If you’re here, reading a game designer blog discussing analysis paralysis, then I’m pretty sure you probably have some idea of what I mean by the words “Analysis Paralysis” (hereafter referred to as AP). If you don’t, don’t fret! Jump back to Part 1 and read the “What is AP?” section for a primer on the subject.

This is the seventh and final article in a series of 7, each article in this series has gone into depth on one potential cause of AP, examples of situations where it can be problematic, and present some solutions that can improve the situation.

If you have any suggestions, examples, questions, or want to point out something I’ve missed, please do so in the comments. This is not a scientifically rigorous examination of AP, and I would be happy to include any contributions you have!

Bigger vs Better

The problem of scale.

Category: Clarity

Player Symptoms:

Reluctance to make agreements due to overvaluation of minor assets.
Making mistakes in numeric comparisons or math.
Hesitation in calculating value.
Spending more time on performing basic mental operations than on making decisions.
Recalculating value due to uncertainty or failure to remember.

Cause of Problem:

The root of this problem is the false assertion that Bigger is Better, or that Accuracy and Precision are both necessary for Quality. This is the problem of numbers and the consequences of scale. Although this problem might be more appropriate in an article series about accessibility, we are going to specifically look at how the barriers of numeric accessibility cause analysis problems that lead to a breakup of the flow of a game, delays, and yes – paralysis.

To get a better grasp of the problem, we are going to focus on one example that I am sure nearly everyone reading this is familiar with: Monopoly. Now you may cringe at that sound of that name (as I do) but by comparing the classic version of Monopoly with the new, updated, modern version - this example provides the perfect illustration of the problem at hand. So, let’s dive in.

Example: Monopoly – Here & Now

How many of you have played a game of Monopoly with the original, classic, $1, $5, … $500 paper money denominations? Whether or not you use the Free Parking Jackpot, or you happily ignore the auction rules, it doesn’t matter. What we are going to consider are those white, pink, yellow, green, blue, orange, and reddish paper bills.

Do not pass Go, do not collect $200. The classic line for this classic game.

The original version of the game was simple. Everyone knows that the winner of the beauty pageant gets $10, or that a bank error in your favour nets a cool $200. Although irritating, the Income Tax calculation of $200 vs 10% was reasonably easy to judge – quickly start counting money and properties and if you pass $2000 then you paid the $200. It was also easy to assess that regardless of the size of your stack of bills, the $100 and $500 bills were what separated the winners from the losers… everything else was just pocket change.

Then in 2006 Hasbro decided to update the game of Monopoly to produce Monopoly: Here & Now edition, a version with new property names and more accurate pricing. In order to do this, all prices and money denominations in the game were multiplied by 10,000 but retained the same distribution of values. But making this change also introduced layout challenges (because every numeric value added 4 additional 0’s) which were overcome by using “k” and “M” abbreviations to represent thousands and millions. Although the bills included both abbreviated and non-abbreviated value – properties and cards only displayed abbreviated prices leading to a situation where numeric values (in ascending order) were represented in the following way: $10k, $50k, $100k, $200k, $500k, $1M, $5M.

The impact of this change resulted in a cascade of problems which we are going to examine next.

Problem 1: Inappropriate Scale

Many board games depend on numbers in one way or another, whether that is victory points, meeples, currency, or countless other examples. These numbers are organized into distinct systems. Victory points are a system of numbers that determine a winner, currency is a system of numbers that determine purchasing power, meeples are a system of numbers that determine the placements available to be made (as one example). Each of these systems is separate from one another. Although a game may provide a translation between them (1 meeple costs $5, 2 meeples = 3 victory points, 3 meeples = 5 victory points) each set of numbers is distinct and could be changed, tweaked, or replaced independently of each other.

In order to avoid a complex discussion of numeracy, when we talk about scale we are going to focus on the base unit of a game’s number systems. Based on the limited example of three number systems that I outlined above, we have enough information to draw some conclusions about the base units of each.

Meeples – the information above describes situations where meeples are converted into currency and into victory points in units of 1, 2, and 3. This implies that the base unit of the meeples number system is “1”.
Currency – the information above only describes that 1 meeple costs $5. With no other information, we may expect that currency is only useful in multiples of $5 and implies that the base unit of the currency number system is “5”.
Victory points – we see victory points described as being awarded in units of 3 and 5. Since 5 is not a multiple of 3, the base unit is going to be the largest number that can be multiplied to produce any possible combination of 3 and 5. This is called the Greatest Common Factor and it has the property that both 3 and 5 can be divided by it evenly. In this case the base unit of the victory point number system is “1” because there is no larger number that divides both 3 and 5.

Any number system in a game with a base unit that is NOT “1” has an inappropriate scale.

Why?

Good question. The answer is because it adds an unnecessary* layer of complexity and inaccessibility. Counting by 2’s, 5’s, 10’s, or 27’s is more challenging to understand, process, and accurately calculate than counting by 1’s. Using a base unit of anything other than “1” will require a player to spend more time thinking and increase the potential for miscalculation.

*Probably. For the purposes of this article I am specifically ignoring practical applications of board games where natural/integer number systems are not applicable – like geometry – the arguments I present are strictly for the purposes of artificially applied systems that are based on an abstract natural number system to begin with.

Returning to the Monopoly example, the base unit of currency in the Here & Now edition of the game has been increased from $1 to $10,000. A dramatic change for an abstract system in the interests of “accuracy”. The problem is that the game is an inherently abstract and unrealistic system to begin with. Improving the “accuracy” of property values serves no actual purpose, and only results in increasing the frustration level of its players (which, being Monopoly, is already significant).

Adding 4 extra 0’s to the end of every number results in a situation where:

Players have more difficulty performing simple addition/subtraction
Players must dedicate more memory to storing the extra digits/placeholders
Values are more difficult to interpret at a glance, the extra 0’s provide a buffer that reduce the visual impact of “1” vs “500”

Consider the following two sets of numbers:

A - 3 vs 58
B - 21000000 vs 410000000

Which set of numbers has a larger difference in magnitude? Did you have to count the zeros?

One step taken by Hasbro to improve this problem that was taken was the use of the “k” abbreviation to represent units of 1000. Although we will discuss the mixing of units in the next problem, the use of “k” is an improvement over writing out each number in full – but it only reduces the base unit from “10,000” to “10”, better but still more challenging than “1”.

Problem 2: Mixing Units

Part of the consequence of the scale adjustment in Monopoly Here & Now is that all values are inflated. In the original game that uses a base unit of “1”, property values ranged from $60 to $400 and the maximum rent (Boardwalk with a Hotel) is $2,000. With the new scale, property values range from $600,000 to $4,000,000 and rent hits a maximum of $20,000,000.

As mentioned previously, the abbreviation “k” was introduced to the printing to shorten printed values by using it to represent units of 1000. The resulting change to values could then be displayed as $600k to $4,000k and rents up to $20,000k.

Compared to the original version, this adjustment is more complicated to read, understand, and process. But, in a clever and convenient bit of math – this also caused the most important currency denomination (the $100) to be changed to $1,000k which could be represented as $1M. Suddenly, by using both “k” and “M” abbreviations, property values could now be written as $600k to $4M with rents up to $20M and most of the time players are going to be dealing with smaller base units of $1M to $20M than the original which would be $100 to $2,000.

Except… by choosing to use 2 related units “k” and “M” players are still required to deal with numbers across a similar range of values from “1” to “1000”, but the game has now switched high values and low values. All the large numbers in that range “60” to “950” use the “k” unit and are smaller than the small numbers in the range “1” to “20” which use the “M” unit. With high and low reversed, players are now required to constantly convert between the two by adding or removing “0”’s in order to compare values.

By introducing mixed units, a player’s ability to quickly compare two values is compromised by requiring extra work to read, interpret, and process which units are being used. If the two units were isolated and most of the time used individually (everything over $1M was a round multiple of $1M) then the situations where converting between the two would be limited and pose much less of a problem.

Which brings us to:

Problem 3: Decimation

The third problem with the choice currency denomination in Monopoly Here & Now is that very few costs require perfectly round multiples of $1M. Most property costs and rents end up somewhere in the range of $1M to $4M and as soon as a cost exceeds $1M it is represented as a decimal.

Now players are required to deal with base units that are larger than “1”, 2 different units of value, frequent conversion between those units, a mismatch of big numbers = smaller value and vice versa, as well as being required to interpret decimal values.

Although an argument could be made that people do regularly deal with decimals in everyday life when dealing with money, while true it is an additional layer of complication compared to whole numbers, but the comparison in this game is not accurate. A value of $1.23M is not $1M + $23k, but it is $1M + $230k. This adds a 3rd layer of translation that players are required to do in their heads on the fly during nearly every transaction that they will make in the game – between values represented in “k”, “M”, and fractions of “M”.

Altogether this doesn’t sound like a huge problem, but each incremental departure from the simplest base system of numbers is a barrier to both accessibility, and to speed. The more layers that are added the more delay that is introduced to the game, the more potential for incorrect calculation, and the more time is spent recalculating each time two values need to be compared.

Problem 4: Excessive Precision

Although this last problem is not present in Monopoly, it is an important challenge to be aware of. The core of the problem is using more digits to specify a value than the minimum required for purpose it is being used for. The fallacy that designers fall into is that using more digits (either using more decimal places – just in case, or specifying very larger numbers right down to the 1’s position) gives the appearance of being more accurate. But, accuracy and precision are two different things. I could say that the price of a hamburger at a local fast-food chain is $598,394.24 which is a very precise number (I used 8 digits!) but is wildly inaccurate.

The problem lies in the fact that it takes more effort to read, remember, and compare numbers with a large number of non-zero digits than those with a small number of non-zero digits. If those extra digits are not serving an important purpose, then they are getting in the way of clarity.

To illustrate this problem, consider the game Pandemic. At the beginning of the game each player starts with a number of city cards, and by the rules the player with the city card with the highest population takes the first turn. Examples of city card populations include Chennai: 8,865,000; Miami: 5,592,000; and Chicago: 9,121,000. With 48 cities in the game whose populations range from just over 1 million to more than 25 million, including population values down to the 1000’s digit is an unnecessary level of precision. Rounding city values to the nearest 100,000 residents would result in 240 unique options within the defined range of populations – more than enough to provide unique values for the 48 selected cities. Also considering the volatility of population changes that occur in cities – easily in the range of 10,000 per year for cities of these sizes – rounding to the nearest 100,000 would result in values that remain more consistently accurate for a longer period of time.

Solutions:

As mentioned in the beginning, the problem of numeric complexity in board games is generally more of an accessibility problem than an AP problem. The reason it has been included here is that it can play a significant role in compounding other AP issues that may exist in a game. Complex numeric comparisons can multiple the effort and difficulty in analyzing the state of a game and possible next steps, and as such can cause a dramatic impact on the perception and effect of decision-based AP.

The solution for these problems is to simplify – but may often depend on the designer’s purpose in making the game in the first place. A game that is intended to teach the player about doing their taxes, probably needs to retain high levels of precision and use values that are reasonably accurate to what someone might see in the real world. But most board games are more abstract than that. Board games as a rule are abstract representations of a system, and thus the numeric systems used in most games are already contrived for the purpose of achieving balance and entertainment. Therefore adjusting those systems in most cases will not meaningfully impact the game except to make it easier to understand and play.

Keep It Simple:

This is the one and only solution to the challenges we’ve described. Board games are abstract and require significant mental effort on the part of the player to remember the rules, apply them correctly, and think creatively about how to use those rules to achieve a goal. A poorly chosen scale of numbers simply makes that task harder.

The most important systems to simplify are the ones that are most often manipulated and necessary for decision making. Start by using a base unit of “1” and stick to natural numbers. Avoid fractions or decimals, if they are necessary consider adjusting your scale to avoid them (if possible) or try a rounding rule. Only be as precise as absolutely necessary, and accuracy is not as important as fun.

Apply the Katamari Principle:

Are you in a situation where you find yourself dealing with a single number system that requires both very small values any very large ones and thus also needs a high degree of precision? The Monopoly Here & Now currency system is a minor example (and a poor one considering how well the original Monopoly implemented the same system), but a better example is money in World of Warcraft.

The way money works in World of Warcraft is that it is broken up into Copper, Silver, and Gold. There is a simple and automatic conversion system – 100 Copper = 1 Silver, 100 Silver = 1 Gold. Item costs in the game range from a few Coppers to auction house items that sell for more than 10,000 Gold or the equivalent of more than 100,000,000 Copper.

So how does this differ from the Monopoly example? The answer is that: denominations are not abbreviations for large units, and multi-denomination costs are never presented as a single value. For example, you will never see a cost shown as 1.5363 Gold, or 1,045.2 Silver. Each denomination is presented uniquely and independently as 1 G - 53 S - 63 C; or 10 G - 45 S - 20 C. In Monopoly this would translate a cost of 2.75M would be shown as 2M - 750k.

Separating a single number system into distinct denominations, and maintaining presentation of those denominations as separate items removes the need for players to perform implicit conversions and allows them to continue to work with whole numbers as much as possible.

This kind of separation can be further emphasized by the example of Katamari Damacy. In Katamari you roll a ball that picks up objects and grows larger – but you can only pick up objects that are relatively similar in size. As the ball grows past certain thresholds the game transitions into pick up larger scaled objects, and the smaller scale objects become irrelevant. The same can be applied to number systems, by allowing conversion between small denominations and large denominations but only ever requiring one to be used at a time you can effectively separate a single number system into two distinct systems that can be scaled independently.

The End

If you have any comments, suggestions, or examples that you would like to share about this week’s topic, please tell us about them in the comments.

This is the final article in the series on Analysis Paralysis, and we hope that it has been informative and useful. Remember: It is up to you, the designer, to test, observe, and determine if your players are showing signs of problematic levels of AP and whether or not it needs to be addressed.

Good luck, and thank you for reading!

Designer Blog

Breaking the Chains of Analysis Paralysis – Bigger vs Better (Part 7 of 7)