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Sabermetrics student Stephen Lee is our guest blogger for this installment of By The Numbers. He mentions some of the greatest hitters ever in this piece.

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Stephen Lee: Throughout this offseason, baseball has seen some dramatic moves and major free agents signing large contracts with new teams, such as Albert Pujols and Prince Fielder.  Pujols signed an astronomical 10-year, $240 million contract, which is essentially three separate contracts covering actual play, personal accolades and what will happen in the event he retires prior to the 2021 season.  This type of contract astounds me as an individual.

How can a team justify paying someone that much money to play baseball?  I asked myself, ‘Is he really that much better than everyone else?’  I was looking at his statistics, and he is definitely a one-of-a-kind player.  With a career batting average of .328, 445 homers, a .420 OBP and .617 SLG, he is truly an outstanding player.  But I still wonder how much better he is than everyone else that would warrant him being one of the highest paid athletes in sports history?

In trying to answer that question, I came across an article which described a statistic called weighted runs created plus, or wRC+.  After looking at what makes up wRC+, it is essentially an improved version of Bill James’ original Runs Created statistic.  This measure, wRC+, not only takes into account the benefit a player adds to his team in the form of Runs Created, but it also normalizes him with the rest of the league, giving players a score of 100, being the traditional league average.  So, for example, if you were to take a player and he received a wRC+ score of 140, that player contributed 40% more runs for his team than the average player in baseball.

Another added bonus of using wRC+ is that it adjusts for both ballparks and leagues. In a sense, this allows one to compare not only across different leagues, but also across different time periods.  The calculation for this statistic is:

(1+ League runs per PA/(wRAA/PA))*100 where, wRAA= ((wOBA-league wOBA)/wOBA scale)* PA and  wOBA= [(1.95*HR)+(1.56*3B)+(1.24*2B)+(.90*1B)+(.75*HBP)+(.62*(BB-Intentional BB))]/PA.


PUJOLS (2009)

HR 47
3B 1
2B 45
1B 186
PA 700
wOBA .5245
wRAA 124.09
wRC+ 168


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This being said, now let’s look at how Pujols compared with the rest of the MLB when he won the National League MVP Award in 2009 with 100% of the votes. According to, in 2009 the average runs per PA was .1198, the league wOBA was.328 and the wOBA scale was 1.21.  According to these statistics, Pujols has an outstanding wRC+ of 168, which is 68% above the average MLB player score of 100.

Now let’s compare Pujols’ number with one of the most prolific hitters of all-time, Ted Williams.  Using arguably one of Williams’ best seasons, 1949, in which he won the MVP, we will compare Williams’ wRC+ with that of Pujols’ in 2009.  In 1949, Williams had a wOBA of .566, a wRAA of 128.37 and a wRC+ of 168.  The Thumper’s wRC+ score was the same score as Pujols’ in 2009.

The bottom line? Using this statistic, coupled with Pujols’ outstanding career up to this point, the Angels’ decision to give Pujols his astronomical contract can be justified.


Slowinski, Steve. “wRC and wRC+.” Fan Graphs. 16 February 2010. (accessed 4 March 2012).

Wraithpk. “’OPS+ vs. wRC+’ or ‘The Battle of the Stats.’” Pinstripe Alley. 19 January 2010. (accessed 4 March 2012).

Tango, Torn M. “The Book- Playing the Percentages In Baseball.” Inside the Book. 11 December
2010. . (accessed 4 March 2012).

Klaassen, Matt. “Custom wOBA and Linear Weights Through 2010: Baseball Databank Dump
2.1.” Sabermetric Primers. 4 January 2011. (accessed 4 March 2012).

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Is Pujols worth the absurd amount of money he got from the Angels? Let us know…