Statistics Question

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Ikoma
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Statistics Question

Postby Ikoma » Sat Apr 25, 2020 12:56 pm

OK... question for all the other big brains out there. This is a math / statistics questions based off a game. Just a few explanatory details before I get to the question...

Basically, I want to be able to simulate a season of Blood Bowl. Take a submit rookie roster, roll a few dice, and a have a realistic roster of what a team would look like after one season. Each player has the chance during the season to earn Star Player Points based on five actions (TDs, Passes, Interceptions, Casualties, & MVPs). Each player also runs the risk of being hurt.

So I want to be able to calculate some kind of easy dice rolls that would simulate a bell curve of possible results based on a data set. The data I am pulling comes from the Goblin Spy: (http://www.mordrek.com/goblinSpy/web/goblinSpy.html). It's a web site that can scrape all kinds of data from the Blood Bowl 2 computer game (on PC, Xbox, & PS4). I can scape insane amounts of data. Basically, I know all the players, their base stats and skills, and then have access to a hug pile of actual SPPs earned over actual seasons worth of games against actual other coaches. I can generate an average, minimum, & maximum result for each of the five actions. I can also see the likelihood of a player competing in all games per season (and thus the odds of getting hurt).

What I would like to be able to do is create a dice roll based off a average, max, min data set that assumes a normal bell curve distribution. It would be cool if that dice roll could be modified by player stats. (i.e. a 4AG player will score more TDs, make more passes & interceptions). In an absolutely perfect world, I would create a dice roll for all linemen (as an example) that is modified by the stats (Move, Agility, Strength, Armor) to output the random results of SPPs earned in a season. In a less perfect, but still awesome, world, I would have a different dice roll for each team/position that would already have the stats/skills baked due to being based on actual data.

Anyway, I hope that makes sense. Any suggestions? Questions? Concerns about my sanity? :D
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Ikoma
Actually Slew the Baron
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Re: Statistics Question

Postby Ikoma » Sat Apr 25, 2020 1:12 pm

Some digging tells me a useful rule of thumb can calculate the standard deviation of a dataset by taking (MAX-MIN)/4. Then a bell curve has 68% of all data within 1 SD of the mean, 95% of all data within 2 SD of the mean, 99% of all data within 3 SD of the mean. So based on my AVE, MAX, MIN data, I can generate all the 'break' points.

I'm just not sure how to turn all that info into a 2d4-2 (or whatever it would be).
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Ikoma
Actually Slew the Baron
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Re: Statistics Question

Postby Ikoma » Thu Apr 30, 2020 1:37 pm

So the big problem I am running into is that the numbers are just pretty small. A lineman might have a max number of 3 TDs, a min of 0 TDs, and an average of 0.5 TDs per season. Such small numbers are pretty much pushing me to Fudge/Fate dice. Each dice can then be a small granular nudge of +/- 1.

Still 2dF+1 give me a tiny curve from -1, 0, 1, 2, 3. Obviously any dice roll would have a minimum result of 0. But that roll is still going to overestimate the possibility of a 2 or 3 TD season. That might not be the end of the world though. Gotta think that through.
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