Pebble Hunting: The Hall of Fame 50 Percent Probability Test

I was wondering whether Andrew McCutchen, after winning his first MVP award, was on a Hall of Fame track. So I went to look at what the typical Hall of Famer had at the same age, then realized with shame that the thing I’ve been doing all these years—looking at what the typical Hall of Famer had at the same age—doesn’t make any logical sense. Yes, the average Hall of Famer might have had (X) WARP through age 26, but

• the average Powerball winner has an IQ of 80
• the average person with an IQ of 80 does not win Powerball

or any of billions of similar examples that make the point that my way wouldn’t have shown how many non-HOFers at the same level washed out. So if I can’t just look at what the median Hall of Famer had at McCutchen’s age, what can I do? Find the Wins/Age combination at which exactly 50 percent of players (or as close as possible) end up in the Hall of Fame. And then use that to name all the active players who are likely to make the Hall of Fame, times two.

(Definition of terms: We’re using Baseball-Reference’s WAR for this, as WARP is limited to seasons since 1950. We’re ignoring pitchers. That’ll be a post for a different day. And to account for players who are retired and, in my opinion, likely to make the Hall of Fame but ineligible or unapproved yet, I am assigning eight future Hall of Famers into the historical count: Craig Biggio, Jeff Bagwell, Barry Bonds, Ken Griffey Jr, Chipper Jones, Mike Piazza, Frank Thomas, and Jim Thome. Of course, there’s a logical problem with this approach, too, which we’ll get to.)

Age 20
20 of 40 players with at least 2.1 wins through age 20 made the Hall of Fame.
Half-probably Hall of Famers: Bryce Harper, Manny Machado

Harper’s 9.0 wins are the fourth-most in history; Mike Trout almost certainly surpassed the 2.1-win threshold in a single month at least once during his age-20 season. Machado is solidly into the likely zone, but the names immediately around him are especially distinguished:

• 22. Roberto Alomar
• 23. Bill Mazeroski
• 24. Machado
• 25. Rickey Henderson
• 26 (tie). Hank Aaron

Bob Horner marks the lowest limit of probability—that is, he had exactly 2.1 wins through age 20.

Age 21
26 of 48 players with at least 4.8 wins through age 21 made the Hall of Fame.
Half-probably Hall of Famers: Mike Trout

Quick fact about Trout: The youngest active player with more wins than he has already: McCutchen! Five-years-older McCutchen.

Willie Randolph marks the highest limit of improbability, with 4.7 wins through age 21.

Age 22
32 of 62 players with at least 7.7 wins through age 22 made the Hall of Fame
Half-probably Hall of Famers: Nobody. On the other hand, Yasiel Puig produced 5.0 wins in 104 games, so you might expect him to clear the age-23 or age-24 mark.

Grady Sizemore is the low end of Hall of Fame probability: [all the sad face emoticons go here]

Age 23
49 of 98 players with at least 10.2 wins through age 23 made the Hall of Fame.
Half-probably Hall of Famers: Jason Heyward, Giancarlo Stanton, and Brett Lawrie, who represents the lowest line of probability at this age. Just missing is Freddie Freeman; considering the stats that make up his value and the stats that make of Lawrie’s value, you might be tempted to adjust expectations in your head accordingly.

A year or so ago, I wrote briefly about Starlin Castro’s chances of making the Hall, based solely on his playing time and age. “Knowing nothing about Starlin Castro except his age and how much he has played, we can say he is in a group from which 44 percent of players have become Hall of Famers.” Castro never felt like a future Hall of Famer, but he was an actuary’s version of a future Hall of Famer. Fittingly, so far in his career he has straddled these thresholds, too. Through age 20, he was 0.7 wins short of qualifying as likely; through age 21, he was 0.4 wins short; through age 22, he was 0.3 wins ahead of pace; and now, after a lost season, he is nearly three wins short. He’s tied with Willie McCovey at the same age, but he’s also tied with Eddie Murphy—who, like the other Eddie Murphy, didn’t age well. Only 39 percent of players with 7.4 wins or more, as Castro has, made the Hall.

Age 24
51 of 102 players with at least 13.8 wins made the Hall of Fame
Half-probably Hall of Famers: Elvis Andrus.

Andrus, unlike Castro, has kept his head above the line from age-20 on, and at age 24 he’s comfortable ahead, with 17 wins. About 62 percent of players with 17 wins made the Hall, but even though Andrus has more wins than Frank Thomas I’d bet my house against your car that he won’t make the Hall.
Darryl Strawberry, with 13.6 wins at this age, is the upper limit of improbability.

Age 25
60 of 119 players with at least 17.5 wins through age 26 made the Hall of Fame.
Half-probably Hall of Famers: None.
Ruben Sierra and Ralph Kiner are tied at the upper end of improbability for this age.

Age 26
73 of 146 players with at least 19.9 wins through age 26 made the Hall of Fame.
Half-probably Hall of Famers: McCutchen. You might have noticed, incidentally, that we still haven’t reached Mike Trout’s career total yet. Untitled Fox-Dreamworks Animation/Fox-Blue Sky Studios animated film is scheduled to be released in North America on Dec. 21, 2018. Mike Trout could spend the next five seasons waiting in line for that movie and still be on pace to make the Hall of Fame.

Austin Jackson just, just misses making the age-26 half-probables. Buster Posey misses, too, and isn’t nearly as close. That seems like an oversight by the method. I’d probably bet on Posey over anybody named thus far except Trout, Harper, Stanton and perhaps McCutchen.

Jason Kendall is the lowest end of probability. This was the year that Chipper Jones (20.0, with a career path not unlike Posey’s) edged into likelihood.

Age 27
83 of 166 players with at least 23.0 wins by age 27 made the Hall of Fame.
Half-probably Hall of Famers: Evan Longoria.

Upper end of improbability: Fred McGriff

Age 28
88 of 176 players with at least 26.0 wins through age 28 made the Hall of Fame.
Half-probably Hall of Famers: Ryan Zimmerman, Troy Tulowitzki. Zimmerman doesn’t particularly seem like a Hall of Famer—he’s a bit behind Scott Rolen’s pace, and Rolen never particularly seemed like a Hall of Famer (though he should have)—but Evan Longoria needs a four-win season this year to match him through age 28.

Dale Murphy and Juan Gonzalez are the low end of probability.

Age 29
90 of 179 players with at least 29.2 wins through age 29 made the Hall of Fame.|
Half-probably Hall of Famers: Dustin Pedroia, Ryan Braun, Joey Votto, Hanley Ramirez

For players who want to stay on pace, the biggest jumps come from ages 23 to 24, ages 24 to 25, and ages 25 to 26: about 3.6 wins per year, peaking at a 3.7-win jump for 25-year-olds. Then it settles around three wins a year for the traditional prime seasons; age 29, at 3.2 wins, is the last year before the real decline starts for the group. The next year’s Hall of Fame probables will add only 2.4 wins, and the typical Hall of Famer will be only about a league-average player through his 30s. He’ll be Raul Ibanez, basically.

The upper end of improbability is Graig Nettles, followed by a bunch of fun names: Sammy Sosa, Kirby Puckett, Carlton Fisk, others.

Age 30
97 of 194 players with at least 31.6 wins through age 30 made the Hall of Fame.
Half-probably Hall of Famers: Miguel Cabrera, David Wright, Robinson Cano, Joe Mauer, Jose Reyes.
From ages 24 to 25 we got one player, Andrus, who isn’t actually going to make it; from 29 to 30 we got nine, seven of whom (all but Hanley Ramirez and Jose Reyes) actually seem likely to make it on merits. (Braun probably won’t on other grounds; on the other hand, Ramirez and Reyes each has a pulse left.) I don’t know if this is a glitch that happens as this exercise moves into older groups, or just a cluster.

Age 31
101 of 200 players with at least 34.1 wins through age 31 made the Hall of Fame
Half-probably Hall of Famers: Carl Crawford, Ian Kinsler. Neither of whom seems likely. Kinsler is extremely close to falling out of this group.

Age 32
105 of 207 players with at least 36.3 wins through age 32 made the Hall of Fame
Half-probably Hall of Famers: Nobody. Guess it wasn’t a glitch.

Age 33
110 of 220 players with at least 38.0 wins through age 33 made the Hall of Fame
Half-probably Hall of Famers: Albert Pujols, Mark Teixeira, Matt Holliday.

I told you there was a different problem with this method, and here’s where it’s most obvious. Pujols and Teixeira are both over 38 wins; combined, they are each 50 percent likely to make the Hall of Fame; and, in reality, only one is going to make the Hall of Fame. But Pujols and Teixeira aren’t really in a group at all; Pujols has produced well over twice as many wins as Teixeira has. He’s a 100 percent lock to make the Hall (on merits, anyway). So

• if 50 percent of the players who have at least 38 wins make the Hall, and
• 100 percent of the players who have at least 88 wins make the Hall, and
• some players have at least 88 wins,
• then less than 50 percent of the people under 88 won’t make the Hall.

In this case,

• 100 percent of players with at least 70 wins through age 33 made the Hall of Fame.
• 70 percent of players with 50 to 69.9 wins through age 33 made the Hall of Fame.
• 33 percent of players with 38 to 49.9 wins through age 33 made the Hall of Fame.

In Teixeira and Holliday’s cases, I can just about buy that.

This doesn’t seem to be much of a problem when the players are young. A player’s chances don’t go up much whether he has, say, seven wins or 10 by age 21. But by now the 50 percent talk is totally misleading; there are just way too many sure things, guys who have already passed not just the on-pace mark but the guaranteed-enshrinement threshold. Which is just to note that we have named 25 players so far. About half will make the Hall of Fame. They are not, obviously, all 50 percent likely to.

Age 34
111 of 220 players with at least 39.4 wins through age 34 made the Hall of Fame
Half-probably Hall of Famers: Adrian Beltre, Chase Utley, Jimmy Rollins

Age 35
113 of 226 players with at least 40.4 wins through age 35 made the Hall of Fame
Half-probably Hall of Famers: None. Which is just as well. By 35, probability doesn't count for much.