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What is the best way to represent the following formula as a graph?

Overall Score = 70% × [ 50% × Sub-factor A + 20% × Sub-factor B + 5% × Sub-factor C + 25% × Sub-factor D ] + 30% × [ 15% × Sub-factor A + 50% × Sub-factor B + 10% × Sub-factor C + 25% × Sub-factor D ]

For example, if: Overall Score = 70% × [ 50% × 44% + 20% × 3.75% + 5% × 14.4% + 25% × 20.5% ] + 30% × [ 15% × 10% + 50% × 10% + 10% × 16.67% + 25% × 25% ]

Then, one way of possibly representing the data would be this way:

A pie chart with three layers; outer later is labelled "Overall Score" and represents the evaluated value of the formula previously mentioned; the 2nd inner layer shows the two fixed factors A and B with their fixed influences, 70% and 30%, respectively; and under each arch of the previously mentioned inner layers are sub-layers, representing the sub-factors, broken down to either completely fit or fit partially within the arches of the parent layer.

(Note that if all sub-factors were 100% then the graph would be completely filled with no grey areas under factor A and factor B.)

However, is it a good graph? What are the pros and cons of this approach? And it is the best graph to use for the formula provided? Could a different graph work? Or is a graph even necessary?

Thanks for your feedback.

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  • What is the purpose of the overall score? An absolute value in percentage or some comparison (two or more items against each other)?
    – Mike
    May 15, 2018 at 7:59
  • Are you asking about the sub-factors? Ultimately, the overall score is a KPI dependent on multiple factors with various degrees of importance (reflected by their different maximum values) within two different contexts.
    – Glasspopsicle
    May 15, 2018 at 12:19
  • No, I mean what you are planning to do with the calculated KPI: present it next to the item for which the KPI is calculated or use it for comparison between the items (e.g. products)?
    – Mike
    May 15, 2018 at 13:08
  • I will not use it directly for comparison. However, the user may indirectly compare the graph by changing the filter options. Only one graph will appear on screen.
    – Glasspopsicle
    May 15, 2018 at 13:12
  • It's getting clearer, thanks. To summarise: for an item you have 4 scores (sub-factors) out of which two factors (different aspects) are calculated that in certain proportions form the overall score. Are there any ranges for the scores (sub-factors)? Why is the overall score in the picture you've provided around 80%?
    – Mike
    May 15, 2018 at 13:40

2 Answers 2

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The concentric pie chart you have proposed looks very good. At a glimpse of an eye the user can see how far on the scale (0 - 100%) the overall score is.
It is also visible that the overall score consists of two components (customer satisfaction and coverage) and what contributes to each component.
This is where the things get tricky - the same 4 sub-factors contribute to two main factors. Hence, using the same colours for both main factors components keeps the composition consistent.

I would, however, keep the chart "pac-man" like - fit all sub-charts in the overall score frame:
enter image description here
Pros:

  • overall score seen immediately
  • requires only linear (one dimension) understanding of the chart

Cons:

  • once overall score gets smaller, an in-depth analysis becomes difficult.

I was also thinking about proposing something two-dimensional.
Have a look at the following graph:

enter image description here

The top bar represents the overall score. Regardless of the score (low or high) its composition is explained on the same size of a right triangle where the legs represent your factors A and B and each leg is split proportionally to the sub-factor part.

Pros:

  • overall score seen immediately
  • regardless of the overall score (high or low) the composition is always readable

Cons:

  • requires multi-dimensional sight to understand the composition
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  • I would have to spend several minutes figuring out what the triangle means, and I think most viewers would as well.
    – Acccumulation
    Apr 11, 2019 at 18:38
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I don’t think anyone here has enough information to meaningfully answer your question, but we can probably give you the tools to answer it yourself.

  1. How important are the intermediate values numerically? If someone’s Factor A, Sub-factor B score is 84%, is that meaningful to them? Is that something they know how to improve?

  2. How important is the change in these values over time? Do you need to be able to compare if Factor B, Sub-factor C is bigger this month than last month?

  3. Are factors A and B dependent on each other? If some overall score is very low but the Factor B score is very high, is that significant to the reader?

  4. Do you need to be able to directly compare the overall weighted score of two sub-factors (e.g. is Factor A, Sub-factor C larger than Factor B, Sub-factor C)?

  5. How granular is the data? Is it significant that you can tell the difference between a 5% and a 6% score on a single sub-factor?

Charts shouldn’t be used decoratively; they should convey specific information. To figure out how to design the chart (or indeed whether or not to use a chart at all), you need to start from the information you want to convey, and work backwards to a design solution.

Depending on your answers for the above, you could look into stacked area charts, stacked bar charts, weighted bar charts, and clustered bar charts.

Remember, too, that pie charts are pretty terrible at conveying information, so the best solution is probably not a pie (or donut) chart.

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