How does the fielding of 2nd and 3rd baseman compare to when they play the opposite position?

Question: How does the fielding of 2^nd and 3^rd baseman compare to when they play the opposite position?

Why I asked the question: Mark Teahen of the Royals is being asked to practice at 2^nd base for the up coming season. Using other players as comparison, how should Mark project at 2^nd.

Analysis: I used UZR as the defensive metric which is available at Fangraphs.com. UZR is the best freely available defensive metric I can find. As with any defensive metric, it is far from perfect, but for now it is the best to use. I looked at all players from the last 3 season that played at least 100 innings at both 2^nd and 3^rd base. I came up with 43 players. To equally weight the weight the at bats I determined the Harmonic mean in at bats between innings and UZR at 2^nd and 3^rd

Harmonic mean =2/((1/innings at 2nd)+(1/innings at 3rd))

Note: I had a discussion with Tom Tango on his blog on the best way to measure the differences.

I then added the UZR and innings for all players at 2^nd and 3^rd and got the following results:

Average UZR/150 games at 2B: -1.90
Average UZR/150 games at 3B: -0.85

Then I group the the players that played the majority of time at 2B and got the following results

Average UZR/150 games at 2B: -1.73
Average UZR/150 games at 3B: -0.49

Finally I group the the players that played the majority of time at 3B and got the following results

Average UZR/150 games at 2B: -2.21
Average UZR/150 games at 3B: -1.49

There are the general numbers showing how it seems that 2^nd base is harder to play than 3^rd base for this group of players over the last 3 years.

Lets take this data and extend it further to see how it effects the Royals and the decision to move Mark Teahen to 2^nd. From the above data, we can determine that Mark then should see a change of -1 UZR/150 from his lifetime 3^rd base average (-11.6) to -12.6, which would make him the worst defensive 2^nd baseman when comparing his -12.6 UZR/150 to all 2^nd baseman with over 400 innings played last year. So if Mark played 2^nd base for 150 games next season, his defense would cost us 15 runs compared to your average defensive 2^nd basemen.

Callaspo on the other hand rates at 5.9 UZR/150 at 2^nd base. Using a Run Generator calculator to determine the difference, the Royals will score 6 more runs with Teahen in the lineup vice Callaspo if they were each to play 150 games at 2nd. As a whole, the Royals are -12.5 runs worse as a team if they were to play Teahen at 2^nd vice Callaspo, or ~1 win.