Determining the most well-rounded player seasons

In baseball, well-rounded five-tool player production is highly coveted. Which players have produced baseball's most statistically well-rounded seasons?

Trivia time: What do Eddie Eagan, Jacob Tullin Thams, Christa Luding, and Clara Hughes have in common? They all were medalists in both the Summer and Winter Olympics in different sports. Eagan received golds in boxing and bobsled, Thams medaled in sailing and ski jumping, Luding won five medals (two golds) in cycling and speed skating, and Hughes won six medals, also in cycling and speed skating.

Why bring this up? Well, because I've always had great respect for and great interest in polymaths. I always am interested in the well-rounded individuals, including athletes who distinguish themselves on the playing field and in academia. Because of that, following athletes such as Myron Rolle (2008 Rhodes Scholar) and Craig Breslow (BA in Molecular Biophysics and Biochemistry from Yale, considered one of the smartest professional athletes) has been an extra pursuit of mine.

Of course, we have our own version of the baseball polymath: the "Five Tool Player." The player who can hit for average, hit for power, run the bases, throw, and field at plus levels. In terms of player value, these traits can be seen in the components of WAR, specifically fWAR in this case. fWAR has a batting component (wRAA), a base running component (UBR plus wSB), and a fielding component (UZR), which we could look at to determine well-roundedness.

What started me on this kick? Well, it actually goes back to all the Hall of Fame debates. I was thinking about Larry Walker's case for induction, and stumbled across the following fun fact. When looking at fWAR for outfielders with 3,000+ PAs since the creation of the AL in 1901, there are 5 players who rank in the top 10% of wRAA, BsR, and UZR: Barry Bonds, Hank Aaron, Ricky Henderson, Willie Mays, and Larry Walker. I personally hadn't realized that Walker had such a well-rounded resume, and it got me thinking what the most well-rounded seasons in MLB history are.

So, we have the basic premise. The stats we'll look at are the three components of fWAR defined above. Now, we'll look at the ranks of players in each of the three statistics for that season, where the player pool is all players who had at least 200 PAs. In each category, a player earns a certain number of points for a finish in that category. For example, in 2013, there were 356 players who received at least 200 PAs. Miguel Cabrera led all players in the wRAA category. Therefore, he'll get 356 points. Mike Trout, who came in second, gets 355. Alcides Escobar, who came in last, gets 1 point. Then, to keep all seasons on the same scale, we divide by the number of players who qualified that year, so (roughly), the range of scores for each component in each season is from [0,1].

In addition to putting all seasons on the same scale, it makes higher finishes in seasons with more players more impressive. To me, finishing second in a season with 356 qualifying players (A score of 0.9972) is more impressive than finishing second in a season with only 78 players (0.9872). The difference isn't large, but it still makes a slight difference.

This procedure is repeated for BsR and UZR, and finally the scores for the three categories are averaged, created a Well-Rounded Index for each player-season. So what seasons land in the top 10 of the most well-rounded?

So we've recently seen an all-around season from the ages in Mike Trout's 2012 rookie campaign. Also on the list are 6 Hall of Fame players (making up 8 seasons), and an early vintage Bonds. Without a doubt, these are some of the greatest players ever performing at their peak.

Now we expect every major league player to excel in at least one category. However, even the incredible athletes that populate the MLB have their down seasons.

Finally, it's interesting to see those players who had the highest average Well-Rounded Index over their whole career. To look at this, we limited the field to players who had at least 10 seasons with 200 PAs.

Again, we have 7 Hall of Famers, two active players with over 50 fWAR, and Barry Bonds. Definitely a solid list to be a member of. Now, before you ask, Mike Trout's two seasons lead to an average index value of 0.9504. So he could be well on the way to breaking all the well-roundedness records (If any such ones existed).

WR Index For All Seasons 1900-2013

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Statistics courtesy of FanGraphs.

Stephen Loftus is a featured writer at Beyond The Box Score. You can follow him on Twitter at @stephen__loftus.

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