The 2018 Hall of Fame election cycle is over, giving us six players who’ll receive plaques in Cooperstown this summer. Congratulations to Chipper Jones, Jim Thome, Vladimir Guerrero, Trevor Hoffman, Alan Trammell, and Jack Morris.

Every year the Hall of Fame voting raises debates, polemics, and snark about the process. Most of these discussions revolve around who should be inducted. Over the years, writers and analysts have created tools to bring objectivity to this subjective process. Two of the most popular are Bill James’ Hall of Fame Monitor and Jay Jaffe’s Jaffe WAR Score System (JAWS).

These metrics have advanced the “who should be inducted” questions considerably. But I’m interested in a different question: Who will get inducted?

The distinction is important. Take 2018 inductee Morris. The BBWAA declined to elect him and many fans think he shouldn’t be in. Yet he is. Ditto with Guys like Travis Jackson, Harry Hooper, and Jim Bottomley. If the Hall kicked everyone out and had a sport-wide re-vote, these guys wouldn’t make the cut.

Conversely, many fans and writers believe guys like Kenny Lofton should be in the Hall. Yet he is not. Jim Edmonds and Ted Simmons are two other “pet cause” guys I read about a lot, not to mention current candidates Larry Walker, Mike Mussina, and Edgar Martinez.

Approach

It’s clear that “should be inducted” is often different from “will be inducted.” Here’s how I approached the latter question.

Broadly speaking, baseball players have a limited amount of time to create enough value to be considered eligible for, and possibly get inducted to, the Hall of Fame. We typically measure passage of time by a player’s age, and we typically measure a player’s value by WAR.

For these reasons, I began assessing a player’s Hall of Fame chances by understanding:

• How old they are
• How much WAR they’ve accumulated through that age

To complete the analysis, I added one more data point: the player’s position. The Hall of Fame is unbalanced in this regard. For example, counting Jim Thome, the Hall contains 23 first basemen but only 16 catchers. Almost all Hall of Fame discussions include positional context; Jaffe’s excellent book The Cooperstown Casebook is organized in this way.

Methodology

This approach allows me to frame “who will make the Hall of Fame?” as “given a player’s age, cumulative WAR through that age, and position, what are the chances they’ll make the Hall of Fame?” Mathematically I ask this question using Bayes’ theorem which states:

(Probability of Outcome given Evidence) = ((Probability of Outcome) * (Probability of Evidence given Outcome)) / (Probability of Evidence)

In the case of Hall of Fame elections, we have the following definitions:

• P(Outcome) — the probability a player at position p, who has had a chance to appear on a ballot, is a Hall of Famer.
• P(Evidence given Outcome) — the probability that, given that a player at position p is a Hall of Famer, this player accumulated between x and y WAR through age z, where x = the player’s current WAR minus (1.5 * the number of seasons they’ve played) and y = the player’s current WAR plus (1.5 * the number of seasons they’ve played). This model compares each player to others at their position and age who had a chance to accumulate the same WAR they did.
• P(Evidence) — the probability any player at position p accumulated between x and y WAR through their age z season, regardless of whether they made the Hall.

This Bayesian approach has several compelling benefits:

• It accounts for the fact that some positions are inherently more likely to get elected than others. Shortstops get elected the most often, at a 3.2 percent clip, while pitchers get elected at a glacial 1 percent clip.
• It accounts for the fact that cumulative WAR is not the only factor voters consider when determining who should make the Hall.
• It’s based on empirical data: WAR that players have accrued through a certain age, which players have made the Hall, and which haven’t. There is no subjectivity in any of this data.
• Because of this approach’s empirical basis in WAR and Hall inductees, we can analyze players at any stage in their career, from rookies to veterans to those long retired. As players age and accrue value, and as more players get elected, we simply re-run the analysis to get updated probabilities.

The end result is similar to what what Sam Miller did in 2013 but a bit more refined and with players’ positions accounted for.

Let’s see how this works.

Example

Corey Seager is a shortstop with 14.6 WAR through his age-23 season, his third in the big leagues.

• P(Outcome) = 0.0328084. Of the 762 shortstops in my dataset, 25 have made the Hall of Fame.
• P(Evidence given Outcome) = 0.28. Of these 25 Hall of Fame shortstops, 7 accumulated between 10.1 and 19.1 WAR through their age-23 seasons: Lou Boudreau, Joe Cronin, George Davis, Travis Jackson, Joe Tinker, Alan Trammell, and Robin Yount.

10.1 is Seager’s floor because it equals 14.6 WAR - (1.5 WAR * 3 seasons), where 1.5 is a constant and 3 is how many seasons Seager’s played. 19.1 is the same math, just in the positive direction from 14.6 WAR.

• P(Evidence) is 0.01574803. Of the 762 players identified as shortstops, 12 accumulated between 10.1 and 19.1 WAR through age 23. The seven guys above plus Donie Bush, Bill Dahlen, Jim Fregosi, Vern Stephens, and Garry Templeton. These five guys are not in the Hall.

Putting it together: Seager’s HOF chances are (0.0328084 * 0.28) / 0.01574803 or 58.3 percent. That’s a nice outlook for such a young guy. It might seem high, but consider that shortstops make the Hall at a rate of 3.2 percent, nearly twice the average rate of 1.5 percent, and that 7 of the 12 players to do what he’s done have made the Hall.

For context, the following list shows how Seager’s chances compare to some other shortstops:

Caveats

The biggest caveat with my analysis is positional classifications. Some players are misclassified because they’re listed at multiple positions and I simply took the first position listed. So Stan Musial is in my dataset as a first baseman despite being inducted as a left fielder.

Speaking of left field: outfield positions are not separated out like they are in the actual Hall. Further, relievers are not separated from starters. This gives relievers short shrift because they’re compared to starters, while over-weighting starting pitchers because they get compared to fringe relievers. Speaking of pitchers, I should note that I combined players’ batting and pitching WAR for this article.

Finally, because no one in the Hall is classified as a DH, guys like David Ortiz don’t get analyzed. Repeating this study with better positional data would help relievers the most and might shift around some of the numbers for position players, especially outfielders.

But overall the results feel right. Let’s dig through them a bit.

Results

These are the guys you’d expect to top a list like this. Seven seasons in, Mike Trout is a lock for baseball immortality. He also leads all active players in terms of HOF chances.

Clayton Kershaw is the best pitcher in baseball and is 2/3 of the way to induction. Bryce Harper is right on his heels. For me, the most surprising name on this list is Mookie Betts. I know he’s good and had a close AL MVP race with Mike Trout in 2016, but I wouldn’t have put his HOF chances at nearly 50 percent already. That’s what 20 WAR through age 24 will get you.

He’s spent the last couple seasons being near replacement level, so we sometimes forget that Albert Pujols is one of the best to ever play the game. He destroyed pitching for a decade in St. Louis, winning three MVP’s and two World Series. It’s sad to see him struggle so badly in Los Angels, no longer a feared hitter, but when he appears on the Hall of Fame ballot we’ll have a chance to reminisce about his amazing career.

The writers I read discuss Adrian Beltre as if he’s a lock for the Hall of Fame. In reality, third basemen have a tough time getting inducted. In my dataset, just 1.8 percent of third basement make it in, the third-lowest rate of all the positions. Bayes’ theorem accounts for this rarity when computing Beltre’s chances. That said, I think his chances are higher than predicted here. He’s passed the 3,000 hit milestone, is pretty close to 500 HR, and is widely perceived as a good guy.

I included this table mostly just to show you the chances of Ichiro Suzuki and Carlos Beltran. No one’s planning an induction ceremony for Koji Uehara. Ichiro should have no trouble getting in; WAR aside, he has 3,000 hits and is a cultural icon. Beltran’s inclusion is already being debated. His 50 percent chance reflects the fact many see him as a borderline inductee and not a slam dunk.

Alex Rodriguez is the only player besides Trout to be a lock for enshrinement. Of course, my code doesn’t know about Rodriguez’s PED violations and the general distaste fans and writers have for his character. Even though he’s rehabilitating his public persona, these stains will keep the BBWAA from voting him in for at least a few years. I suspect he’ll get in on his 9th or 10th try; voters will make him wait that long as punishment but ultimately will acknowledge he was one of the best players in history.

The interesting names here are Dave Concepcion, Bert Campaneris, Bill Dahlen, and Fielder Jones. These guys appear to be pretty bad snubs. Their high chances here mean voters have tended to induct similar players, yet these guys are on the outside looking in.

This list is endlessly fascinating. Cody Bellinger and Gary Sanchez just played their first seasons but already rank highly at their respective positions. The continued excellence of guys like Ian Kinsler, Buster Posey, and Joey Votto shine through in their Hall of Fame chances. Veterans CC Sabathia, Zack Greinke, and Justin Verlander have good chances as well.

Is there a player you didn’t see? The full list is here, minus players who are classified a a DH.

Despite its flaws, the Hall of Fame debate is endlessly fascinating for baseball fans. Discussing who should and shouldn’t get in, or who will and won’t, provides for hours of entertainment — especially during slow offseasons like this one. Bayes’ theorem allows us examine the “will he or won’t he?” question empirically and update our guesses when we receive new evidence. I’m looking forward to running this analysis again after the 2019 vote totals are in.