The Roto Grotto: targeted z-scores

Z-score is a useful statistic to compare player performance in roto categories relative to an average player’s performance in those same categories. But what does average performance really give you in a fantasy league? Well, it depends. In some leagues, likely deeper ones, average performance in home runs may be enough to secure you upper-tier roto points. However, in most leagues, only the best 175 or so hitters will ever be used in the league, and so an MLB-average home run hitter may be nearly worthless in fantasy.

Here is the table of the top-10 hitters from my previous article based on their combined Z-scores:

Player Season zHR zSB zRBI zRun zAvg zTotal
Mike Trout 2012 1.88 4.45 1.33 3.71 1.66 13.02
Ryan Braun 2012 2.64 2.06 2.11 2.13 1.63 10.57
Miguel Cabrera 2012 2.75 -0.51 2.92 1.96 1.95 9.07
Josh Hamilton 2012 3.01 -0.17 2.93 2.09 0.74 8.61
Andrew McCutchen 2012 1.60 1.04 1.41 1.99 1.80 7.85
Edwin Encarnacion 2012 2.82 0.42 2.12 1.54 0.63 7.52
Mike Stanton 2012 3.16 -0.15 1.94 1.50 0.68 7.13
Jose Bautista 2012 3.05 -0.07 1.98 2.09 -0.14 6.92
Matt Kemp 2012 1.89 0.40 1.65 2.11 0.83 6.88
Carlos Gonzalez 2012 1.08 1.36 1.52 1.84 1.07 6.86

It is pretty clear from the table that Mike Trout was the best fantasy player last season, and you would have to be in an extreme circumstance in fantasy for context to change that fact. However, you’ll notice that as soon as you exit the top-five, the differentiation between players gets pretty small. Given their disparate production in various roto categories, it would not be hard to think of situations where you might have rather had Edwin Encarnacion last season than Andrew McCutchen, even though McCutchen provided more total value relative to an average player in each roto category.

So, to really make Z-scores useful to fantasy, I need to change their contexts. I do not want to compare performance to that of an average MLB player. I want to compare it to an average player of the roto points tier I am targeting.

A few posts ago, I linked to this set of tables of average values for each roto point tier of each category in an ESPN standard league. I can use those benchmarks as a replacement for the means in my Z-score calculations.

With that small adjustment, here are a few different total Z-score top-10s based on different roto point targets. First, here is one for all 10s:

Player Season Points zHR zSB zRBI zRun zAvg zTotal
Mike Trout 2012 10 1.34 3.96 0.79 3.13 0.90 10.11
Ryan Braun 2012 10 2.10 1.57 1.57 1.55 0.81 7.61
Miguel Cabrera 2012 10 2.21 -1.00 2.39 1.38 1.10 6.07
Josh Hamilton 2012 10 2.47 -0.66 2.40 1.51 -0.02 5.70
Andrew McCutchen 2012 10 1.06 0.55 0.88 1.41 0.99 4.89
Edwin Encarnacion 2012 10 2.28 -0.08 1.58 0.96 -0.11 4.63
Mike Stanton 2012 10 2.63 -0.64 1.40 0.91 0.07 4.37
Jose Bautista 2012 10 2.51 -0.56 1.45 1.51 -0.60 4.32
Matt Kemp 2012 10 1.36 -0.09 1.11 1.53 0.28 4.18
Carlos Gonzalez 2012 10 0.54 0.86 0.99 1.26 0.36 4.01

Here is one for all eights:

Player Season Points zHR zSB zRBI zRun zAvg zTotal
Mike Trout 2012 8 1.52 4.17 0.95 3.30 1.06 11.02
Ryan Braun 2012 8 2.28 1.78 1.74 1.73 0.99 8.52
Miguel Cabrera 2012 8 2.39 -0.79 2.55 1.56 1.28 6.99
Josh Hamilton 2012 8 2.65 -0.45 2.56 1.69 0.14 6.60
Andrew McCutchen 2012 8 1.24 0.76 1.04 1.59 1.16 5.80
Edwin Encarnacion 2012 8 2.47 0.14 1.74 1.14 0.04 5.53
Mike Stanton 2012 8 2.81 -0.43 1.57 1.09 0.20 5.24
Jose Bautista 2012 8 2.70 -0.34 1.61 1.69 -0.50 5.16
Matt Kemp 2012 8 1.54 0.12 1.28 1.71 0.39 5.04
Carlos Gonzalez 2012 8 0.72 1.08 1.15 1.44 0.51 4.90

And here is one for all fives:

Player Season Points zHR zSB zRBI zRun zAvg zTotal
Mike Trout 2012 5 1.69 4.37 1.12 3.49 1.20 11.86
Ryan Braun 2012 5 2.45 1.98 1.90 1.91 1.13 9.37
Miguel Cabrera 2012 5 2.56 -0.60 2.72 1.74 1.43 7.85
Josh Hamilton 2012 5 2.82 -0.26 2.73 1.87 0.28 7.44
Andrew McCutchen 2012 5 1.41 0.96 1.21 1.77 1.31 6.65
Edwin Encarnacion 2012 5 2.63 0.33 1.91 1.32 0.18 6.37
Mike Stanton 2012 5 2.98 -0.23 1.73 1.28 0.31 6.06
Jose Bautista 2012 5 2.87 -0.15 1.78 1.87 -0.42 5.94
Matt Kemp 2012 5 1.71 0.31 1.44 1.89 0.49 5.84
Carlos Gonzalez 2012 5 0.89 1.27 1.31 1.62 0.64 5.73

You’ll notice that the order of the top-10 never changes, which is what we should expect. Because each roto category is equally valuable and because we maintained a 1:1 ratio of each category, one player never actually passes another. However, the relative value of players does change. That is because the gaps between point tiers are not equal for every roto category, and those differences help and hurt some players more than others depending on the distribution of their production.

To illustrate, consider the relative value of Mike Trout and Miguel Cabrera. In the original table of Z-score values based on the MLB league averages, Trout was worth 44 percent more than Cabrera ((13.02 – 9.07) / 9.07). With a target of five roto points in all categories, Trout was worth 51 percent more than Cabrera. With a target of eight roto points in all categories, Trout was worth 57 percent more. And with a target of 10 roto points in all categories, Trout was worth 66 percent more than Cabrera. The more extreme the target, the more valuable Trout becomes relative to Cabrera because of the improvements we are making in our benchmark player.

So which is the correct target to use? Before the season and without a specific strategy in mind, the answer is probably the all-eight point table. Prior to the 2012 season, Matthew Berry revealed that the average winner of their standard leagues from 2008-2010 scored 80 combined roto points, which is an average of eight points per category. However, that answer will be different for every team, a topic I will discuss next week.

Print Friendly
 Share on Facebook0Tweet about this on Twitter0Share on Google+0Share on Reddit0Email this to someone
« Previous: The daily grind: 5-22-13
Next: Visualization: Handedness through history »

Comments

  1. Hunter said...

    What is the mean and standard deviation for the SB category?  Any way I could see that info?

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>

Current ye@r *