearly enough to bring their WAR values close to their starting counterparts. I’m actually not sure what type of adjustment relievers should get (if any). Without an adjustment, we would have no relievers in the Hall of Stats. I decided to simply use the same adjustment I used for catchers. (This helped Hoyt Wilhelm gain induction while Rich Gossage fell short).
• Most recently, I added an adjustment for 19th century pitchers (specifically, before the mound moved back to its current distance in 1893). These pitching seasons also get a 20% adjustment, but this one impacts them negatively (because of the ease of compiling a ridiculous number of innings).

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:

• Seasons with negative WAA are ignored. adjWAA only wants the seasons where the player was above average. For example, Pete Rose has a huge discrepancy between his WAA and his adjWAA. This is because he hung on for several years as a below average player pursuing the all-time hits record. adjWAA doesn’t penalize him for this as it is already captured in adjWAR.
• In cases where a player’s WAR and WAA are very close to each other, no WAA is counted. The cases where this occurs is where the talent level is low, for example:
  • The 1884 Union Association had the lowest talent level of all Major Leagues. For this reason, the league average is essentially replacement level.
  • League average for pitchers batting value is also typically at replacement level.
• Catchers, relief pitchers, and 19th century (pre-1893) pitchers are adjusted the same way as they are for adjWAR.

The 1.69

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 1.69 to adjust for this.

To get 1.69 (actually 1.6904555774852), I collected all Hall of Fame inductees (as of 2012) and divided their total adjWAR by their total adjWAA.

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:

• WAR Batting Runs
• WAR Baserunning Runs
• WAR Double Play Runs
• WAR Defensive Runs
• WAR Positional Runs
• WAR Pitching Runs
• adjWAR
• adjWAA
• Plate Appearances
• Innings Pitched

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:

• Ken Boyer and Sal Bando are very similar players (right down to three characters in their first name and five in their last). Their similarity score is 80. Once you see a pair of players of their caliber that close, you know they provided very similar value.
• Rob Deer, on the other hand, has a score of 80 or better with 22 players. Deer is closer to an average player and there are many more players at that part of the bell curve to be similar to.
• Lastly, there is basically no good comparison to Babe Ruth. Barry Bonds is the closest with a staggering 896 similarity score.

(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

• All data is based on the Baseball-Reference version of Wins Above Replacement (WAR). This version was originally created by Sean Smith (aka RallyMonkey) and made available at BaseballProjection.com.
• I also utilized the Sean Lahman Baseball Database for things not made available in Baseball-Reference’s WAR downloads.
• The number of Hall of Stats inductees is kept consistent with the Hall of Fame (208 inducted as players). This is to show the difference in quality between the two Halls from top to bottom.
• The Hall of Stats ignores performance enhancing drugs. There’s just no reliable, complete data about it.
• The Hall of Stats ignores lifetime bans. This opens up the Hall of Stats to Pete Rose, Shoeless Joe Jackson, and any other banned players.
• This pains me, but the Hall of Stats does not include Negro League players. The data just isn’t reliable yet, but it is getting better. As soon as I figure out a way to do it, Negro League stars will be recognized by the Hall of Stats.
• The Hall of Stats doesn’t adjust for time lost to military service. This is something I go back and forth on. I’d love to hear your feedback about this.
• The Hall of Stats only has a “player” designation while the Hall of Fame has other designations. For this reason, Al Spalding is a Hall of Stats inductee while he is not considered a Hall of Fame player (he was inducted as a Pioneer/Executive).

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 web designer and developer by day for PatientsLikeMe, 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 tweets about baseball at @baseballtwit and everything else at @adarowski.

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. A current co-worker of Adam’s at PatientsLikeMe, Michael is also a singer/songwriter. 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 Javascript duties. Michael took on special projects like player search, similarity scores, season stats, positional pages, and player rankings.

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:

• Player career totals
• Single season totals

Thank You Back to Top

Thank You to my three favorite 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.