Signing LaRoche Is Money Well Spent

Upon sharing my approval of the signing of Adam LaRoche by the Nationals, I was challenged by my friend William.Hatheway (end of this thread) to demonstrate why paying millions for a player who provides just 2 WAR at 1st base is a winning proposition, when the money could have been spent elsewhere to potentially greater effect in terms of WAR.

As William pointed out, if LaRoche were playing a position like 3rd base he would be more valuable (assuming he is an average defender at both positions).  There is truth in this.  However, being a replacement level player at 1st base requires more offensive production than any other position on the field, so having LaRoche at 1st base has its own value.

Let's dive into the numbers:

Take by comparison a replacement level 3rd baseman.  If he makes the reverse switch, he would have to produce an additional 15 runs just to be replacement level at 1st.  (For those worried, defense only contributes a small percentage of WAR)

Let's look at LaRoche's hypothetical 3rd base WAR.  The closest comparisons by 3 year average WAR at 3rd are Casey Blake and Scott Rolen.  Blake earns $5.25m, Rolen earns $8.75m.  Now obviously in real life, these guys are far better defenders than LaRoche, but if we wanted LaRoche's production at 3rd base, we'd need to spend just as much money.

Paying for a replacement level 1st baseman isn't free either.  Replacement level players don't get played at 1st base for very long, which is why there is no replacement level 1st baseman who's played for all three of the past three years.  Looking at just 2010, we find one 1st base free agent who produced a 0.0 WAR - Jorge Cantu who split time between 1st base and 3rd base (meaning he was actually sub-replacement for 1st).  He made $6 million last year, a contract he got coming off of a 1.3 WAR season.   He produced something in line with Ian Desmond (1.1 WAR; adjusted -0.9 WAR at 1st base).

If we were to use Desmond's bat at 1st base, move Zimm or Werth to SS (Werth can totally swing it) and buy a 3B or RF to replace LaRoche's bat, how much would it cost?  3B we've already looked at - expect a base salary of what 37 year old Casey Blake gets - $5.25 million, but probably something closer to Rolen's $8.75 million.  RF the closest comparisons (position adjusted) are Bobby Abreu, who will make $9 million in 2011 and Vladimir Guerrero (age 35), who made $5.5 million in 2010.

Paying for a free agent with the value in WAR that LaRoche gives us would cost roughly the same amount regardless of what position we pay at.  The equivalent of 2.1 WAR at 1st base costs around $8 million, unless you have a young guy under team control or sign an aging veteran. 

One alternative would be signing Adam Dunn (average 2.1 WAR over 3 years) for $14 million a year.  Not that that's relevant to this discussion.

My conclusion is that paying Adam LaRoche $8 million to play 1st base for us is a solid use of that money.  He's no steal, but he's worth what he is paid, and spending that money elsewhere would not give us a greater return on our investment.