Differences in Standard scoring practice across the IATF led us to make a clarifying post on November 27th, 2024. That post, unfortunately, was unintentionally erased from the website.

In Standard Rules gameplay, both sides of the axe must be measured to determine the score of the throw if the axe head has landed across two point areas.

TL:DR Measure both sides of the axe at the surface of the target. To determine the result of the throw, compare the largest segment in the lower point value area to the largest segment in the higher point value area. Whichever segment is larger, the corresponding point area is the measurement result for that side.

Discussion on Device Measurement

Here we consider, after taking measurements on both sides of the axe head, whether comparing the largest measurements from each side is enough to determine where the majority of the axe head has landed.

Definitions

Let’s say we have 2 target areas A and B. These could correspond to the area outside the black ring circumference and inside the black ring circumference, or the red ring or the blue ring.

We have an axe to measure where some of the axe head is in contact with area A and some is in contact with area B. All of this discussion is referring to contact at the plane of the surface of the target.

Let’s call the measurements on Side 1 of the axe head A1 and B1, where A1 is the total length of the segment of the axe head in contact with area A, and B1 is the total length of the segment in contact with area B. Similarly, let’s call the measurements on Side 2 of the axe head A2 and B2.

Equal Length on Both Sides of the Axe Head

Let’s call the total length axe head in contact with the target X. Let’s assert that X is independent of the side on which it is measured.

So, we would expect:

A1 + B1 = X, and

A2 + B2 = X

=> A1 + B1 = A2 + B2

Some comments about this assertion:

• This equality holds when the faces of the blade are parallel to each other
• Further, this equality holds when the faces of the blade are symmetrical, and not strictly parallel, given the radius of curvature on the face of the blade is not smaller than some value that would introduce a meaningful difference between the straight line path and the path that follows the curve of the side of the blade from the end of the segment and the point of measurement
• This assumption on blade symmetry is reasonable, given real world examples
• This assumption on the radius of curvature is reasonable, since the radii of curvature of the side of real world axe heads are large (axe heads aren’t shaped like mallet heads)

Measurement Agreement on Both Sides of the Axe Head

Suppose we measure Side 1 and determine that

A1 > B1

and we measure Side 2 and determine that

A2 > B2

then it is trivial to see that A1 + A2 > B1 + B2, meaning most of the axe head is in contact with area A.

Measurement Disagreement Between the Sides of the Axe Head

Now, suppose we measure Side 1 and again determine that

A1 > B1

However, we measure Side 2 and determine that

B2 > A2

In this case, we have determined that the measurements on either side of the axe head are in disagreement, Side 1 shows more contact with area A and Side 2 shows more contact with area B.

So, we compare A1 and B2 and determine

A1 > B2

Is this enough information to conclude that most of the axe head is in contact with area A, meaning is A1 + A2 > B1 + B2 always?

Let’s consider A1 > B2

or, to rephrase,

A1 = B2 + ∆, where ∆ is the positive valued difference between A1 and B2

Since A1 + B1 = A2 + B2

=> (B2 + ∆) + B1 = A2 + B2

=> ∆ + B1 = A2

=> A2 = B1 + ∆

Meaning that the difference between the largest measurements on either side is the same as the difference between the smaller measurements on either side.

Comparing the Largest Measurements from Both Sides: Is That Enough?

Now let’s test whether the total of the measurements for area B can ever be larger than the total of the measurements for area A, meaning whether B1 + B2 > A1 + A2 can ever be true.

B1 + B2 > A1 + A2

since A1 = B2 + ∆ and A2 = B1 + ∆ 

=> B1 + B2 > (B2 + ∆) + (B1 + ∆)

=> 0 > 2∆

=> ∆ < 0

Recall that ∆ is the positive valued difference between A1 and B2.

So, ∆ < 0 is false, which means B1 + B2 > A1 + A2 is false.

So, A1 > B2 implies A1 + A2 > B1 + B2

Meaning comparing the largest measurements from both sides of the axe head does indicate the majority measurement if we were to add measurements for each area from both sides.

Crossing a Ring Circumference Twice

Notice that we said A1 and B1 were the total lengths of the segment of the axe head in contact with area A and area B. This means that in the cases where the axe head is in contact with the ring circumference twice, it is necessary to:

• measure the whole length in contact with all areas of the target
• measure the length in contact with the area inside the ring circumference
• subtract the length from the inside area from the whole length to arrive at the total length for the segments in contact with the area ring outside the circumference

Conclusion

In cases where the axe head, measured at the plane of the board, crosses a ring diameter, the procedure is as follows:

Both sides of the axe head must be measured at the surface of the target.

1. To determine the result of the throw, compare the segment in the lower point value area to the segment in the higher point value area. Whichever segment is larger, the corresponding point area is the measurement result for that side.
   1. If the axe head crosses the ring circumference twice,
      1. measure the whole length in contact with all areas of the target
      2. measure the length in contact with the area inside the ring circumference
      3. subtract the length from the inside area from the whole length to arrive at the total length for the segments in contact with the area ring outside the circumference
2. If the result on both sides of the axe head agree, that indicates the result.
3. If they differ, then compare the largest segment measurement from one side to the largest segment measurement on the other side.
4. The target area that corresponds to the larger segment measurement is the result.
   1. In the event that a larger segment cannot be determined, the result is the lower point value target area
      1. This scenario is expected to be rare. Measurements must be retaken to confirm the lengths.

For example, measuring the first side shows that the 3-point segment is larger than the bullseye segment, and the second side shows that the bullseye segment is larger than the 3-point segment. We compare the 3-point measurement from the first side to the bullseye measurement from the second side. If the bullseye segment is larger, then the result is a bullseye. If the 3-point segment is larger, then the result is 3 points. If the segments are exactly equal, then the result is 3 points.