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I'm VERY bad at math - but am trying to find the right statistical technique to use to build a cheat sheet for my fantasy hockey draft. Here's my proposed approach - but I'm hoping for feedback to make sure this is legitimate:

1)I have purchased player value projections for the 2018/2019 season from two different sources, both of which use a "secret sauce" to generate a player "value score" based on the specific settings of my league.

2) However, each source uses a totally different scale for their scores. Since I assume each source has it's own strengths and weaknesses, I want to try to average the two value scores for any given player.

3) I've started by using the Standardize function in excel to generate a z-score value for each player, from each source.

4)Can I now simply average the two z-scores for each player to get an "average value score" for the player, given my two sources? Or am I approaching this the wrong way?

Again, sorry for my innumeracy - hoping the great minds here can help me figure this out. Thanks all,

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  • $\begingroup$ Another approach I considered was converting each value to a percentile rank - but that gives me a rank, rather than an absolute value. $\endgroup$
    – dylan
    Commented Sep 7, 2018 at 2:17

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Welcome to CV! No apologies necessary—I don't think you're as bad at math as you say you are.

I think this is a good approach. What I would do is z-score (standardize) each of the modeled scores you downloaded. Then, I would average these two together. Lastly, I would rank the players from highest value to lowest. This gives you a sorting of the best to worst players (according to an average of both scoring systems you downloaded).

This is better than percentile/rank, in my opinion, because you have more information on the differences between "tiers" of players. Imagine there are 5 elite fantasy players in the league and then a huge drop-off to the next 20, then another drop-off. The average of two standardized variables will show the drop-off, while the ranking will hide it.

You can do a simple average, which weights the scores equally. Let's say, for some reason, you think that one source is twice as good as the other source. You could then do a weighted average, where the one source is weighted twice as much. But if I were you, I would do exactly as you proposed: z-score the two variables, then average them together.

I'm a huge basketball fan, and I really enjoyed the book Basketball on Paper by Dean Oliver. In the third chapter of that book, he talks at length about how useful z-scores can be to compare across different scales. In his context, he is talking about how we can compare a player in the 60s to a player in the 90s. He suggests z-scoring within that given year to see how good a player was relative to an average player at the time in which they were playing.

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  • $\begingroup$ Interesting. Thanks for the validation - glad this method seems to work! That's also a really interesting application; one that'd be useful to compare the NHL era where, say , Gretzky scored 200 points vs. today's highest performers who are scoring around 100. Question - have you used the VONA method at all? The idea is to compare the value of your potential draft pick to the next available player in the same position. Any opinions on trying to use that in a real draft? Thanks again for your input! $\endgroup$
    – dylan
    Commented Sep 7, 2018 at 15:52

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