Table of Contents

Tuesday, October 23, 2007

Player Value, Part 2c: Offense - Positional Adjustments

To view the complete player value series, click on the player value label on any of these posts.

Positional Adjustments

If you go back and compare the RAR numbers in my baselines post to BPro's VORP, one of the biggest differences that you might note is that players playing catcher, shortstop, and second base tend to get higher ratings in VORP than in my numbers. The opposite is true for first basemen, left fielders and right fielders. The reason? VORP includes an adjustment based on typical offensive performance at each position, and my data did not. ... but should they have? Let's take a look.

In the table below, I've grouped NL hitters from '03 to '07 by their primary position and sorted them by their rate of offensive production (runs per game). Here's how those totals break down:
C 43228 4.1 82% 0.319 0.393 0.712
SS 46332 4.4 87% 0.326 0.401 0.727
2B 49834 4.7 94% 0.338 0.414 0.751
CF 45720 4.9 96% 0.335 0.424 0.759
3B 47791 5.2 104% 0.344 0.449 0.793
RF 46754 5.4 107% 0.348 0.454 0.801
LF 48358 5.6 111% 0.353 0.465 0.818
1B 49581 6.0 119% 0.364 0.483 0.847
The rankings here probably don't come as a big surprise to many of you--after all, it's often the case that teams will employ catchers and shortstops that aren't very good hitters (e.g. David Ross and Alex Gonzalez with the Reds). First basemen and left fielders, on the other hand, are often some of the best hitters on any given team. But why is it that the positions vary in their hitting so much? I can think of two possible reasons:
  1. A poor hitting position may be a more "difficult" position to play and thus the pool of players who can competently play that position may be smaller than at a position that is easier to play. Smaller pool of players = less offensive depth.
  2. The players playing a weaker position may not be as talented (defined as total offensive + defensive skill) as those at other positions.
The first is almost certainly true. We expect shortstops, for example, to have tremendous range, great hands, and a canon for an arm, because those attributes are what is needed to get lots of outs at that position. The same expectations are not present for first basemen, and therefore there's a larger pool of players that can play first base...and thus, there's a higher standard for offense at that position than at shortstop.

Therefore, analysts often make positional adjustments to offensive performances based on these observed differences in hitting across positions. The logic is that if teams play players in appropriate positions relative to their defensive skills--and, in general, they probably do--we can give a boost to poor hitting positions and a penalty to plus hitting positions such that the average hitter at each position is given equal value. That way, each player is compared to his peers, putting everyone on an equal playing field. Presumably, in terms of total player value (offense + defense), if a player moved from first base to shortstop, any gains he would make in terms of being a better-than-his-peers hitter would be negated by the cost he would incur to his team via substandard defense.

That's essentially the basis for positional adjustments in VORP. However, there's a major flaw in that approach. And it relates to the second explanation for variation in offense across positions, that of variation in talent level across positions.

Why positional adjustments based on offensive disparities is not the best approach

Let's come at this from a fresh angle: players aren't restricted to one position, but can theoretically "play" anywhere on the baseball diamond. The problem is that some are better defenders than others, and therefore teams tend to put their best defenders at the positions that are the hardest to play (both in terms of the physical demands of the position, and the level of average defensive performance at that position), such as shortstop. But how much harder is it to play shortstop, for example, than first base?

The best study that I'm aware of that has tried to quantitatively answer this question is one by Tom Tango. He used multi-season UZR data to compare how players performed when they played multiple positions. Presumably, a player's absolute defensive skill is a constant, but he'll look better or worse at a position given how he stacks up to his competition at each position (especially once you adjust for experience at a position). By comparing how player defense varied across different positions, in virtually every combination and direction you can imagine, Tango constructed the following defensive "spectrum" (it should still be considered a work in progress):
+5 CF
+4 SS
+0 2B
-1 3B
-4 LF
-4 RF
-8 1B
The units are the typical differences he found in defensive runs saved per season that you should expect when a player moves from one position to another. So, if you move an average fielding first baseman to shortstop (assuming you can do this, i.e. he's not left-handed), you should expect that player to play roughly 12 runs below average per season once he learns the position (players will vary, of course, in how they do based on their specific attributes--speed, arm, hands, etc--these are just the mean differences).

Here's another look at this question, based on data can be gathered from the Fans Scouting Report, which asks fans to rate players in a variety of categories based on their subjective impressions of a player's skills (participants are asked to ignore player position, as well as any defensive stats...hence the "scouting" report). Here are the average total scores for players at each position, all of which are scored in the same categories:
CF 60
SS 59
2B 56
3B 54
RF 50
LF 43
1B 41
The average player across all of these positions got a score of ~52. Therefore, we see that players who play center field or shortstop are generally given substantially above-average ratings on their skills (speed, first step, hands, arm accuracy, arm strength, etc), whereas players in left field or first base are rated as below-average defenders. While the actual numerical differences aren't the same (it is possible to convert differences in these ratings to an approximate runs saved statistic), the overall positional rankings are almost identical to those that Tango generated using UZR data. The only difference is RF'ers being ranked as better than LF'ers. Pretty compelling when two such vastly different datasets come to virtually the same answer!

Now, looking at these two defensive spectra, they look pretty similar to the offensive rankings, right? Shortstops are ranked near the top, while corner outfielders and first basemen are down at the bottom. That's certainly supporting our first explanation--some positions are harder to play defensively, and therefore the pool of players that have sufficient defensive skills to play those positions competently is smaller, meaning there's less offensive depth at those positions.

On the other hand, there are some notable differences between the offensive and defensive positional rankings. Center fielders, for example, were rated as approximately average hitters (96% of league average), and yet were rated as the single hardest position in baseball to play in both datasets. So here we have a position that features players that are average hitters as well as above-average fielders. This means that center fielders are, overall, an above-average position in terms of total player talent! On the other side of the coin are second basemen. They are rated as an average position, defensively, and yet also feature below-average hitting. This means that second basemen, overall, are a position with below-average talent (again, talent = combined offensive + defensive skill).

Now, think about what this means if we use adjustments based on offensive disparities among positions. If a player is at second base, and then is moved to center field, he is moving to a position that is more difficult to play defensively. At yet, because center fielders, on average, tend to hit better than second basemen, he is going to be judged against a higher offensive standard than he was at second base. Therefore, if we use positional adjustments based on offensive disparities, this player is going to suffer a hit to both his offensive and defensive ratings just because he moved to a more talented position!

To put it another way, positional adjustments based on offensive disparities assumes a negative correlation between fielding skill and offensive performance. The fact that we have positions where the average player at that position is both a superior defender and an average hitter means that this assumption cannot be correct.

Therefore, if the point of the positional adjustments is to put all players on an even playing field with respect to our value estimates, it seems to me that adjustments based strictly on offensive variation across positions are inadequate. They will underrate players playing particularly talented positions, and they will overrate players playing talent-poor positions.

To be clear, there is absolutely a need to apply positional adjustments to player value ratings, because the average fielding skill (and thus value) varies across positions: an average-fielding first basemen as far less of a defensive asset than an average-fielding shortstop, and we need to recognize that if we're going to value our shortstops and first basemen appropriately. It's just that using differences in offensive performance is a flawed way to go about this, because overall player talent levels are not constant across positions. Instead, we should be using adjustments that account for differences in the actual fielding value of average defense at different positions, like Tango's UZR spectrum above.

So all that said, here's "my" solution on how to assess player value (it's most certainly not my idea, just what I've come agree is the best way to go about things):
  1. Estimate player offensive value. This can be done relative to overall league averages or replacement level. It should be done without regard to position: in this step, we're strictly interested in offense, so it doesn't matter where the player plays!
  2. Estimate fielding value via two steps:
    1. First, calculate player fielding value relative to overall league average at a player's position (as we saw in my replacement level study, this works for both league-average and replacement-level baselines).
    2. Assign a prorated (by inning) positional adjustment to each player that accounts for the differences in fielding value across different positions. Using Tango's data, a first baseman would be get -8 runs per season relative to the rest of the league, whereas a center fielder would be rated at +5 runs per season, relative to the rest of the league.
  3. Sum all these values together to get a composite estimate of player value.
We know how to do #1 already. The next article(s) in this series will discuss how to do both parts of #2 in detail.

Update: After some additional data analysis and discussion, Tango and others seem to have moved to this spectrum, which is slightly (emphasis on slightly) different from that which I've been using. Numbers are runs per season:
+10 C
+6 SS
+4 CF
+1 2B/3B
-6 LF/RF
-9 1B
-15 DH

This is what I'm going to use moving forward. But it's close enough that I'm not going to revise anything I've done to date. Sometimes you just gotta move forward! :)

And here's more on the apparent fact that the assumption of positional equality in offense+defense is a flawed assumption.

Update #2: As with any field, this research is constantly evolving. Based on several rounds of further discussion and analysis, the current positional adjustments endorsed over at TheBookBlog are:
+1.25 C
+0.75 SS
+0.25 2B/3B/CF
-0.75 LF/RF
-1.25 1B
-1.75 DH
Multiply these by 10 to convert wins to runs and you get the adjustments I'm currently using. I probably should really be multiplying by 9.5 or so (4.75 r/g * 2 teams = 9.5 r/g), but it makes almost zero difference and the round numbers are easier to remember. :)