Reply to thread

Message: <blockquote data-quote="delericho" data-source="post: 4054425" data-attributes="member: 22424">Okay, just to show up the sorts of errors we are dealing with, I have done an analysis of the various movement options.The options:<ul> <li data-xf-list-type="ul">Freeform movement. In this option, 1 'square' diagonally is equivalent to root-2 'squares'. I have approximated to three decimal places in my calculations.</li> <li data-xf-list-type="ul">1-1-1-1. A diagonal square costs 1 square of movement.</li> <li data-xf-list-type="ul">1-2-1-2, resetting. The first diagonal square costs 1 square, the second 2, alternating. Each round, the count resets.</li> <li data-xf-list-type="ul">1-2-1-2, accumulating. The first diagonal square costs 1 square, the second 2, but it does not reset at the end of the round. If in round one you move 1-2-1, then in round 2 you move 2-1-2. Where a fractional number of squares is given, the actual rate alternates. Whether the first or second round gets the 'extra' square varies.</li> <li data-xf-list-type="ul">2-1-2-1, resetting. As 1-2-1-2, except that the order is reversed. Each round, the count resets.</li> <li data-xf-list-type="ul">2-1-2-1, accumulating. Likewise, but accumulating each round. Where a fractional number of squares is given, the actual rate alternates. Whether the first or second round gets the 'extra' square varies.</li> <li data-xf-list-type="ul">2-1-1-1, per round. This is the proposed rule that the first diagonal costs double, but thereafter a square is a square. This one applies the tariff once in the round, so a character taking a double move only pays the price once.</li> <li data-xf-list-type="ul">2-1-1-1, per move. As above, except that a character taking a double move pays 2 for the first square in each move.</li> <li data-xf-list-type="ul">2-2-2-2. As in SWSE, a diagonal square costs 2.</li> </ul>The calculation has been done for movement speeds of 20, 25, 30, 35 and 40 feet per round, these being the most likely speeds to be dealt with in combat. It assumes that the character takes a double move each round, moves as far as he possibly can each round, and moves only on a diagonal. Naturally, this is unlikely to be the case in actual play. These figures can therefore be rightly considered a 'worst case'.Distances travelled are listed in squares. The error is calculated by subtracting the 'freeform' distance from the listed distance - a positive means the character moves further than he should, a negative means he falls short by the listed amount.(At this point, I was going to draw out the table, but I don't know the correct flags. So, instead I'll point you to the attached file. Yes, it's Excel. Sorry if that's difficult for you.)What does all this mean?Well, it shows that while the 2-1-1-1 rule is closer to accurate than 1-1-1-1, it still has a relatively high % error. This error gets progressively worse as movement rates increase, tending towards 41% (ish) as movement tends to infinity. If using that rule, I recommend applying it per-move rather than per round.Finally, it would hypothetically be possible to use a 'Gregorian' movement scheme, where we alternate 1-2-1-2, accumulate fractions over rounds, and considered every nth '2' to be a '1', thus reducing the rounding errors even further (as is done with leap years in the Gregorian calendar). However, doing so is almost certainly more trouble than it would be worth - moving to one more step of accuracy would take you from ~6% error to somewhat less than 1%, at a cost of counting something like 10 diagonals.</blockquote>

Verification