"What about the Math Skills of the Game Designer himself?" Topic

All,

Without a doubt, I agree that the wargamer himself should never be required to resolved any major mathematical computations needed to play the game. The game design should make that facet of play either invisible or at least transparent to him.

However, that statement above does tend to beg the subliminal question, 'What about the math skills of the Game Designer himself', doesn't it?. Because when all else is said and done, all wargame designs are essentially 'mathematical models of combat' in the end.

Accepting that last statement as gospel, then could this be the genesis of an otherwise unknown wargame design paradox?

The paradox being that on one hand, wargame designers typically do not want to be pinned down to explain the direct relationship between their design features and its historical counterpart (i.e. they prefer to deal with those issues philosophically). But, on the other hand, the math that they all have to use to implement these design features, forces them to nail it all down with far greater precision (i.e. a+b=c) and with far less inherent flexibility.

What do you think about designer math skills and this paradox?

Regards,

James

I wrote DEADLY WATERS, recently released by Clash of Arms gamers.
The Math involved was intensive and it was given first priority. Over the years I've seen many rule sets where one wishes the writer had at least used a calculator occasionally.
Therefore I was determined to get it right in all ways possible. The factors that make up a set of rules can be quite boring to the people who are not involved, but I was able to find a couple of people willing to help and check the calculations. I'm pleased to be able to report that they found few errors.

But you are quite right that the math does need to be done with great precision. But I worked with a system that required me to not only use design features with precision, but to also retain a lot of flexibility. In the end I believe it has worked and players certainly seem pleased. But it wasn't easy and I am tempted to suggest that many who want to write rules, would not be prepared to go to the lengths that are really required in order to get it right. I dont blame them, its not easy and its hardly exciting work, but I do believe it to be essential. So if they cant do it, the rules they write will always have some big flaws.

Rocky Russo's approach is intensely mathematical: especially the airplane "envelope" dictating performance. The missile tables in our ancmed rules have a great deal of math behind their creation. But the actual game is almost devoid of any math required during play. If it wasn't I could not bring myself to play it. Our air combat game uses quite a bit more math, but I got used to it (put up with it) because I couldn't see any other way of playing the detail that I wanted….

Interesting question.

I've written a lot of rules over three decades, and will write more. People seem to like them, and nobody seems inclined to drive a bus through the arithmetical structure of the rules. Perhaps they are too polite. Perhaps it's because I deliberately write to be entertaining and offer a 'beer and pretzels' level of detail in the mechanics.

I'm not a mathematics person. I'm a historian by education and a novelist by avocation. I accept that we are using the interraction of numbers to recreate the actions of human beings in conflict, but I see this as a necessary evil required to make the thing work at all. I don't want to cater to accountants (or rules lawyers for that matter). Given a choice, I'll keep the mathiness dead simple.

History is very weak on mathiness as well. The Old Guard felt they were invincible in an intangible way, not in a "We get a +4 in melee, +5 morale tests" manner. At Waterloo they either met an opponent that had much higher dice modifiers than expected OR they rolled very poorly. It's unclear. We don't have a record of the die rolls made that day. Napoleon may have said something about spending too many points on selecting Ney, though.

So, essentially the mathematics needed to make the game work at all carries a limited relationship to the historical narrative. It's a bit like my seeking the secret of an excellent dining experience in the mechanics of stove operation.

So, bottom line to me is that the writer of rules has to have sufficient knowledge of his topic to know what results are typical, possible, possible but unlikely, and "Ain't happening!"

I studied the Battle of the Atlantic for over 50 years before people persuaded me I should put my rules out for others to use. So I developed a math program based on the very things you have mentioned. But it was too often uneventful. So I had to tweak it somewhat to allow that if is after all a game and therefore players dont expect to have an event free convoy run. They want something to happen.

Therefore in the end I changed the modelling from the typical convoy, to being modeled on those during which something did happen. That seems to have worked with the players.

But I did find that to get the real feeling, one had to add campaign and resolution together. It was only in that way that I could achieve what I felt was a reasonable representation of a convoy run.

That is not possible with some rules because they are reacting to tabletop event driven situations, after which the resolution cuts in. I did it with the campaign movement creating the situations, that the rules then resolve. I feel that it gave me an advantage over many rule writers, but accept it is not suited to all types of wargaming.

Hi

As Doug implies, I always start with a mathmatical model…and then someone like him reigns me in when I get to wrapped up in it.

Anyone who has read my posts on guns or bow should have realized this. I really dislike "well, lets call it a plus four because I feel…" stuff. Not something I do.

Most of the games I have played, as numbers "run" in my head constantly, have some point in the system where it is clearly a WAG or just silly. While I consider Craig Taylor and Steve Peek friends and we have had good times over the years. When Air Force came out, they had some planes pulling 22 "gs" in a maneuver. Gave me a headache!

In another thread Gweirda gives me grief, as does Tommyatkins sometimes over this. With the hardware, first I do the math.

I love reading and thinking about other approaches. I love, as most people do, Sam Mustapha's stuff. With his rules, however, the way they work is predicated on evaluating historical commanders. And I am clueless on how that works in his mind.

So, in rules I deal with, there are no such things as commander ratings. You face MY Tercios, not some guess on the putative talent of some long dead commander.

Different strokes.

Rocky

What Howard (Mexican Jack) said.

When I was writing rules for the Alamo, it was nothing but trial and error that produced a formula for resolving Mexican ladder assaults. Match (# of Texians on the wall section x 20) plus (D6 x 10)random factor, against 100 for Mexican column doing the assault, + (10 x # of ladders against wall) + (D6 x 10) random factor. High total wins. For casualties, divide loser's total by 20 = figures lost; divide winner's total by 30 = figures lost.

How'd I come up with that? No idea. But we've played dozens of games. with 100+ ladder assaults, and not gotten an unreasonable outcome. (The Texians can usually throw back one assault, but will take enough casualties that the second, or at worst for the Mexicans the third assault will get over.

By the way, I scored, 40 years ago, high 700's on the math part of the SAT, and have an above average intuition for numbers. Not saying math skills aren't relevant, but in my case not consciously, at least.

I've done extensive math when designing a game, and I've done "what feels right" for games as well. It just depends on the game which method works fine.
For example, you can't really convince me that anyone sat down and calculated all the possible mathematical permutations for the combat systems in Risk, Axis & Allies, D&D, Ogre, and dozens of other extremely popular wargames— nor for that matter, popular tabletop games like DBA. I suspect all were products of "what feels right" and "trial by error," than actual calculation. (Just try determining the odds system for Risk alone!)

I'm not saying that math skill isn't a help— it is! But a good game can be developed without really delving into probability calculations.

"Because when all else is said and done, all wargame designs are essentially 'mathematical models of combat' in the end. "

Nope. They are a representation of combat that uses math to resolve the battles but most of the time is far from a "mathematical model."

Nope. They are a mathematical model. Unless, of course, the outcomes are irrelevant. However fine or coarse the model, it is one, nonetheless, and it may only model certain aspects (e.g., a combat results table that has the possible outcomes weighted in order of probability).

A model is NOT a simulation, although it can be. That it is tempered by experience, trial and error, and gut feel is what makes it an interesting "game" . . . if it is done right.

I expect many good games have been developed without the author exploring far beyond getting reasonable results in a small number of trials – with "reasonably" hopefully sustained by some research into the period.

Still, a game designer must be able to reason numerically if not mathematically. That does not particularly mean he needs any tools not found in a high school math class -- but he must be able to use them.

This is especially true if the designer is not just going to recombine old ideas (a technique I do not intend to put down, it has produced some great games) but try to move on to develop a brand new mechanic.

Also, the more technology influences the period the more the math matters. Getting reasonable results for a game involving men from the same culture with identical muskets is hard enough. Putting those same men in tanks and including all the technical factors of the vehicle, the doctrinal differences of modern armies, the hundreds of different types of weapon to be found on say a WWII and still all the complexities of how men act in combat, and you start to really need a grip on the mathematical relationships if you are going to make any progress over what we already have on our shelves.

Aside from pure math, the designer should do extra work (if possible) so the players have less calculations during the game.

My particular preference is for all die rolls to be biased the same way – either all high rolls are good or all low rolls are good. You don't have to check a chart to know if your roll was good or bad.

So for all high rolls to be good, that requires better morale troops have a lower number – the easier to equal or better it. It's a little more work for the designer than saying guards are 6, miltia are 3, etc.

It bugs me to roll low combat dice, missing everything and then roll high when checking morale and routing.

"If you are gaming a tank battle of Shermans vs Pzkw IVs, how far into the weeds do you need to go? "

Now how many WWII games are going to represent one kind of tank for each side, and nothing else? And who is going to buy it if they do?

Lentulus,

Several years back the Rand Corporation did a theoretical study of tank vrs. tank combat in Post-war Western Europe. They used data from WWII as the basis-it seemed to indicate that the most accurate tool to determine who won was to flip a coin. That's math for you!

A designer had better have a good grasp of math, both functionally and intuitively (though tread carefully there!) BUT a wargame is NOT a mathematical simulation construct-and the farther back you go in history the less true that statement becomes-if for no other reason than a total lack of empirical data. Clausewitz had it right-it's most like a game of cards (with an occasional coin-flip)!

Most of all, miniature wargames are simple entertainments based on history and little more. Some may be more entertaining than others, but none are more realistic than others. Some may illustrate certain factors in more subtle ways, but none are by any stretch of the imagination a mathematical simulation. That's a term that supposedly makes playing with toy soldiers more acceptable for adults whose bootlaces are tied too tight.

I've seen a couple cases where the math skills of the designer effectively blinded him to how complex the game was to play…

There are, on the flip side, more than a few cases where ignorance of statistical analysis caused a game design to be rather odd. Just in RPGs this includes Earthdawn, Alternity, at least one edition of Shadowrun, and Marc Miller's Traveller (aka T4).

Considering this for a bit, and thinking about what I said on the "Math in rules" thread, I think a better stance is probably "they should be invisible".

I should find absolutely no boners – odds should go up or down as the designer says they do, modifiers should combine in reasonable ways -- but beyond that I should have no way to tell if the designer applied every ounce of his combined PhD in operations research and engineering or tossed it all together over a few beers and decided it worked OK in play tests.

FWIW, I just noticed that the new Flames of War market Garden campaign book had a 20% reduction chart that players could use. It went like this:

2000 points = 1600
1500 points = 1200
1000 points = 800

Mexican Jack Squint wisely said:

"So, essentially the mathematics needed to make the game work at all carries a limited relationship to the historical narrative."

Very well put, MJS. When I was writing "The Sword and The Flame", I was more concerned about whether Cutter, McChesney and Ballantine would have approved of the Victoria Cross Award……..

Larry Brom

"That's math for you!"

Ah, but getting someone to pay you to do it -- that's Engineering!

And then explaining why the engineered device failed- That's PR! (AKA "Spin") PR pays better than engineering, by the way!

All,

Thanks for your perspectives on this question.

For the most part, I think it might surprize quite of few of you to know that most mathematicians today agree that mathematics is "the science of patterns".

What the mathematician does is examine abstract patterns, numerical patterns, patterns of shape, patterns of motion and patterns of behavior.

Those patterns can be either real or imagined, visual or mental, static or dynamic, qualitative or quantitative, purely utiliterian or simply recreational.

Now with these comments in mind, who of you out there could reasonably argue against the notion that an increased knowledge of patterns wouldn't be beneficial in defining and developing the combat and behaviorial patterns needed in our wargames?

Regards,

James

Anyone who designs a game involving die rolls that go beyond a simple 'roll a D6 and a 4+ is hit' should at least have knowledge of basic probability theory.

E.g. in a recent game I had a rule for resolving close combat: both figures roll a D6, if the difference is 2 or more, highest roller kills the other. Some people started to complain immediately. 'It's almost impossible to score a hit that way'. Mathematically inclined people realize almost immediately that a hit occuring is roughly 55% (27% for either side).

I see too many rules that state something like 'compare a roll of xDy vs. target number', without realizing what the underlying probabilities are. As a game designer, ideally, you should come up with desired probabilities (and distributions & standard variance), then design a game mechanic around that.

Knoweldge of game theory (in the mathematical sense) might help as well …

the only thing that makes my head hurt more than math is paradox theory….

i guess it would depend on the complexity of the game.

Aside from pure math, the designer should do extra work (if possible) so the players have less calculations during the game.

It is quite interesting to sit down and analyse some of the game systems on the market, where there are lots of + thins and – that. Often with a bit of patience you can establish ways in which the author could have done without some of them by tackling things in a different way. And often if they were worth worrying about in the first place.

I've seen a couple cases where the math skills of the designer effectively blinded him to how complex the game was to play…

Cough…choke…errrr..ummm…

Nah…I had better not say anything!

I'd add "English language skills" to that in some cases as well.

More cases than I care to think about, really, and some of them from shockingly educated writers.

This also ties in with the rules style. Some rules are easy to read casually, others are easy to reference. At the extremes you get books you can find NOTHING in while at the table, or rules that are a surefire insomnia cure. The proper balance is not easy to attain.

Math skills !!
These are a must during the research phase. It is also crucial during the consolidation of data phase and the conversion of the data to workable mechanics and resolution charts.

The key is also a focus on being able to comprehend abstract concepts and make them understandable. A firm foundation in geometry due to arcs of fire and angles of combat are good to know as well.

An old stopry that I tell to game designers at seminars.And true at that. One gentleman back in the late 1980s had worked out a set of colonial rules with firing at three ranges. long, short and medium. On his dice rolls to hit the target, the number needed was,
It was 1 and 2 for short range, 3 and 4 for medium; long range was 5 and 6. I was never able to convice him that his chart had a 33% chance to hit at all ranges.

JJ (aka:Terrement), Rudy & Phil,

I'm sure that you and the rest of this forum's readership recognize that 'Math finesse' would only be important to you if you were trying somehow to achieve a higher level of historical fidelity in your game design.

I doubt that it would be of much help to you if your main interest was in designing 'game engines' similar to the ones used in "Candy Land" or "Shutes & Ladders".

The point here being, that you can use mathematics to describe the real world patterns of weapon performance, situational awareness, target acquisition and YES,…even human behavior.

These patterns take the form of statistical distribution shapes (i.e. such as expoential & bell curves) that 'functionally' can transcend across all periods of warfare and time.

Which is what, "I thought wargaming was all about", taking real life patterns of warfare and applying them to a game/simulation format for personal education and enjoyment.

Regards,

James

I doubt that it would be of much help to you if your main interest was in designing 'game engines' similar to the ones used in "Candy Land" or "Shutes & Ladders".

Probability theory plays a bigger role in those games than you might think. They are masterful examples of "doing all the math ahead of time", so the players need only flip cards or tap the spinner.

IMHO there is a huge difference between 'going with the guts' and being able to achieve it with available tools. A designer lacking basic skills in probablity and perhaps combinatorics will often assume things when trying to achieve results that he wants, and quite often choose methods that give him very different results without him ever realising it.

Another issue is choosing the right tool for right job. I've seen rulesets where outcome was determined by three or four consecutive dice rolls, but granulity of the end result was such that the entire procedure could have been decided by a single dice roll and thereby reducing the complexity of the game and play time.

Hi

I always enjoyed the 70s fashion of lists of "plusses and minues" that had to be consulted for every combat on every unit…that worked and worked and basically canceled out!

One hour game turns are a joy!

Rocky

Analsim wrote: I'm sure that you and the rest of this forum's readership recognize that 'Math finesse' would only be important to you if you were trying somehow to achieve a higher level of historical fidelity in your game design.

Partly.
Even if you design a complete abstract game such as Chutes & Ladders, you might at least want to calculate what the average number (and perhaps minimal) of turns is before the game ends. Any game involving dice requires at least some application of probability theory.

If you design a combat resolution mechanism between two units of x figures each, it's useful to be able to compute what the spread of possible outcomes is. Even if your game is fantasy, and there is minimal historical analysis to be done, such computations are a basic requirement from the gameplay design point of view.

Also for designing resolution procedures of any kind (combat, morale, …). I've seen games with the following tables:

D6 Outcome
1 X
2 roll again
3 roll again
4 Y
5 Y
6 Z

That's bad design, and shows that the game designer doesn't know what the relative final probabilities are of (X, Y and Z) of his procedure. This could have been resolved without the need for a D6 and use a D4 instead (unless of course, other factors play a role, such as the irrational love some people have for using only D6's during a game).

Gentlemen Wargamers,

There can be many unforeseen consequences stemming from even the simplest of numerical relationships. Consider the data in the Increase and Decrease Tables below.

INCREASES:
A 3 with a +1 factor increased to 4 = 33% increase.
A 4 with a +1 factor increased to 5 = 25% increase.
A 5 with a +1 factor increased to 6 = 20% increase.
A 6 with a +1 factor increased to 7 = 16.67% increase.
A 7 with a +1 factor increased to 8 = 14.28% increase.
A 8 with a +1 factor increased to 9 = 12.5% increase.

DECREASES:
A 4 with a -1 factor reduced to 3 = 25% decrease.
A 5 with a -1 factor reduced to 4 = 20% decrease.
A 6 with a -1 factor reduced to 5 = 16.67% decrease.
A 7 with a -1 factor reduced to 6 = 14.28% decrease.
A 8 with a -1 factor reduced to 7 = 12.5% decrease.
A 9 with a -1 factor reduced to 8 = 11.11% decrease.

Something as simple as where you set the center of mass of your Unit Combat Values (CV) can have a considerable influence on the relationship between units and combat.

Example. If you set the combat value of your average unit at 5, it would be 20% more powerful than a 4, and 20% less powerful than a 6. Now, if you increased the combat value of your average unit to 10 it would be 10% more powerful than a 9, AND it would also be 10% less powerful than a 11.

To make this a little clearer, suppose that two game designers are both working on a WWII game design that uses the same combat resolution system. Both are in the process of assigning combat values to their units. Designer A sets his SS Panzer Grenadier Division at 5 and his American Infantry Division at 4, while Designer B chooses 9 for SS Panzer Grenadier Division and 8 for American Division.

Thus, Designer A says that his SS Panzer Grenadier Div. is 25% stronger than an American Div., while Designer B using the same +1 difference between his combat units (CV: 8 & 9) is unwittingly stating that it's only 12.5% more powerful. Who is right in this case?

Additionally, there are also some downstream effects from this s3election that manifest themselves in the form of combat ratios. Example. In Designer A's game when 4x Pz Gren Divisions (5-CV ea) attack an American Div (4-CV) the initial odds are 20-CV vs 4-CV or 5:1. The same attack in Designer B's game 4x Pz Gren Divisions (9-CV ea) attacking an American Division (8-CV) the initial odds are 36-CV vs 8-CV or 4:1.

So, what appeared on the surface to be arbitrary and of little significance, actually does have a considerable impact on combat. One than the designers may not have even intended.

Regards,

James

Good Data James but when some rules use level adjustments the percentage change is not as revalent.

For example a Level 4 (Average) unit is fighting a level 4 enemy unit The chance to win is 50%. Based on a general presence command advantage the unit is raised one level (+1). So the attacker is fighting at a Level 5 Veteran status. On a matrix combat table to increase of a 5 vs 4 is a 60% chance to win. So the net increase is 10% rather than the 25% in your chart.

Anotehr example is that the defending 4 is reduced (-1) due to being understrength due to casualties. So now they are fighting as a level 3 Green unit. So the attacker advantage is changed from a 4 vs 4 at 50% chance to win to a 4 x 3 60% chance to win.

Your relative change percentage is only valid when applying it to a chance to hit/win die roll.