Currently I am in the process of conducting a mathematical analysis of the Elthos 'One Die System'.

Out of curiosity, how many of the game designer folks here have done a mathematical analysis of their game rules?  If you did, how did you go about it? What aspects did you analyze? So far my analysis includes:

- Character Class Levels Advancement Rates
- Combat between individuals at various levels, requisites, equipment
- Combat Magic
- Wealth requirements per level and class to obtain standard equipment

I'm looking to add to this and would like to get any additional ideas, or refine the existing analysis. If you have any thoughts on what would make for good analyses I'd be much obliged. Thanks.

Hi!
  One thing I do for combat oriented games is:
Offensive DPS per point of relevant stat
Defensive DPS reduction per point of relevant stat

  Usually, I try and have a design goal in mind before I crunch these numbers, so it doesn't lead to endless tinkering

  Also, for skill/hit rolls, I look at extreme circumstances. Like Highest attack roll versus lowest defense roll, etc. Just trying to cull out anomalies that you don't normally see by using average/nominal average values in the early design phases.

  Again, I try to have a design goal in mind before I crunch these number too. In other words, I try and figure out how it SHOULD work, before I crunch them. Then I look at the results through that lens. Like Should a high level fighter ALWAYS hit a low level farmer? Should they EVER miss, etc.

  Its good to know that I am not the only one who yuses Excel to design their games, lol

  I think I still have the sheets I used to design LoL, if you want to see them, let me know.

Quote from: dindenver;226364Hi!
  One thing I do for combat oriented games is:
Offensive DPS per point of relevant stat
Defensive DPS reduction per point of relevant stat

  Usually, I try and have a design goal in mind before I crunch these numbers, so it doesn't lead to endless tinkering

  Also, for skill/hit rolls, I look at extreme circumstances. Like Highest attack roll versus lowest defense roll, etc. Just trying to cull out anomalies that you don't normally see by using average/nominal average values in the early design phases.

  Again, I try to have a design goal in mind before I crunch these number too. In other words, I try and figure out how it SHOULD work, before I crunch them. Then I look at the results through that lens. Like Should a high level fighter ALWAYS hit a low level farmer? Should they EVER miss, etc.

  Its good to know that I am not the only one who yuses Excel to design their games, lol

  I think I still have the sheets I used to design LoL, if you want to see them, let me know.

Heh... Yeah excel is handy if you know how to use it.  Some people find it frustrating and wind up spending waaaaayyyyy too much time tinkering with excel's features than actually analyzing, but that's life.   For me it's very handy.  

I like your analysis idea in terms of spotting anomalies.  And yes, I totally agree.  You should have a "It should come out like this" concept before you design the rules.  The analysis should either confirm your rules conform to your design specifications, or provide you with the information you need to modify the design so that it does.

For example, I found out via the analysis that adding to armor class per level sounded like a good idea, but resulted in combats that would take too long (average number of melees for 1st level vs 1st level went from 8 to 18).   Therefore I curtailed that rule and now add 1 AC per every six Character Levels.   The analysis allowed me to accurately view the results quickly and easily.

Sure I'd be delighted to see the excel you put together if it's still around.  Thanks.

Quote from: VBWyrde;226347Out of curiosity, how many of the game designer folks here have done a mathematical analysis of their game rules?  If you did, how did you go about it? What aspects did you analyze?

Most of the effort went into combat (all types), at the defined baseline and out to the edges. Including and balancing equipment was the main influence here.

Also looked at advancement but that part was very simple.

I have one rule for all math analysis: The crunch must prove the fluff.   AKA, if my setting says that you should dodge for cover, then the combat math must prove that cover = great defense and no cover = lotsa pain.  

Whatever the fluff says, must come through in the game mechanics.  There must be near-zero disconnect.

OK, digging around I found some stuff:
Here is one I did for a friend who was designing a supers game:
He already had a list of powers, I was trying to show him a way he could assign costs based on more objective analysis:
http://spreadsheets.google.com/ccc?key=pJsDLey3h-2nUoRkgpnTQew&hl=en

Here is a sheet I made for a D20 Steam Punk hack I was trying:
http://spreadsheets.google.com/ccc?key=pJsDLey3h-2kdJmxnfft6UA&hl=en

For my new Supers game:
http://spreadsheets.google.com/ccc?key=pJsDLey3h-2kt7MwtKtIOcQ&hl=en

A worksheet I did to determine Faction aligbnments
http://spreadsheets.google.com/ccc?key=pJsDLey3h-2limhqi2ac4MQ&hl=en

Here is one tab of the combat modelkling, Googledocs is givng me fits, I'll post more when I get it up there, k?
http://spreadsheets.google.com/ccc?key=pJsDLey3h-2lEaav_DiksHw&hl=en

OK,
  The last sheet has the widest analysis of my Legends of Lanasia game. It looks at a lot of stuff from pretty much every angle.
  Some of the terminology might only make aense to me so feel free to ask if anything doesn't make total sense...

I have never done deep math analysis for anything I design.

I am more of an old-school deep playtest fan.

That said, I have modified my playtest methodologies many times, because some of the ways I playtest, through class vs. class (for balancing classes against each other) has shown some holes from time to time.

Still, I personally feel playtesting is much more valuable than math analysis. I learn more about my games by watching and listening player behavior than anything else.

Chuck

Quote from: dindenver;226517OK,
  The last sheet has the widest analysis of my Legends of Lanasia game. It looks at a lot of stuff from pretty much every angle.
  Some of the terminology might only make aense to me so feel free to ask if anything doesn't make total sense...

Thanks for posting that.  I took a look but yes, it was not so easy to figure out what is going on with the spreadsheet.   Could you shed a little light on it.  What I'm interested in is this:  What does the spreadsheet show you about your system's mathematics in terms of things like Game Balance, Life Expectancy, or whatever.   I guess the right way to put my question is this:  What questions does your Spreadsheet answer and how does it do so?   You don't have to go into much detail, but a little guidance would be helpful.  Thanks again.

Quote from: RPGObjects_chuck;226557I have never done deep math analysis for anything I design.

I am more of an old-school deep playtest fan.

That said, I have modified my playtest methodologies many times, because some of the ways I playtest, through class vs. class (for balancing classes against each other) has shown some holes from time to time.

Still, I personally feel playtesting is much more valuable than math analysis. I learn more about my games by watching and listening player behavior than anything else.

Chuck

Thanks Chuck.   I agree Play Testing is a very good idea.  Essential in fact.  However, I think having an understanding of the mathematics of the system is important.  For example, Play Testing my rules may or may not have revealed that it was the adding of a +1 Armor Class per Level that was making combat melees too long on average.   I might have noticed that combat seemed to be taking a bit long in some cases, but I doubt that I would have really understood why without a mathematical analysis of the game.   Once I did that it was immediately obvious which variable was causing the melees to take too long.   Anyway, though, its no big deal if you do like to do the analysis or not.   Many games like D&D have been fun for 30 years and I can pretty much guarantee that Gygax & co did not mathematically model the rules before publishing.   So you're totally right that it's not necessary for a successful game.  But then again, there are certain flaws in the D&D system that had they been modeled would have come to light and been easier for TSR to deal with early on.   ON the other hand - D&D rules by adding new charts and new systems for each detail of the game makes such an analysis highly problematic.   I would not want to be tasked with doing the analysis for D&D any edition.  However, for my game system, which has a vastly simplified, generic and modular design the analysis is feasable.  So therefore I'm happy to do it.   ... but yes - Play Testing is an absolute requirement.

I did statisical analysis the old fashioned way.    I made some archetypal characters. I aged them to various benchmarks of experience.  

I then determined their  Initiative Attack and Defend percentages, damage done (for all characters).

For power uses, I determined their benchmarks for "casting" some common spell effects.

For skill specialists, I determined their percentages for performing some classic gamer actions.

I first saw to it that the chances were acceptable at the various degrees of experience.  I saw what could of been tweaked in the character design (i.e. was the character designed well to do the job) and what was the mechanics would generate.

I ended up doing three versions of each benchmark character, one done stupidly, one done by an average player, and one done by the sharpest rules lawyer.  I then saw the range of what would be possible for characters of the same experience level.
This ended up being important. This helped me tighten up the rules, finding flaws and misconceptions that players would have (ohhh, I want First Aid, not professional skill doctor, ....) . It also gave me what the general range of success would be from stupid character gen to smart character gen.

I saw how the percentage chance of success changed over time for all of those.  I did do a rough graph, but I could hold the percentages in my head pretty well.

I basically tweaked the rules a little (and came down on the rule abuses) and smoothed out my experience progression until these numbers came out to something that I would game and be happy with as a player and the players I knew well.

Hi!
  OK, looks like the formulas got borked when I converted it to googleedocs, sorry.

  Basically, I made a sheet for the following:
Relative value of each combat stat in practice (e.g., if my accuracy goes up 1, my DPS goes up X amount, what about DMG stat? etc.)
Then used those numbers to balance the weapons
Then used those numbers to balance the armor

I also used math (binary math actually) to setup a political alignment system so that different factions hated each other fro real reasons. Columns were New vs Old, Static vs Nomadic, etc.

  I also have used the columns and other functions to try and balance how many nations prefer which skills, etc.

  And of course playtesting is important. I don't think anyone in their right mind would say otherwise.
  But, the point of this analysis is to get a lot of the bugs squashed before you subject your playtesters to it.
  For instance, I playtested 1-3 different campaigns per week for a year when I was writing LoL...

  Hope that helps...