The Ultimate Flow

Figures & data

Figure 1. Ultimate Field Layout. Conveniently fits within the dimensions of regulation football and soccer fields. A pull and a five pass scoring possession are also displayed.

Figure 2. The RUFUS Scoresheet for recording an Ultimate game.

Table 1 Eight RUFUS fields describing an Ultimate possession.

Label Description		Values Details
SP	Starting Position	A	Within 10 yards of own endzone
		B	10 to 35 yards from own endzone
		C	Opponent's half
D	Defense	Z	Zone
		M	Man-to-man
NP	Number of Passes
wt	Within Ten		Did the possession come within 10 yards of opponent's endzone
PR	Possession Result	G	Goal
		X	Incomplete
		D	Defensive block by player guarding receiver
		P	Point block by player guarding thrower
		S	Stall
GD	Goal Distance	S	Scoring pass was thrown from less than 10 yards from the endzone
		M	10 to 35 yards
		L	More than 35 yards
PL	Players Involved		Players who participated in scoring pass, turnover, or defensive stop
TO	Time Out		Up to 3 per half

Table 2. Parameter Estimates and Likelihood Values for men's championship game between the University of Colorado (A) and Carleton College (B). The last line has likelihood ratio test statistics (and asymptotic p-values).

Counts	Field Condition Model	Possession Model	Independence Model
nBAD = 3
nAAU = 4
nBAD = 2
nABD = 0
nABU = 2
Likelihood	3.8 × 10^−6	4.9 × 10^−7	2.0 × 10^−8
loglikelihood	−12.5	−14.5	−17.7
4.1 (0.13)
-2 Difference		6.4 (0.01)
10.5 (0.01)

Figure 3. (a) Histogram and (b) QQ-plot of the 39 LRT-values for testing H_o: Possession Model vs. H_A: Field Condition Model. Graphs indicate the Field Condition Model is not necessary.

Figure 4. (a) Histogram and (b) QQ-plot of the 39 LRT-values for testing H_o: Independence Model vs. H_A: Possession Model. Graphs indicate the Independence Model is not sufficient.

Table

		Next Point
		AU	AD	BU	BD
	AU	0	1-pBU	pBU	0
Last	AD	1-pBD	0	0	pBD
Point	BU	pAD	0	0	1-pAD
	BD	0	pAU	1-pAU	0

Figure 5. The distribution of the longest run statistic conditional on 17 successes in 28 trials under the Bernoulli model of independence. Probability of a run of 10 or more (shaded) is 0.018.