Sport

Statistics in sport such as Sydney to Hobart yacht race and AFL draws.

AFL DRAWS

Australian Rules Football (AFL) is a football code in which there are "goals" and "behinds".
A goal scores 6 points and a behind scores 1 point. An example score is "13 10 88",
which means 13 goals, 10 behinds = 88 points. Because a large range of total
scores in a game are possible, draws are quite rare.

The current AFL national competition involving 16 teams had its origins in 1897 in the state of Victoria, in the Victoria Football League (VFL). The records of the VFL and AFL are often considered together, representing the elite Australian rules football competitions over that time period.

There have been 109 seasons between 1897 and 2005 (inclusive).

The distribution of the number of draws per season is as follows:

Number of draws	Count
0	28
1	47
2	21
3	8
4	4
5	1

The rarity of draws suggests that a Poisson distribution could be fitted to these data. The average number of draws is 1.229. Using a Poisson distribution with this mean gives predicted frequencies shown in the graph, with the observed frequencies.

The predicted frequencies are similar to the observed frequencies. The data fit a Poisson model quite well.

The year 1977 was particularly unusual: the Grand Final was a draw, and hence was replayed the following week, and in round 7 of that year there were two draws.
In one of them the points scored by both teams were 98, and in the other, 99.

Grand Final draws between 1897-2005

Row	Year	Draws	Row	Year	Draws
1	1897	1	56	1952	3
2	1898	1	57	1953	1
3	1899	0	58	1954	2
4	1900	0	59	1955	0
5	1901	1	60	1956	2
6	1902	0	61	1957	2
7	1903	1	62	1958	0
8	1904	1	63	1959	1
9	1905	1	64	1960	2
10	1906	0	65	1961	3
11	1907	0	66	1962	1
12	1908	0	67	1963	1
13	1909	3	68	1964	2
14	1910	1	69	1965	0
15	1911	3	70	1966	1
16	1912	0	71	1967	2
17	1913	1	72	1968	2
18	1914	4	73	1969	1
19	1915	1	74	1970	0
20	1916	1	75	1971	2
21	1917	2	76	1972	2
22	1918	0	77	1973	1
23	1919	1	78	1974	2
24	1920	0	79	1975	0
25	1921	5	80	1976	1
26	1922	2	81	1977	4
27	1923	1	82	1978	1
28	1924	1	83	1979	1
29	1925	1	84	1980	3
30	1926	1	85	1981	0
31	1927	1	86	1982	1
32	1928	1	87	1983	0
33	1929	2	88	1984	0
34	1930	0	89	1985	1
35	1931	0	90	1986	0
36	1932	1	91	1987	2
37	1933	1	92	1988	1
38	1934	1	93	1989	1
39	1935	4	94	1990	1
40	1936	0	95	1991	2
41	1937	1	96	1992	2
42	1938	0	97	1993	1
43	1939	1	98	1994	1
44	1940	0	99	1995	3
45	1941	0	100	1996	3
46	1942	0	101	1997	1
47	1943	1	102	1998	1
48	1944	4	103	1999	1
49	1945	1	104	2000	2
50	1946	1	105	2001	0
51	1947	2	106	2002	2
52	1948	2	107	2003	3
53	1949	0	108	2004	0
54	1950	1	109	2005	1
55	1951	2

SYDNEY TO HOBART YACHT RACE WINNING TIMES

The Sydney-Hobart yacht race starts from Sydney Harbour on Boxing Day
(26 December) and finishes several days later in Hobart.
It is a 630 nautical mile ocean race.

Sydney to Hobart in 1990: A flotilla going through the Sydney Harbour taken from North Head.

The data for 1945-1993 comes from The Sydney Morning Herald (24 December 1994). The more recent data are from the official race website, the Sydney Morning Herald and Wikipedia. The data originally published included an error in the 1965 results; it has been amended here.

The winning time (first across the line) varies quite a bit due to weather and improvements in boat design and sailing techniques. What has been the pattern of improvement over time?

Winning times have generally decreased, from around 6 days to around 2.6 days on average.

How can we describe the pattern further? Using statistical methods to put a straight line on the graph (regression) gives this:

One way to describe the decrease is with a straight line. The straight line above was fitted by linear regression, giving time in days = 98.6 - 0.0480 x year. This describes the decrease quite well. However, we should be cautious about applying this model to future races. For instance, extrapolating suggests that by the year 2033 it will take, on average, around 1 day to win, and by the year 2055 the winning boat will arrive before it leaves!

Are there other ways to describe the changes? Another alternative method fits lines to only parts of the data and joins the results, like this:

This type of method allows for some curving by fitting straight lines to subsets of consecutive years. It makes some other adjustments and is known as 'locally weighted regression', or 'lowess' for short. The lowess curve is shown above. It shows that after about 1975 the rate of improvement slowed down. The lowess curve helps visualize the changes over time, but it does not give us a formal mathematical model of the change over time.

HERE ARE THE WINNING TIMES FOR 1945 TO 2011

Year	Line Honours Winner	days	hours	Minutes	Time
1945	Rani	6	14	22	6.60
1946	Morna	5	2	53	5.12
1947	Morna	5	3	3	5.13
1948	Morna	4	5	1	4.21
1949	Waltzing Matilda	5	10	33	5.44
1950	Margaret Rintoul	5	5	28	5.23
1951	Margaret Rintoul	4	2	29	4.10
1952	Nocturne	6	2	34	6.11
1953	Solveig	5	7	12	5.30
1954	Kurrewa IV	5	6	9	5.26
1955	Even	4	18	13	4.76
1956	Kurrewa IV	4	4	31	4.19
1957	Kurrewa IV	3	18	30	3.77
1958	Solo	5	2	32	5.11
1959	Solo	4	13	33	4.56
1960	Kurrewa IV	4	8	11	4.34
1961	Astor	4	4	42	4.20
1962	Ondine	3	3	46	3.16
1963	Astor	4	10	53	4.45
1964	Astor	3	20	5	3.84
1965	Stormvogel	3	20	30	3.85
1966	Fidelis	4	8	39	4.36
1967	Pen Duick III	4	4	10	4.17
1968	Ondine II	4	30	20	5.26
1969	Crusade	3	15	7	3.63
1970	Buccaneer	3	14	6	3.59
1971	Kialoa	3	12	46	3.53
1972	American Eagle	3	4	42	3.20
1973	Helsal	3	1	32	3.06
1974	Ondine III	3	13	51	3.58
1975	Kialoa	2	14	36	2.61
1976	Ballyhoo	3	7	59	3.33
1977	Kialoa II	3	10	14	3.43
1978	Apollo	4	2	23	4.10
1979	Bumblebee IV	3	1	45	3.07
1980	New Zealand	2	18	45	2.78
1981	Vengeance	3	22	30	3.94
1982	Condor of Bermuda	3	0	59	3.04
1983	Condor	3	0	50	3.03
1984	New Zealand	3	11	21	3.47
1985	Apollo	3	4	32	3.19
1986	Condor of Bermuda	2	23	26	2.98
1987	Sovereign	2	21	58	2.92
1988	Ragamuffin	3	15	29	3.65
1989	Drumbeat	3	6	21	3.26
1990	Ragamuffin	2	21	5	2.88
1991	Brindabella	3	1	14	3.05
1992	New Zealand Endeavour	2	1	19	2.80
1993	Ninety Seven	4	0	54	4.04
1994	Tasmania	2	17	48	2.74
1995	Sayonara	3	0	53	3.04
1996	Morning Glory	2	14	7	2.59
1997	Brindabella	2	23	37	2.98
1998	Sayonara	2	20	3.5	2.84
1999	Nokia	1	19	48	1.83
2000	Nicorette	2	14	2	2.58
2001	Assa Abloy	2	20	46	2.87
2002	Alfa Romeo	2	4	58	2.21
2003	Skandia	2	15	14	2.63
2004	Nicorette	2	16	1	2.67
2005	Wild Oats XI	1	18	40	1.78
2006	Wild Oats XI	2	8	53	2.37
2007	Wild Oats XI	1	21	25	1.89
2008	Wild Oats XI	1	20	34	1.86
2009	Alfa Romeo II	2	9	2	2.38
2010	Wild Oats XI	2	7	37	2.32
2011	Investec Loyal	2	6	14	2.26