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?