All-time Comparisons

Over the last week or so I have spent a lot of time evaluating players on an all time basis, for an all time draft I am participating in, and for articles on the site.

There is a tremendous difficulty ranking players on an all time basis, because you have to take into account so many factors.

Take for example, Hank Aaron, and Mickey Mantle.

A fan new to baseball may look at these two players’ numbers, and conclude Hank Aaron was the far better player. After all, he had the higher batting average (.305 to Mantle’s .298), more hits (3771 to 2415), and more home runs (755 to 536). He must be the better player, right?

A more experienced fan might know exactly why Aaron has the distinct advantage in several categories. For one thing, he played 3298 games, compared to 2401 for Mantle. We are looking for the better player right? On a game by game (or rather 162 game by 162 game) basis, Mantle was better right? I mean, he did have a higher OBP (.421 to .374), SLG (.557 to .555), OPS+ (172 to 155), and wOBA (.431 to .405). Both were fantastic players, but Mantle was clearly better. Right?

Well, both fans would be wrong. Hank Aaron has more hits, home runs, etc. because he played more games. But he also has a lower OBP, SLG, and wOBA for the same reason. Mickey Mantle retired at the age of 36, before he had a chance to completely fall apart. Hank Aaron, however, played until the age of 42, and his numbers the last few seasons of his career leave something to be desired. Plus, Aaron needs to be given some credit for being a good player for a much longer time than Mantle. Longevity matters in this game, and Aaron contributed far more value. Aaron was also far less injury prone.

So how do we find a middle ground? Enter Bill James. In his 2003 “New Historical Baseball Abstract,” Bill James used the following formula to rank players. He called it “objective function” and it was meant to value players on an all time basis. The formula is:

Objective function = 2/(1/25 + 10/[Career Win Shares]) +[ Best Three Seasons]/ 3 + [Best Five Seasons]/5 + [Win Shares per Season] + ([Birth year] – 1800)/10.

This formula factors in a few different things. How many win shares did a player accumulate during their career, which accounts for longevity; how many win shares did the player accumulate during their best three and five seasons, which accounts for a player prime; how many win shares did the player accumulate per season, which accounts for sustained success, as well as the players birth year, which accounts for the assumed greater talent level each season.

We are going to use that formula slightly different, and just look at offense for now. Our new objective function:

Objective function = 2/(1/25 + 10/[Career wRAA]) + [Best Three]/3 + [Best Five]/5 + [wRAA per 162 games].

Instead of looking at win shares, we are going to look at wRAA, so that we just look at offense. We will take out the part about birth year to simplify things, and we will count wRAA per 162 games (instead of per season) to make things simpler. So, let’s take a look at the two players:

Mantle = 2/(1/25 + 10/[860.3]) + (262.3)/3 + (394/5) + 58.05.
Mantle = 38.76 + 87.43 + 78.8 + 58.05 = 263.04.

And…

Aaron = 2/(1/25 + 10/[961.6]) + (200)/3 + (311.2/5) + 47.23.
Aaron = 39.68 + 66.67 + 62.24 + 47.23 = 230.83

So now that we see this, we can conclude that yes, Mantle was better. What do we know? Well we know Aaron’s advantage in the first category, career wRAA, was because he played longer. Mantle has better rate stats because he played a shorter amount of time, and did not decline as much. They both have great primes, but Mantle’s advantage there makes him the better player overall. But, this makes it look much closer than looking simply at raw counting numbers (HR, H, 2B, SB, etc.) or looking simply at rate stats (BA, OBP, SLG, wOBA).

BTW, this gets even close when we consider a couple of crucial facts:
1. Aaron played later, so time adjustments would help him.
2. Mickey Mantle was a butcher in CF, while Hank Aaron was decent in RF.

There are plenty of ways to evaluate players on a career basis, and using wRAA just covers offense, but using Bill James objective formula is a good way to balance out career total value, sustained success, and dominance in a player’s prime.

I’m sure my Frankenstein adaptation of James’ formula has it’s flaws, but the basic principals are the same. There are many ways to evaluate players on a career basis, all of which need to be accounted for to get the full picture.