Thursday, November 20, 2008

Evaluating a Player's Career "Range" (Part I)

The following pair of posts grew out of a discussion on the Bill James Online forums. The original concept was proposed by Bill James user alljoeteam, and I took an initial stab at answering.

alljoeteam originally posted this idea:
But lets look at a players greatness as a mountain. How do we measure the greatness of the mountain? How high it is? How wide it is? We would need to combine those factors to determine the greatest of the mountain. Peak season are like the height of the mountain and career value is like the volume of the mountain. James also included a per 162 games factor in his rating. That is like a some average of the heights of the mountain at different points or something. What I am suggesting is a find the volume of the mountain that is above a certain point, say 2000 feet from the base or something. Different mountains will have a different percentage of their volumes above that cutoff.

A tall, steep mountain (McGwire) will have about the same volume as a plateau (Murray) depending on the exact numbers. Now a really high plateau (Gehrig)is both wide and tall and we could see that in this one number. He would rank above McGwire and Murray as he should, but McGwire and Murray would be about the same.
Here's my initial work on his idea:
I found this to be a pretty intriguing idea, actually. I understand the analogy you gave in the "Peak Seasons in Player Rankings" posting (about measuring the scope and breadth of a "mountain" above a certain "elevation"), and I agree with it in principle. So I looked at the numbers.

I ranked players in the two ways you proposed, looking at total Win Shares above a certain annual level and also at a weighted listing, using the average of each player's three peak seasons as the weight. I ran the numbers twice, using 20 WS and 27 WS as the two "base camps". I did that mostly to see if the 20 WS value was too low of a threshold.

You should be able to see the lists at:

My first thought upon looking at the list was that it seemed to favor older players (I ignored people who played their final game before 1901... I would've ignored all people who played before 1901, but I didn't think it was right to leave off Honus Wagner or Cy Young). However, that just may be me. I mean, Tris Speaker, Walter Johnson, Eddie Collins, Rogers Hornsby, Nap Lajoie, and Christy Mathewson aren't exactly slouches.

Both lists are definitely dominated by pre-1980 players, though, with only Barry Bonds (#2) and Mike Schmidt (~#17) showing up in the top 20 on every version of the list (A-Rod shows up in the top 22 of every list). The players in the top 25 who benefit the most from the weighted list are Lou Gehrig and Hank Aaron, both jumping 2-5 slots when the weights are taken into consideration. This should tell us that these two have the most (positive) consistency between their peak seasons and their "all-star WS" seasons. Surprisingly, the two players who are harmed the most by the weighted lists are Nap Lajoie and Mickey Mantle. They both drop 6-7 slots on the list when their weights are taken into account.

As for (very) recent players, the biggest surprises lie just outside the top 25. Albert Pujols and his 7 full seasons (these data are through 2007) is already in the top 30 (or so). Gary Sheffield, Jeff Bagwell, and Frank Thomas are all also in the top 40 (on all lists). In fact, Sheffield actually benefits from the weighted lists while Pujols drops. Bagwell and Thomas both hold their spots on each list.

Other players of note are players like Rickey Henderson, Pete Rose, and Joe DiMaggio, who are all in the top 30 on the 20 WS list but who drop into the 40s in the 27 WS list. To me, this seems to say that these players all have a large clump of 20-30 WS seasons, with only a few higher WS seasons.

In the end, I'm not sure what I think about this list. It seems to make sense, as the players that it has identified are obviously high-value, high-WS players. I think I just may be disappointed in the lack of diversity of the top players. I can't decide if this is an issue with the method, or if this is a limitation of Win Shares. I'm still new when it comes to playing with real, hard-core numbers, so I haven't been able to develop a full opinion on stats like Win Shares.
Continue on to Part II...

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