Here is what Wikipedia says about it: "A geometric mean is often used when comparing different items- finding a single "figure of merit" for these items- when each item has multiple properties that have different numeric ranges." In fact, some of the values I will be using will have much larger ranges than others.
Here are the measures I will use:
Fielding: I use FRAA from the Lee Sinins Complete Baseball Encyclopedia (fielding runs above average). Sinins got them from Michael Humphreys' recent book Wizardry. I don't have a way of easily breaking this down into throwing (arm) and catching (glove), but I have something in mind that I will use in a future post. I converted it into a rate relative to the league average (like 1.10 means that you saved 10% more runs than average).
Hitting for Average: I will use average relative to the league average.
Hitting for Power: I will use isolated power relative to the league average.
Speed: I use a player's 3B/(2B + 3B) relative to the league average. This is an idea from Voros McCracken. The idea is that it is a % of the time you hit an extra-base hit that you get a 3B. The faster players will have a higher rate here. It is relative to the league average. Handedness is adjusted for. Triples were taken out of the relative isolated power calculation (for both the player and the league average) since they get used in the speed rating. Actually, for isolated power they were considered doubles. Both the speed and power ratings had ranges far beyond those of fielding and hitting for average.
A park adjustment was also made to each player's overall rating (this was based on hitting only).
The four ratings, each relative to the league average, are multiplied times each other and then I take the 4th root of that number (the geometric mean). I used all players who had 5000+ PAs through 2011. The table below shows the top 25.
Some players are not too surprising while others are. One possible weakness is that some players played long careers and in their later years, the averages and rates were dragged down. So I also tried to create a rating for "all-aroundness" above replacement level. If the average level would be 1.00, then replacement could be .8 (what I used). This might be reasonable because 80% of 81 is about 65 wins, an acceptable replacement level (if we want to go down to say 54 or 52 wins, we could assume that the replacement level pitchers would get you the rest of the way there-remember, these are only position players and their hitting, fielding and running).
So how was this calculated? Mays has 1.385. That minus .8 gets us .585. That is how far above replacement Mays was, qualitatively. To quantifiy this, I assumed a 700 plate appearance levl for a full season. Mays had about 17.85 full seasons. So that times .585 gets us 10.44. He is the leader here.
Alot of all-time greats here. But Steve Finley really jumps out as a surprise.
I hope to post more in the next week or two on some of the assumptions I made and how I came up with some of the measures. Other issues include using SBs instead of 3Bs for speed (Rickey Henderson would rank higher then), using HR% instead of isolated power, how park affects play a role in the 3B/(2B + 3B) rate, the handedness adjustment for that stat, including the ability to get a walk as a "tool" and the earlier mentioned issue of breaking up the fielding rating into throwing and catching (it is possible that someone got a good fielding rating and was not really well balanced, that is, it was all due to their arm or their glove). I also need to explain how I turned FRAA into a rate and how I adjusted for handedness in 3B/(2B + 3B). Same for how I calculated and used the park effect adjustment.