Luyman's Terms #11: The Value of a Bat, Part 2

In part 1, I discussed the concept of run values, and how we can use them to quantify a players offensive value to his team. I concluded the post saying that Jermaine Dye being worth 0.168 runs with his bat was a good thing, despite looking less than impressive. So why is 0.168 runs a good thing? What if I told you that that the average MLB player was worth -0.777 runs with his bat over the course of the 2002 season?

I understand if that strikes you as counter-intuitive, if the average player was worth negative runs to his team how did anyone score? The answer is simple: while this metric scores an out as a negative event, an out does not result in runs (literally) being taken off of the scoreboard. This explains why a player can be worth negative runs to his team, even though a "negative run" is not a thing the scoreboard measures.

What follows is a list of all MLB players who ended the 2002 season with 300 or more plate appearances. Sheet 1 contains the raw number of times each even occurred for each player. Sheet 2 contains the number of runs each player produced with each event. The last column of sheet 2 contains the total number of runs produced by that player (note that all of the "value" columns measure value in runs):

I explained where these numbers came from in part 1, but it's been a couple months so I will explain again. Each "value" column is calculated by taking the count of a certain event and multiplying by how many runs that particular event is worth. Let's so a sample calculation using Jim Thome and singles:

Jim Thome hit into 73 singles in 2002

A single was worth .475 runs in 2002

73 singles * .475 runs = 34.675 runs generated by singles by Jim Thome in 2002

Add up all of the non-out values for each player and you get the "hit value" for each player. This number is the total number of runs generated by that player's hits.

Unfortunately, we cannot stop our analysis here. While score is kept by only counting up, the value that a player provides for his team is certainly not only positive. This is why we must also include the value of the outs a player generates as well. To account for the full value of a player, all we have to do is add his hit value and out value:

Jim Thome Hit Value = 162.777 runs

Jim Thome Out Value = -99.866 runs

Jim Thome Offensive Value = 162.777+ -99.866 = 62.911 runs

I started this piece by saying that Jermaine Dye's 0.168 runs of offensive value being a good thing, that number seems to the dwarfed by the offensive value generated by Jim Thome! In fact, there are quite a few players who dwarf the value put up by Jermaine Dye! How is 0.168 runs of offensive value a good thing? Well, even with the massive values put up by the top of our list, the players at the bottom of the list also played in the major leagues. We must also consider their contribution.

To find the average value of a player with his bat, all we have to do is add up the total offensive value for each player, and divide by the total number of players in the sample (or, in this case, let the spreadsheet do it for us). The total offensive value for the group was -210.508 runs, spread over all 271 players means that the average player was worth -0.777 runs to his team with his bat. If Barry Bonds is removed from the sample (which I will do, since he is such an outlier), the number goes all the way down to -1.169 runs.

Using the average player as benchmark, we can see that Jermaine Dye is ever so slightly above average. He actually ranks 105th out of the 270 players in the sample (remember, we are excluding Bonds)! What this tells me is that an average player is actually quite valuable, even if the average player doesn't seem so good on the surface.

Are there any burning questions you have about baseball that you would like for me to attempt to answer using math (poorly)? The next topic I will attempt to answer will be pertaining to pinch hitting in some form or fashion, but I would love to hear what you guys would like to see analysed!