VGAMdata (version 1.1-9)

wffc.points: Point System for the 2008 World Fly Fishing Championships

Description

Point system for the 2008 World Fly Fishing Championships: current and some proposals.

Usage

wffc.P1(length, c1 = 100, min.eligible = 0.18, ppm = 2000)
wffc.P2(length, c1 = 100, min.eligible = 0.18, ppm = 2000,
        c.quad = 12700)
wffc.P3(length, c1 = 100, min.eligible = 0.18, ppm = 2000)
wffc.P1star(length, c1 = 100, min.eligible = 0.18, ppm = 2000)
wffc.P2star(length, c1 = 100, min.eligible = 0.18, ppm = 2000,
            c.quad = 12700)
wffc.P3star(length, c1 = 100, min.eligible = 0.18, ppm = 2000)

Value

A vector with the number of points.

Arguments

length

Length of the fish, in meters. Numeric vector.

c1

Points added to each eligible fish.

min.eligible

The 2008 WFFC regulations stipulated that the smallest eligible fish was 0.180 m, which is 180 mm.

ppm

Points per meter of length of the fish.

c.quad

Constants for the quadratic terms. The defaults mean that a fish twice the minimum legal size will award about 50 percent more points compared to wffc.P1() and wffc.P1star(). See below for examples.

Author

T. W. Yee.

Details

The official website contains a document with the official rules and regulations of the competition. The function wffc.P1() implements the current WFFC point system, and is `discrete' in that fish lengths are rounded up to the nearest centimeter (provided it is greater or equal to min.eligible m). wffc.P1star() is a continuous version of it in that it is piecewise linear with two pieces and it is discontinuous at min.eligible.

The function wffc.P2() is a new proposal which rewards catching bigger fish. It is based on a quadratic polynomial. wffc.P2star() is a continuous version of it.

The function wffc.P3() is another new proposal which rewards catching bigger fish. Named a cumulative linear proposal, its slope is ppm between min.eligible and 2 * min.eligible, its slope is 2 * ppm between 2 * min.eligible and 3 * min.eligible, its slope is 3 * ppm between 3 * min.eligible and 4 * min.eligible, etc. One adds the usual c1 to each eligible fish. wffc.P3star() is a continuous version of wffc.P3().

The function wffc.P4() is another new proposal which rewards catching bigger fish. Named a cumulative linear proposal, its slope is ppm between min.eligible and 2 * min.eligible, its slope is 2 * ppm between 2 * min.eligible and 1.5 * min.eligible, its slope is 3 * ppm between 1.5 * min.eligible and 2 * min.eligible, etc. One adds the usual c1 to each eligible fish. wffc.P4star() is a continuous version of wffc.P4().

References

Yee, T. W. (2014). Scoring rules, and the role of chance: analysis of the 2008 World Fly Fishing Championships. Journal of Quantitative Analysis in Sports. 10, 397--409.

See Also

wffc.

Examples

if (FALSE)  fishlength <- seq(0.0, 0.72, by = 0.001)
plot(fishlength, wffc.P2star(fishlength), type = "l", col = "blue",
  las = 1, lty = "dashed", lwd = 2, las = 1, cex.main = 0.8,
  xlab = "Fish length (m)", ylab = "Competition points",
  main = "Current (red) & proposed (blue&green) WFFC point system")
lines(fishlength, wffc.P1star(fishlength), col = "red", lwd = 2)
lines(fishlength, wffc.P3star(fishlength), col = "darkgreen",
      lwd = 2, lty = "dashed")
lines(fishlength, wffc.P4star(fishlength), col = "orange",
      lwd = 2, lty = "dashed")
abline(v = (1:4) * 0.18, lty = "dotted")
abline(h = (1:13) * wffc.P1star(0.18), lty = "dotted") 

# Successive slopes:
(wffc.P1star((2:8)*0.18) - wffc.P1star((1:7)*0.18)) / (0.18 * 2000)
(wffc.P3star((2:8)*0.18) - wffc.P3star((1:7)*0.18)) / (0.18 * 2000)
(wffc.P4star((2:8)*0.18) - wffc.P4star((1:7)*0.18)) / (0.18 * 2000)

# More successive slopes:
MM2 <- 0.18 / 2
ind1 <- 2:12
(wffc.P4star((ind1)*MM2) - wffc.P4star((ind1-1)*MM2)) / (MM2 * 2000)

# About 50 percent more points:
wffc.P2    (2 * 0.18) / wffc.P1    (2 * 0.18)
wffc.P2star(2 * 0.18) / wffc.P1star(2 * 0.18)