Fig 1.
Draft Value Indices (DVI) by selection number.
(A) The DVI (solid line) used by the Australian Football League (re-scaled to 3000 at selection number 1). Solid black points are salary data from which the DVI is derived. Solid grey points are draft values at selections 1, 9 and 18. (B) The DVI for the National Football League (NFL).
Fig 2.
Draft value across alternative selections.
Boxplots of draft value from a hypothetical example showing the mean (triangle), median (solid black line), central 50% of the distribution (box) and lower 5th percentiles (circle). (A) The draft value from selections 1, 9 and 18 (S1, S9, and S18 respectively). (B) The draft value from selection 1 (S1), two of selection 9 (2 × S9), and three of selection 18 (3 × S18). (C) The draft value from selection 1 (S1), two of selection 9 and one selection 18 (2 × S9 + S18), and three of selection 18 and one selection 9 (3 × S18 + S9).
Fig 3.
Observed DVIg values (grey points) and the mean value at each selection (black point). Error bars depict two standard errors of the mean and approximate a 95% confidence interval for the mean.
Fig 4.
(A) Observed and best-fit estimate of the probability a player fails to play a game in relation to their selection. (B) Observed (grey circles) and best-fit DVIg distribution for players that played at least one game. Black circles depict medians of the observations. Variation in DVIg is modelled using the Weibull distribution. Solid line depicts the predicted median. Short- and long-dashed lines depict the bounds associated with the 95% and the 80% prediction intervals, respectively.
Table 1.
Examples of risk and mean equivalence with DVIg.
Fig 5.
Comparison of selection distributions for AFL trades using DVIg.
Probability distributions describing uncertainty in DVIg for individual selections predicted by the best-fit model (left column) and the predicted cumulative distribution of the summed DVIg when traded (right column). The probability distributions show the probability DVIg = 0 (leftmost probability) and the remaining probabilities depict the likelihood of DVIg values lying within bins of width 0.005. Dashed horizontal lines indicates the 5th percentile. Crosses indicate the expected summed DVIg (i.e. mean) of the trade. A club is deemed to have benefitted if its cumulative curve is always to the right of its trading partner’s. (A-B) Adelaide and Geelong trade in 2014 [Adelaide: S10 + S47, Geelong: S14 + S35]. (C-D) Hawthorn and St. Kilda trade in 2013 [Hawthorn: S19, St. Kilda: S24 + S59]. (E-F) Geelong and Adelaide Dangerfield trade in 2015 [Geelong: D + S50, Adelaide: S9 + S28 + S55].