For awhile, traditionalists have been using the argument that player A might be better than player B, but player B meant more to their team than player A. I and other people have thought this was bad in the past, but I have seen the light. In fact, the actual ballot states that the award should be based on a players value towards his team. I decided to take a systematic approach to that reasoning and devise a simply way to estimate how much a player really meant to their team. The key figure that allows us to do this is a simply concept, diminishing marginal returns (wins) to each run created or saved. Take for example, the pythagorean win-loss formula. Hold the runs allowed portion constant at league average of 797 runs. If you were to graph their expected wins based on runs, you would get this:
It's nearly a straight line, but it isn't. If each run created created exactly .1 runs then we would expect this function to have a constant slope of 1/10. However once we differentiate it, we'll find the marginals wins to each run scored, in simple terms that is how much each run is worth. Graphing the slope would give us this:
As you can see, each run is worth less the more you score. Run number 800 is worth about .09 wins and the 900th run is worth about .08 wins in terms of their expected win loss record. To make this long story short, if you add two similar offensive players one to already good offense and one to a bad offense, the one you add to a bad offense is certainly going to be more important to his team winning. Adding more offense to a team that already has a lot of offense is overkill. There is a similar effect to runs saved for pitchers as well. Now take for example Derek Jeter and Carlos Guillen. The two teams functions are going to be different, their pitching staffs aren't the same so we are going to let that equal to their actual teams pitching. We'll get graphs like so:
Now for actually looking at their contributions. So what would happen if we took Jeter off the Yankees and Guillen off the Tigers. The Yankees are already starting towards the top of their curve because of their better offense and the Tigers are lower, so they will lose more. It's relatively easy to take off their runs by using VORP. Jeter's VORP was 79.2 this season and Guillen's was 67.0. We can easily use the pythag win loss to measure how many wins we would expect to take off their win-loss record because of losing that offensive player. Once you do this we find that Jeter's VORP translated into approximately 6.61 wins for the Yankees and Carlos Guillens VORP translated into approximately 6.62 runs for the Tigers. This is assuming that both players have equal defensive ability. A general consensus on defensive stats for the last few seasons is that Guillen is better there making the seperation a bit larger.
So you are thinking, oh great you had a huge thread just to show that Carlos Guillen was .01 wins better than Derek Jeter? The answer is yes, but there are other things to consider. One of them is of course payroll. No, I am not going to say that Jeter makes more and that's the reason to discredit him, I am going to say that the Yankees would have an easier time replacing Jeter than the Tigers would have replacing Guillen. Guillen's actual value over the player the Tigers replace him with is likely going to be higher than Jeter's value over the replacement the Yankees get (buy). This may seem unfair to Jeter, but it's a simple truth. Finally there's another issue at stake, getting into the playoffs. Take 6.5 wins off the Yankees and they still make the playoffs by a couple games. Take 6.5 wins off the Tigers and they don't make the playoffs. When two players have essentially the same value to their team, all three of these off the field reasons are huge when fully analyzing a players value to his team.
Lastly, there's the whole argument that Jeter did better so he is better and is more valuable. No Yankee fan has taken the time to simply analyze why Derek Jeter has a higher VORP. The main reason is simple - he's on the New York Yankees. No, there is no hidden if/then function in the formula for VORP that gives bonus points for being the Captain of the New York Yankees, but there are some effects being on the Yankees that have given Jeter a clear-cut advantage just because he is a Yankee. VORP consists primarily of three things, plate appearances, marginal lineup value rate (MLVr) of the player in question and a replacement players MLVr at the same position. MLVr is formulated by a function of a players slugging percentage, on-base percentag, batting average and stolen base rate(s) on a teams' runs scored for a season. Replacement level is defined as about the 40th best player at that position (roughly 35 points below average OBP and SLG at the position).
Looking through the lines of the players, you will notice that Carlos Guillen has a better MLVr than Derek Jeter .279 to .268 (runs per game). However, once we extend this to VORPr (essentially playerMLVr - replacementMLVr) is quite a bit higher than Carlos Guillen. We'll remember this later as it has a lot to do with the usage of Jeter compared to Guillen. You will also notice that Derek Jeter has a 715 plate appearances and Carlos Guillen had just 622, a difference of 93. I found this peculiar because Derek Jeter only played a few more innings than Guillen overall and appeared in just one more game. So I dug deeper.
The first bit of information also echoes a point made a lot earlier. There's a second byproduct of the Yankees being a better offensive team, the turn the lineup over more. The Yankees' team OBP is over .360 while the Tigers' is under .330. A significant difference. Each spot in the Yankees lineup batted approximately 22 more times than the corresponding slot in the Tigers' lineup. 22 times may not seem like a lot, but it's going to be worth a couple runs.
The second and bigger bit of information has to do with Jim Leyland's stupidity and Joe Torre's lust. Jeter batted second most of the season and he got 50 or so PA batting third. Despite being the Tigers' best hitter, Leyland stuck Guillen in the five hole most of the season with an additional 70 PA's coming in the seventh spot. It was not the right move. It's a huge reason that Jeter has a higher VORP. Each spot in the batting order gets about 20 more PAs than the spot behind it. The difference in Jeter batting second and Guillen batting fifth is worth about 60 PAs and then there are another 8-10 PAs when Jeter batted third and Guillen batted seventh.
All of these are going to add up to about 90 more PAs for Derek Jeter just because of the teams they were on. If you guys want to seperate that teams you have to adjust. Both players spent about the same amount of time on the field. However, Jeter got 90 PAs because of the Yankees for the most part. Even using their standard VORPr an adjusting this on Guillen, compensating for the Yankee-Jeterness would give him 10 more runs on his VORP. This would bring the difference between the two to 79.2 to 77.0 with Jeter getting a 2.2 run advantage.
Of course for all of the reasons mentioned above, Guillen would probably be more valuable. Also those 2.2 runs would be made up if Guillen was a better defensive shortstop, and the general consensus is that he is. Now, if you will recall I said that Jeter's replacement player was lower than Guillen's. Why is this? It has to do with Jeter being a Yankee and Guillen being a Tiger. Guillen got into 8 games as a 1B. Due to various reasons Leyland was forced to play him there. Joe Torre would never ask Jeter to play 1B even though he had the chance. If you factor out the difference here, Guillen's VORP is going to be over 80, clocking in at 81.5.
So in conclusion, there are a lot of reasons that Carlos Guillen is the League's Most Valuable Player to his team. One of the big ones is that his overall value to his team is higher than Jeter's. Secondly, the only reason Jeter produced more in absolute terms are factors caused by the teams the played on, not the players themself. It's pretty cut and dry, Carlos Guillen is better than Derek Jeter and deserves the MVP over him.
It's nearly a straight line, but it isn't. If each run created created exactly .1 runs then we would expect this function to have a constant slope of 1/10. However once we differentiate it, we'll find the marginals wins to each run scored, in simple terms that is how much each run is worth. Graphing the slope would give us this:
As you can see, each run is worth less the more you score. Run number 800 is worth about .09 wins and the 900th run is worth about .08 wins in terms of their expected win loss record. To make this long story short, if you add two similar offensive players one to already good offense and one to a bad offense, the one you add to a bad offense is certainly going to be more important to his team winning. Adding more offense to a team that already has a lot of offense is overkill. There is a similar effect to runs saved for pitchers as well. Now take for example Derek Jeter and Carlos Guillen. The two teams functions are going to be different, their pitching staffs aren't the same so we are going to let that equal to their actual teams pitching. We'll get graphs like so:
Now for actually looking at their contributions. So what would happen if we took Jeter off the Yankees and Guillen off the Tigers. The Yankees are already starting towards the top of their curve because of their better offense and the Tigers are lower, so they will lose more. It's relatively easy to take off their runs by using VORP. Jeter's VORP was 79.2 this season and Guillen's was 67.0. We can easily use the pythag win loss to measure how many wins we would expect to take off their win-loss record because of losing that offensive player. Once you do this we find that Jeter's VORP translated into approximately 6.61 wins for the Yankees and Carlos Guillens VORP translated into approximately 6.62 runs for the Tigers. This is assuming that both players have equal defensive ability. A general consensus on defensive stats for the last few seasons is that Guillen is better there making the seperation a bit larger.
So you are thinking, oh great you had a huge thread just to show that Carlos Guillen was .01 wins better than Derek Jeter? The answer is yes, but there are other things to consider. One of them is of course payroll. No, I am not going to say that Jeter makes more and that's the reason to discredit him, I am going to say that the Yankees would have an easier time replacing Jeter than the Tigers would have replacing Guillen. Guillen's actual value over the player the Tigers replace him with is likely going to be higher than Jeter's value over the replacement the Yankees get (buy). This may seem unfair to Jeter, but it's a simple truth. Finally there's another issue at stake, getting into the playoffs. Take 6.5 wins off the Yankees and they still make the playoffs by a couple games. Take 6.5 wins off the Tigers and they don't make the playoffs. When two players have essentially the same value to their team, all three of these off the field reasons are huge when fully analyzing a players value to his team.
Lastly, there's the whole argument that Jeter did better so he is better and is more valuable. No Yankee fan has taken the time to simply analyze why Derek Jeter has a higher VORP. The main reason is simple - he's on the New York Yankees. No, there is no hidden if/then function in the formula for VORP that gives bonus points for being the Captain of the New York Yankees, but there are some effects being on the Yankees that have given Jeter a clear-cut advantage just because he is a Yankee. VORP consists primarily of three things, plate appearances, marginal lineup value rate (MLVr) of the player in question and a replacement players MLVr at the same position. MLVr is formulated by a function of a players slugging percentage, on-base percentag, batting average and stolen base rate(s) on a teams' runs scored for a season. Replacement level is defined as about the 40th best player at that position (roughly 35 points below average OBP and SLG at the position).
Looking through the lines of the players, you will notice that Carlos Guillen has a better MLVr than Derek Jeter .279 to .268 (runs per game). However, once we extend this to VORPr (essentially playerMLVr - replacementMLVr) is quite a bit higher than Carlos Guillen. We'll remember this later as it has a lot to do with the usage of Jeter compared to Guillen. You will also notice that Derek Jeter has a 715 plate appearances and Carlos Guillen had just 622, a difference of 93. I found this peculiar because Derek Jeter only played a few more innings than Guillen overall and appeared in just one more game. So I dug deeper.
The first bit of information also echoes a point made a lot earlier. There's a second byproduct of the Yankees being a better offensive team, the turn the lineup over more. The Yankees' team OBP is over .360 while the Tigers' is under .330. A significant difference. Each spot in the Yankees lineup batted approximately 22 more times than the corresponding slot in the Tigers' lineup. 22 times may not seem like a lot, but it's going to be worth a couple runs.
The second and bigger bit of information has to do with Jim Leyland's stupidity and Joe Torre's lust. Jeter batted second most of the season and he got 50 or so PA batting third. Despite being the Tigers' best hitter, Leyland stuck Guillen in the five hole most of the season with an additional 70 PA's coming in the seventh spot. It was not the right move. It's a huge reason that Jeter has a higher VORP. Each spot in the batting order gets about 20 more PAs than the spot behind it. The difference in Jeter batting second and Guillen batting fifth is worth about 60 PAs and then there are another 8-10 PAs when Jeter batted third and Guillen batted seventh.
All of these are going to add up to about 90 more PAs for Derek Jeter just because of the teams they were on. If you guys want to seperate that teams you have to adjust. Both players spent about the same amount of time on the field. However, Jeter got 90 PAs because of the Yankees for the most part. Even using their standard VORPr an adjusting this on Guillen, compensating for the Yankee-Jeterness would give him 10 more runs on his VORP. This would bring the difference between the two to 79.2 to 77.0 with Jeter getting a 2.2 run advantage.
Of course for all of the reasons mentioned above, Guillen would probably be more valuable. Also those 2.2 runs would be made up if Guillen was a better defensive shortstop, and the general consensus is that he is. Now, if you will recall I said that Jeter's replacement player was lower than Guillen's. Why is this? It has to do with Jeter being a Yankee and Guillen being a Tiger. Guillen got into 8 games as a 1B. Due to various reasons Leyland was forced to play him there. Joe Torre would never ask Jeter to play 1B even though he had the chance. If you factor out the difference here, Guillen's VORP is going to be over 80, clocking in at 81.5.
So in conclusion, there are a lot of reasons that Carlos Guillen is the League's Most Valuable Player to his team. One of the big ones is that his overall value to his team is higher than Jeter's. Secondly, the only reason Jeter produced more in absolute terms are factors caused by the teams the played on, not the players themself. It's pretty cut and dry, Carlos Guillen is better than Derek Jeter and deserves the MVP over him.
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