Cliffski's Blog

I’ve been doing some number crunching to check that I am moving in the right direction regarding balance on Democracy 4.

The game has a series of ‘events’ which are triggered by various inputs. Some of these events are pretty ‘informational’, in that they mark changes the player has made and their impacts, other affect the games difficulty by stopping the player racing too far ahead or too far behind. Others are there as a random curve-ball that the game throws to the player to shake things up. There are about 120 of them.

Because they are not triggered purely randomly, the frequency with which each event shows up is determined by the complexity of the neural network that forms the basis of the games simulation. This means that some events may end up triggering much more than others, if the inputs to those events are not balanced correctly.

In an ideal world, the whole game would be a truly self-balancing neural network, but I don’t trust the systems enough to unleash anything like that, so I collect statistical data on which events trigger in each game version, and then change some of the inputs each update so that things balance out for the better.

In an ideal world, every player gets to see 100% of the content in the game, so they are effectively getting what they paid for, and not being constrained to a tiny subset of the content because of poor balance. In other words, if I have an event called ‘school shooting’ and its triggering one tenth as often as ‘scientific breakthrough’, then the balance may be off, in that the inputs to the first event are too strong, and the second too weak.

Note that I am talking in grand statistical terms over thousands and thousands of players. An *individual* player may never see school shooting, or scientific breakthrough, depending on the countries they choose and their play style and skill, but I need to check I’m not adding content to the game that hardly anybody sees!

By collecting all this data, I can build up tables for each game version showing the total events triggered for players of that version, AND the number of times each event triggered. Like this:

1.27
Event Name	count
shareiposuccess	7790
shareipocancelled	7112
hugehurricane	4515
dubiousrolemodel	4190
resourcesobsolete	3913
multinationalcompanyheadquarters	3810
militarycontractscandal	3780

..and so on. Because I am looking at 120 events, I can work out that for version 1.27, if every event was equal, they would all trigger 1,406 times given the number of version 1.27 games played. I can then store the difference between the ACTUAL number of triggers, minus the target, and express this as a deviation in percentage terms from the target:

1.27
Event Name	count	percentage deviation
shareiposuccess	7790	453.78%
shareipocancelled	7112	405.58%
hugehurricane	4515	220.96%
dubiousrolemodel	4190	197.86%
resourcesobsolete	3913	178.17%
multinationalcompanyheadquarters	3810	170.85%
militarycontractscandal	3780	168.71%

So you can see that back in version 1.27, the top event (Share IPO success) is triggering 4.5 times as often as I would like.

I can then add up all of those percentage deviations and get a final number representing the total percentage deviation (in absolute terms) over all events. That gives me this:

Version	Absolute Deviation
1.27	6426.89%
1.28	5717.38%
1.29	6128.34%

In an ideal world, this number trends down over time as each version comes out.

Another way I looked at things was to just look at the absolute value of the top 10, and bottom 10 events, to see if I am effectively ‘squashing’ the trigger probabilities to prevent extremes. This is a major goal, because players will not notice and event triggering 5% more than another, but if one triggers EVERY game, or NEVER, then that does get noticed. When I look at this data I get these values

Version	Absolute Deviation	Extremes Deviation
1.27	6426.89%	2941.48%
1.28	5717.38%	2239.64%
1.29	6128.34%	2433.29%

By doing this for a whole bunch of different game versions, I can end up with a chart showing my progress!

More helpfully, I can quantify that the uneven-ness of the event triggering has improved by 14.73% since version 1.27. The extremes have been reduced more, by 30.29%

This probably sounds stupidly maths-y and the system is full of issues, such as events that only trigger in a few countries, and therefore SHOULD be seen less… but there are limits to which a single coder/designer/bizdev/marketer person like me can spend time crunching all this.

TBH its just a big relief that the numbers DO seem to be trending in the right direction, especially as I keep adding new countries and complex simulation elements (meaning that the simulation is in flux, and thus just remaining the same would be a balance-win of sorts.

It might be bizarre but I really enjoy this kind of analysis :D Now go tell your friends how well balanced Democracy 4 is :D

So… I am currently working on adding Japan as a playable country to Democracy 4, which is still in Early Access. Although I think Japan is super interesting in many ways, especially cultural (very conservative on prisons, super-generous on maternity leave, amazingly high percentage of retired people, very high tech, super-low immigration…), its economics are absolutely batshit crazy. Lets look at some numbers.

The current GDP of Japan is 559 trillion yen and its debt is currently 1.328 quadrillion yen, which gives us a debt to GDP ratio of 237%. The country in 2019 (pre-covid) had a deficit of 17 trillion yen. Compare this to the USA in 2019 which had a GDP of $21 trillion, debt of $22trillion, which is a ratio of 104% and a deficit of under $1trillion.

The USA has the dollar, which is the reserve country of the whole world, and I think its fair to say both countries have fairly similar stability in political terms. They are both monetizing this debt by using some form of quantitative easing. The US flirts with helicopter money, but the amounts are relatively small. I think its fair to say the biggest difference between the two is that the US debt to GDP ratio is dramatically lower than that of Japan. In other words, its riskier to lend money to Japans government than the US< by quite a margin, as the economy of Japan looks way less likely to repay that debt than the US. This *should* be reflected in the interest people demand to lend to Japan. lets look at 10 year government bonds:

United States 10 year bond yield: 1.59%

Japan 10 year bond yield: 0.09%

HELP. At this point I feel that someone like me with a decent (but hardly expert) understanding of economics is basically in this position:

This makes no sense. Would you lend any money to the US government for just 1.59% return? me neither, especially when just splatting the money onto the S&P500 would get you 13.6% a year over the last 10 years, but OMG why on earth would anybody lend money to the Japanese government for 0.09%. It makes no sense, and much more fundamnetally than this..it breaks the simulation for my game Democracy 4!

Basically the game has hard coded into it the attitude of the international bond market when it comes to government debt. The general principles of the code are that every six months the bond market evaluates your country and looks at the debt/gdp ratio, the deficit/gdp ratio, the level of ‘stability’ and inflation in the country, and then decides on what the credit rating should be. The interest rate on the debt is then applied, based on that credit rating. The game assumes that the maximum conceivable debt/GDP ratio is 250% (Japan has broken this!). As the game stands right now, a few turns into a new game on Japan instantly triggers a really bad debt crisis:

The game also assumes that this upsets everybody, really badly, but in fact, this may be outdated because it seems that people generally seem very unconcerned by the size of japans debt. This is possibly because right now the world has other concerns with covid, and also because we have had a post-2008 general global credit crunch which has meant global use of QE to the extent that global interest rates have collapsed. Every country has bad debt and low interest rates, which maybe makes japan look not so crazy…

But it still should be WAY worse than the USA. Japan *is* in a debt crisis, and the way in which it seems to be given a free pass on staggering levels of debt is baffling…and yet this needs to be somehow handled in democracy 4… Hence we reading a lot, and looking for some justifiable ‘fudge factor’ I can code into the game that justifies all this. By any standard Japans credit rating should be something like D right now. In fact… its A.

The clearest explanation i have found so far is “A large portion of wealth is held by seniors who lack financial literacy and prioritize stability rather than return” (source). This also states that most Japanese govt debt is owned by Japanese citizens. This kind of implies I need to hard-code in something that says ‘Japanese tendency to not realize they are making shit investments’, as a modifier to boost the credit rating of Japan. That can’t be right!

There is an argument for saying that the country is more stable, and less vulnerable to external pressure on its debt because its mostly owned by its own citizens. The current economics of the game are actually giving Japans super-high debt about the right impact on the finances, so the problem is mostly that the debt crisis is triggering when it probably should be put off a bit by these factors.

So I suspect my actual solution here is to add a special modifier (domestic debt ownership) for the debt crisis situation , but leave the credit rating and interest rate stuff alone. I suspect this works because although the current bond yield on japans debt is super low, some of it will be much older and potentially paying out higher amounts.

Anyway….fun fun fun. I guess its different to balancing games with laser guns and magic spells.