ANAYLSIS OF EFFECTIVENESS
Before we move on to analysis, let’s discuss what makes a character effective in Overpower. Fans who have played Overpower will agree that there are 5 general things that make a character effective:
1) Overall offensive and defensive ability
2) Ability to cause K.O.
3) Ability to win a venture
4) Special card armamentarium – not related to Power Grid
5) Inherent ability – not related to Power Grid
Let’s now do some basic analysis to see how the Player’s Hands created by the Power Grids relates to the Character’s effectiveness. Again, the exact mathematics used to calculate all these factors is mind-numbing, so that level of detail won’t be covered here. Rather, only enough information to demonstrate the point being made, then a quick summary of the results of statistical analysis, will be presented.
1) Overall offensive and defensive ability
Overall offensive and defensive ability would be measured by two things, firstly the highest value offensive/defensive card in a hand. Character X can potentially have up to a value 8 in his hand, while Character Y can potentially only have up to value 5 in his hand. In this field, Character X already has the advantage.
The second measure of offensive and defensive ability would be the total number of useable offensive/defensive cards in a hand. Knowing that all Power Cards with the same value cannot be held in a hand at the same time, the total pool of offensive cards Character X can access would include 8 Power Cards, 5 Teamwork cards, and 7 Ally cards, creating a total pool of 20 offensive cards. The total pool of defensive cards would only include the 8 Power Cards, since Teamwork and Ally cards cannot be used for defense. Character Y can access 8 Power Cards, and 4 Ally cards, creating a total pool of 9 offensive cards. The total pool of defensive cards would only include the 5 Power Cards.
Even without going into the calculations, it is clear that out of a possible hand of 8 cards, Character Y’s smaller pool of cards would result in being more than twice as likely to draw duplicates, and have a smaller number of useable offensive and defensive cards in a hand.
Statistical Analysis: The defensive ability is fully dependant on the primary (i.e. highest) stat in the Power Grid. The ability increases exponentially with linear increase of the primary stat. The offensive ability also increases exponentially with linear increase of the primary stat, but has a contribution from any other stat above 6.
Result: Character X clearly wins out with regard to offensive and defensive capabilities by a landslide.
2) Ability to cause K.O.
There are only two ways to cause K.O. in Overpower – cumulative and spectrum. So let’s firstly compare the abilities of both Characters to cause a Cumulative K.O. From the total pool of offensive cards created by Character X, the best case scenario creating the maximum points of damage from a Player’s Hand would be 4 Power Cards (5+6+7+8) and 4 Teamwork cards (6+6+6+6), coming to a total of 44 points. Looking at Character Y, the best case scenario creating the maximum points of damage would be 5 Power Cards (1+2+3+4+5) and a possibly an Ally card (3) assuming there is an offensive special. This comes to a total of 15 points without the Ally card (18 points with the Ally card).
Statistical Analysis: The Cumulative K.O. ability again increases exponentially with linear increase of the primary stat, with contributions from any other stat above 6.
Spectrum K.O. ability cannot be demonstrated as easily, but we can try our best. Spectrum K.O. ability would be affected by overall offensive and defensive ability, but this has already been accounted for. We are purely looking at the ability to create variability of power types in a hand. The variability at each level of Power Card needs to be assessed, as higher level Power Cards are easier to hit, and therefore have a greater likeliness of contributing to a Spectrum K.O. MultiPower should also be considered a 5th power type, as it also contributes to Spectrum K.O. Looking at the quick chart of the power types available at specific values, both of them actually have comparable variability of power type choice up till level 4, since Character X is able to use MultiPower Cards which do not have a specific requirement to play. If you were to add in the Ally cards as well, the 5 or less to use cards which function as a level 3 further increase the spectrum capabilities of character X. Only when we reach level 5 does Character Y really have a distinct advantage with variability of power types.
Fig 3. A graphical representation of the variability of Power Types available for use at each level based on Power Grid.
Statistical Analysis: The Spectrum K.O. ability increases exponentially based on power type variability (which is derived from number of playable power types) created within each stat value category (level 1, 2, 3, etc.). The variability increases exponentially with number of playable power types (e.g. being able to play 5 power types creates exponentially increasing variability compared to being able to play 4, 3, 2 and 1 power types respectively). The weighting of the variability increases exponentially with increasing stat value category (e.g. weighting of being able to play 5 power types at level 4 increases exponentially compared to being able to play 5 power types at level 3, 2 and 1 respectively). The data is then amalgamated to determine the overall Spectrum K.O. ability.
Result: Character X is clearly far superior in ability to cause Cumulative K.O., whilst character Y’s ability to cause Spectrum K.O. is superior, but not by as large a factor.
3) Ability to win a venture
This is based largely on the maximum points of damage that can be created by a hand at any one time, but also slightly affected by the total number of useable offensive and defensive cards.
Statistical Analysis: This has already been covered in the aforementioned sections relating to offensive and defensive effectiveness and Cumulative K.O. effectiveness.
Result: Character X has the clear advantage.
OVERALL RESULT: Character X is statistically far more effective than Character Y.
Back to top
CORRECTING THIS DISCREPANCY
Clearly, the discrepancy of effectiveness between Character X and Character Y is too large given that they are assigned the same point value. A mathematical formula was derived to generate a point value based on a character’s Power Grid. (This took ages to calculate significance of all factors and then crunch all the numbers!) A basic form of it is listed below:
PV - Point Value; 1º, 2º, ... - Primary, Secondary, ... Stat (highest rating, 2nd highest rating, ...);
x - stat value exponential; w - stat category weighting; m - stat category exponential modifier; a - adjustment factor
As you can see formula takes the contribution of each of the stat’s to the overall effectiveness. Higher values within each stat category create exponentially greater contributions. The weighting of each subsequent stat reduces exponentially as well. A bit of playtesting (albeit without special cards to reduce confounding factors) revealed that these new point values were quite a good representation of the playability of the character. However, problems still existed within this new system. The severely low point values of some characters meant that the only reason they would be added to a team would be to allow selection of three other characters which were far too powerful, or resulted in them not being selected at all. As previously mentioned, the goal of Power Balance was to allow ALL characters to actually be useable and competitive. It was clear other measures needed to be taken to balance the game. The formula will be revised once all other measures have been taken into consideration.
One of the main issues identified was that characters with a high primary stat, like Character X used in our demonstrations, were given too much of an advantage. Characters with all-round stats like Character Y simply have no options. Clearly, to help balance the game, characters with high primary stat need to be “nerfed” a little, and characters with good all-round stats given a few more options to play with.
Back to top
BALANCING SPECTRUM K.O. ABILITIES
Characters with a high primary stat are superior in offensive, defensive, venture winning AND Cumulative K.O. capabilities, and yet they were still able to maintain a good ability to create Spectrum K.O. due to the presence of MultiPower Cards. To balance this, there is a new rule.