Previous articles in this series addressed games that rewarded players for their position; schemes for scoring first place, second place, etc. Those articles supposed that scoring comes in in discrete packets which are more-or-less independent of one another. Painting the northwest section of the Chapel ceiling is worth the same 10 points regardless of what other sections you completed. Coming in first in the 100 meter dash awards the same gold medal regardless of your performance in the relay.
To examine those games, we set aside set collection games. Now is the time to give them our attention. These games award points based on quantity rather than position. In these games, the player is asked to gather sets of chapel paintings, Olympic medals, animals, gems, stocks, widgets or the like. These sets are then evaluated and the player earns points for each set.
This is the simplest scoring system for set-collection. Under linear scoring, each object in the set is worth the same amount of any other. The first is worth the same as the second is worth the same as the third and so on. For example, widgets might be worth 3 points each. If you have 6 widgets then you score 3 x 6 = 18 points.
Under a square scoring system, widgets earn points equal to the square of the number in the set. Each widget is worth more than the previous one. The first is worth 1 but the second is worth 3 (making the total value of the set equal 4) while the third is worth 5 (9 total), the fourth is worth 7 (16 total), the fifth is worth 9 (25 total), and so on.
Increasing the value of each widget over the previous is a good thing. It makes player interest (and therefore competition) increase at every step. The square scoring system can be problematic however because scores can get big quite rapidly.
For this reason, many eurogame designers employ triangular scoring instead. Like squaring, triangular scoring values the first widget in the set at 1 but the second is worth 2 (making the total value of the set equal 3) while the third is worth 3 (6 total), the fourth is worth 4 (10 total) , the fifth is worth 5 (15 total) and so on. Triangular scoring keeps the value of each widget increasing but at half the rate (for the mathematically curious, the slope of square scoring is 2n while the slope of triangular scoring is n + 0.5).
Under an exponential system, each additional widget multiplies the total value of the set by a fixed value. For example, imagine a system in which each widget doubles the value of the set. The first widget is worth 1 and the second is also worth 1 (because the set value doubled from 1 to 2). The third widget is worth 2 (2 doubles into 4). The fourth is worth 4 (4 doubles into 8). The fifth is worth 8 (8 doubles into 16).
Exponential schemes can feature multiplication by any number to make their rate of growth accelerate or decelerate as needed.
Every lover of mathematics knows the Fibonacci sequence. Despite this popularity, it seldom makes an appearance in scoring systems. Under a Fibonacci system, each quantity is worth the value of the previous two sets. You as the designer must choose a value for the first two quantities. The Fibonacci algorithm takes over from there.
For example, you may have set the value of one widget at 1 point and a with two widgets at 2 points. Fibonacci scoring then makes a set of three widgets is worth 1 + 2 = 3 points (the third widget is worth 1 point, the value of the first set). A set of four widgets is worth 2 + 3 = 5 points (the fourth widget is worth 2 points, the value of the second set). A set of five widgets is worth 3 + 5 = 8 points (the fourth widget is worth 3 points, the value of the second set) and so on.
I have seen Fibonacci scoring systems employed only occasionally by game designers. This is a type of scoring that would benefit from further exploration, I believe.
How about you? Do you have a favorite scoring system for set collection? Please share it with your fellow designers by adding it to the comments below. And if you’re enjoying what you’re reading, subscribe to this blog. It makes a difference.
In three days we expand our examination of set collection scoring systems by comparing and contrasting each of today’s systems. We will look for their best applications and look for opportunities to blend them in the same game. See you Friday!
4 thoughts on “Ties, Damn Ties, and Statistics, Part 5”
When there are scoring systems with multiple types of items to be collected, I like a mechanism where your total score is the value of your smallest set: if I have 8 gold, 7 notoriety, and 6 swag, my score is 6. I think I first saw this in Tigris and Euphrates. It seems like a good mechanism for encouraging the players to pursue a balanced strategy instead of trying to dominate the game in just one area.
That’s an excellent point, Carl!
Knizia also used the worst = score scheme in Ingenious. It seems to serve him well. 🙂