Manny Machado's Hall of Fame chances are higher than you think

When you think of Manny Machado, do you think "Hall of Famer"?

You should.

Last week’s Hall of Fame voting got me thinking about who on the Orioles right now could eventually make the cut. I bet most people think of Adam Jones, and indeed he’s a great player who is performing at a high level right now. But he is only "very good" when compared to Manny Machado’s "excellent".

Jones has never topped 4.8 WAR, as measured by Baseball Reference, in a season. Meanwhile, Manny has had one season of 6.7 rWAR and another of 7.1. Sprinkled around those fantastic years have been 1.6 rWAR in 51 games (in 2012) and 2.4 rWAR in 82 games (in 2014).

To find Manny's chances of entering baseball's pantheon, I turned to my favorite conditional probability tool: Bayesian analysis. This equation gives us the probability (P) of a belief (B) given some evidence (E). Its form is:

P(belief given evidence) = P(belief) * P(evidence E given belief B) / P(evidence).

or

P(B|E) = P(B) * P(E|B) / P(E)

I like Bayesian analysis because it symbolizes a natural way of thinking. We get evidence all the time and have to make decisions based on what that evidence means or doesn't mean. Given that it snowed yesterday, what are the chances it'll snow today? Given that the person I have a crush on texted me back, what are the chances they want to go out with me? Given that I've tested positive for this condition, what are the chances I actually have it? These questions and more can be analyzed with Bayesian thinking.

The evidence: Machado has accumulated 17.7 rWAR in 1,979 plate appearances through age 22. What are the chances that players like him enter the Hall of Fame? I defined players similar to him as those who’ve accumulated 13.7 - 21.7 rWAR in 2,000 PA or fewer through age 22. I chose this range of 8 rWAR because it allows for a difference of 2 rWAR each season over four seasons. 2 rWAR is about what separates tiers of players in terms of value.

The Bayesian variables are as follows:

• P(B) is the probability that any player is a Hall of Famer. Of the 14,399 players whose careers ended in 2010 or earlier, 217 have made the Hall of Fame. This makes P(B) equal to 217/14399 or 0.01507 (1.5%).

• P(E|B) is the probability that, given a player is a Hall of Famer, they accumulated 13.7-21.7 rWAR in 2000 PA prior to age 22. Ten Hall of Famers -- Eddie Matthews, Frank Robinson, Johnny Bench, Jimmie Foxx, Hank Aaron, Arky Vaughan, Stan Musial, Rogers Hornsby, Rickey Henderson, and Tris Speaker -- meet these criteria. This makes P(E|B) = 10/217 or 0.04608 (4.6%).

• P(E) is the probability that a player will accumulate 13.7-21.7 rWAR in 2,000 PA through age 22 regardless of whether they become a Hall of Famer. Eleven players meet these criteria: the above list plus a certain John Phalen "Stuffy" McInnis who is not in the Hall of Fame. This makes P(E) = 11/14399 or 0.00076 (0.076%).

Putting it all together: P(B|E) = (0.01507 * 0.04608) / 0.00076 = 0.91372. Yes, given the fact that Manny has accumulated so much rWAR in just 2,000 PA at such a young age, there is a 91% chance he will make the Hall of Fame.

That very high probability may be surprising at first glance, but it shouldn’t be. If you get called up to the big leagues at 19 years old like Manny did, typically that means you’re very good. Here's the list of players since 1955 who received at least 150 PA in their age-19 season:

• Bryce Harper

• Edgar Renteria

• Justin Upton

• Melvin Upton

• Adrian Beltre (likely HOF)

• Ivan Rodriguez (likely HOF)

• Ken Griffey, Jr. (HOF)

• Jose Oquendo

• Robin Yount (HOF)

• Claudell Washington

• Cesar Cedeno

• Ed Kranepool

• Ed Kirkpatrick

• Tony Conigliaro

• Rusty Staub

• Bill Mazeroski (HOF)

That’s a pretty good list.

Also, because Manny started so young, he has plenty of time to rack up Hall of Fame numbers. Consider that through 2,000 PA at age 22 Manny has accumulated more rWAR than the following players had at the same period in time: