Re: Musings on combat distance
A model so removed from reality lacks any utility. If you want to make a useful point about maai, you need have a basic understanding of the system you are attempting to model. Maai takes momentum, intent, and ability into account. It is not simply distance from point a to b.
A hypothetical example from Muai Thai: A right cross is strong, but short range. A left jab covers more ground but packs less punch. A thai roundhouse kick is generally ranged somewhere inbetween, but slower and far more powerful. These are often thrown as a 123 combo, jab to cover the initial distance, cross to raise the guard and eyes, and kick right above the now exposed knee.
You can avoid this by circling in away from the side of the cross and kick, because after throwing the jab that same side leg will be planted and the powerful attacks must come from the other side. Being out of position will nullify the attack somewhat, and leave you in good position to react.
The mistake would have been to back straight up, because the combo can continue moving in faster than you can back up. Your system might indicate that backing up is the safest option.
The outcome does not depend on the legnth of their limbs so much as an understanding of dynamic combat range (in this case nearer being safer). The assumptions of your system are wrong. The circle is dynamic.
If you'd like to create simple models of attacks along different vectors feel free, it has been done before and is of some utility. If you'd like to alter your model of ma ai you'll need to add the dynamic nature of the attacks, else it is not ma ai, simply distance with extraneous spheres.
"Note, however, that if Person1's leg attack fails, then Person2's arm attack is able to get to Person1's center first, barely." What does that have to do with anything? Really, is it like tag?
If you want to use math on martial arts, let me recommend you do a statistical study of mixed martial arts and document the success ratio of various individual techniques and combinations. What land's most often with most effect - does it come in combination or individually? Which techniques are highest percentage (really, not just claimed to be.) I don't think that's been done yet and it would be well received.