Radar Charts

At a glance 9 rules

1. 1Radar as a tableEach spoke is one parameter and each polygon one series. Copy the values into a small table (spokes down, series across) before any question.
2. 2Value per ring$\text{step} = \dfrac{\text{outer value} - \text{centre value}}{\text{number of gaps}}$$\text{ring } k \text{ out} = \text{centre value} + k \times \text{step}$
3. 3Count the winsFor 'on how many parameters does A beat B', go spoke by spoke and tally. A tie is not a win; 'at least as high' counts ties.
4. 4Compare totals by gaps$\text{total}_A - \text{total}_B = \sum (a_i - b_i)$$a_i, b_i = \text{A's and B's values on spoke } i$
5. 5The missing spoke$\text{needed} = \text{target avg} \times n - \text{rest}$$n = \text{spokes},\ \text{rest} = \text{sum of the others}$
6. 6Weighted score$\text{score} = \dfrac{\sum \text{weight} \times \text{value}}{\sum \text{weights}}$$\text{A} - \text{B} = \dfrac{\sum \text{weight} \times \text{gap}}{\sum \text{weights}}$
7. 7Different scalesIf each spoke has its own maximum, turn every value into a percent of its spoke's maximum before adding or averaging.
8. 8Rule first, then rankApply the stated rule first (head-to-head wins, drop the best and worst), then rank; the highest plain total often loses.
9. 9Room to the cap$\text{room on a spoke} = \text{cap} - \text{value}$$\text{tie: room} \ge \text{gap};\ \text{lead: room} > \text{gap}$