Creating Your Rankings? Start with Z-Scores


One of the greatest fantasy tutorials I’ve ever received came in Jeff Zimmerman and Tanner Bell’s, The Process. In the book, there is a breakdown of two very important valuation systems; standing gains points and z-scores. Our auction calculator, for example, is built around z-scores. For a further dive into both, I highly suggest purchasing a copy of the book. In general, z-scores help us understand how good player A is compared to the rest of the draftable player pool and it can be used as a great jumping-off point for your rankings. I use the word “rankings” because they are not projections and that’s the beauty in z-scores. You are not trying to outsmart projections. Instead, you are using a projection system of your choice to create your rankings. In this post, I’ll be creating z-scores for shortstops in 2022 using Steamer projections.

A z-score is a simple mathematical calculation:

z = (x – μ) / σ

μ = sample mean

x = observation

σ = standard deviation of the sample

In our case, we’re calculating a z-score for each of the relevant 5 x 5 counting stats and I’ll also do it for AB and BB projections since Steamer does predict ABs. In The Process, Zimmerman and Bell go into detail on how to calculate z-scores for rate statistics and I’ll leave you with that. In this post, I’ll just be looking at the following:

R, RBI, SB, HR, PA, and BB.

The first step is to find a player pool of draftable players. I’ll keep it really simple and pretend that I am in a 12-team league and each team can only roster one SS. Obviously, that would be a weird league and you’ll have to adjust those numbers accordingly. For example, if you’re in a 12-team league and your roster has a slot for SS and a slot for a MI, then maybe you want to open the pool up to something like 20 shortstops, knowing that some second basemen will fill in that MI spot. Onward!

Looking at the top 12 shortstops sorted by Steamer WAR (sort by whatever you want), I get a list that looks like this:

SS Steamer Projections

*Sorted by WAR

 

Maybe you don’t like the fact that Oneil Cruz has entered the top 12. Another advantage of this system is that you can move players above or below the cut-off line. Once again, I initially sorted Steamer’s rankings on projected WAR. You can experiment with that. Another viable option would be to sort by projected ABs and exclude them from the z-score calculation. That’s what I like about this system, you get to tinker without having to project.

Now, let’s calculate z-scores. Going back to our equation from above, we can fill it in as such:

RBI_z = (Player RBI Projection – Player Pool RBI Average) / Player Pool RBI Standard Deviation

Bo Bichette looks like this:

RBI_z = (96 – 86.9) / 9.90 = 0.96

Once we do this calculation for each counting stat (which should be done in excel or python or whatever environment can do it with a few clicks), we get an output like this:

Top 12 SS Z-Scores

Name H_Z R_Z RBI_Z SB_Z HR_Z PA_Z BB_Z $
Fernando Tatis Jr. 0.61 1.94 2.12 1.58 2.86 0.68 1.37 $11.16
Trea Turner 1.39 1.09 -0.41 1.71 -0.33 0.74 -0.47 $3.72
Bo Bichette 1.39 0.67 0.96 0.56 0.13 0.53 -1.23 $3.01
Marcus Semien 0.00 0.52 -0.31 -0.33 0.43 0.74 0.78 $1.83
Francisco Lindor -0.42 0.10 0.33 -0.07 0.43 0.51 0.45 $1.33
Trevor Story -0.73 -0.25 0.11 0.82 -0.03 0.32 0.03 $0.27
Xander Bogaerts 0.18 -0.25 0.54 -0.96 -0.33 0.22 0.70 $0.10
Carlos Correa -0.36 -0.39 0.22 -1.60 0.13 -0.24 0.95 -$1.29
Gleyber Torres -0.36 -0.54 -0.41 0.05 -0.63 -0.06 0.45 -$1.50
Wander Franco 0.91 -0.25 -0.31 -0.46 -1.24 0.25 -0.81 -$1.91
Corey Seager -0.18 -0.25 -0.52 -1.35 -0.33 -0.65 0.11 -$3.17
Oneil Cruz -2.42 -2.37 -2.31 0.05 -1.09 -3.03 -2.31 -$13.48

*Based on Steamer Projections

But, we’re not done! We need to adjust these scores to show that these are all players worth drafting and above replacement value. This is easy enough as we can just look at the last player on the list and mark him as a replacement-level player. We then subtract all of that players’ scores, in this case, Oneil Cruz, in effect zeroing his value out and increasing the value of all the other players to get a final product along with a dollar value that is the sum of all the z-scores:

Top 12 SS Z-Scores – Above Replacement

Name H_Z R_Z RBI_Z SB_Z HR_Z PA_Z BB_Z $
Fernando Tatis Jr. 3.03 4.31 4.43 1.53 3.95 3.71 3.68 $24.64
Trea Turner 3.81 3.46 1.90 1.66 0.76 3.77 1.84 $17.20
Bo Bichette 3.81 3.04 3.27 0.51 1.22 3.56 1.08 $16.49
Marcus Semien 2.42 2.89 2.00 -0.38 1.52 3.77 3.09 $15.31
Francisco Lindor 2.00 2.47 2.64 -0.12 1.52 3.54 2.76 $14.81
Trevor Story 1.69 2.12 2.42 0.77 1.06 3.35 2.34 $13.75
Xander Bogaerts 2.60 2.12 2.85 -1.01 0.76 3.25 3.01 $13.58
Carlos Correa 2.06 1.98 2.53 -1.65 1.22 2.79 3.26 $12.19
Gleyber Torres 2.06 1.83 1.90 0.00 0.46 2.97 2.76 $11.98
Wander Franco 3.33 2.12 2.00 -0.51 -0.15 3.28 1.50 $11.57
Corey Seager 2.24 2.12 1.79 -1.40 0.76 2.38 2.42 $10.31
Oneil Cruz 0.00 0.00 0.00 0.00 0.00 0.00 0.00 $0.00

*Based on Steamer Projections

 

It is once again evermore important to point out that this idea has been around for a long time, it has its downsides and other writers have detailed its uses much, much better than I have done here. It should also be pointed out that these dollar values should not be considered auction values. It would be pretty sweet to get Trea Turner for $17 anywhere. No, these are a jumping-off point for those who like to tinker without thinking they are going to better an established projection system. Do you have a measurement, like barrel rate or O-contact% that you would like to incorporate? Go right ahead, toss in an extra $0.25 for every shortstop above in the top 60 percentiles in whatever stat you like. Again, it’s a jumping-off point. For those who are more inclined to tinker than others, buy Jeff’s book and create your own process that keeps you going through the winter months of cold, baseball-less nights. Reading is good for the brain.



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