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I am looking to simulate the results for MLB hitters in terms of their FanDuel and DraftKings fantasy scores. I'm wondering if this is doable given only the following information per player:

Mean
Median
Standard Deviation

For normally distributed outcomes, this would be fairly easy. The issue is that I know these values skew right. Because of how the scoring works -- and how events based a baseball game is -- there are a lot of 0's and low scores.

As an example, here are the statistics for Trea Turner's last 5 seasons of games in FanDuel scoring. I included some additional data (that I will not have for other players):

mean    12.5
stdev   10.7
median  9.5

q1      3.0
q3      18.7
max     64.6
min     0.0
skew    0.85

If I wanted to simulate a game from Turner using ONLY the mean, median, and standard deviation -- is this doable? Ideally, I would do this in Google Sheets, but would be curious on other solutions.

EDIT -- SOLUTION

It looks like a good solution here is to use a Gamma distribution:

alpha = mean^2/stdev^2
beta = stdev^2/mean

GAMMAINV(rand(),alpha,beta)

This yields very similar summary numbers and skew value.

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  • $\begingroup$ There's not enough information here to suggest a solution, nor to evaluate the merits of any proposed solution. An effective approach proceeds by studying how the standard deviations vary with the means. For instance, when the SDs tend to be proportional to the means, that suggests using a lognormal distribution. A spread vs. level plot is a simple and effective way to perform that evaluation. $\endgroup$
    – whuber ♦
    Commented Feb 28, 2023 at 15:10

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Basically kluged this together, but it seems to work okay when comparing it to last season's data. I was using last season's data to make the avg, med, stdv. Just kind of started with the regular values and modified weights and things until it looked right. Quick and dirty until you or anyone else on here gets to the elegant solution.

MAX(0,ROUND(NORM.INV((RAND()0.95+RAND()0.05),RANDBETWEEN(avg0.55,avg0.9)+avg-med,stdv+(avg-med)),0)))

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  • $\begingroup$ This looks like a truncated Normal. It would be unlikely to be a good fit to actual data. $\endgroup$
    – whuber ♦
    Commented Feb 28, 2023 at 15:10

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