# 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 drawsCount
028
147
221
38
44
51

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

RowYearDrawsRowYearDraws
118971 5619523
218981 5719531
318990 5819542
419000 5919550
519011 6019562
619020 6119572
719031 6219580
819041 6319591
919051 6419602
1019060 6519613
1119070 6619621
1219080 6719631
1319093 6819642
1419101 6919650
1519113 7019661
1619120 7119672
1719131 7219682
1819144 7319691
1919151 7419700
2019161 7519712
2119172 7619722
2219180 7719731
2319191 7819742
2419200 7919750
2519215 8019761
2619222 8119774
2719231 8219781
2819241 8319791
2919251 8419803
3019261 8519810
3119271 8619821
3219281 8719830
3319292 8819840
3419300 8919851
3519310 9019860
3619321 9119872
3719331 9219881
3819341 9319891
3919354 9419901
4019360 9519912
4119371 9619922
4219380 9719931
4319391 9819941
4419400 9919953
4519410 10019963
4619420 10119971
4719431 10219981
4819444 10319991
4919451 10420002
5019461 10520010
5119472 10620022
5219482 10720033
5319490 10820040
5419501 10920051
5519512

## 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 WinnerdayshoursMinutesTime
1945Rani614226.60
1946Morna52535.12
1947Morna5335.13
1948Morna4514.21
1949Waltzing Matilda510335.44
1950Margaret Rintoul55285.23
1951Margaret Rintoul42294.10
1952Nocturne62346.11
1953Solveig57125.30
1954Kurrewa IV5695.26
1955Even418134.76
1956Kurrewa IV44314.19
1957Kurrewa IV318303.77
1958Solo52325.11
1959Solo413334.56
1960Kurrewa IV48114.34
1961Astor44424.20
1962Ondine33463.16
1963Astor410534.45
1964 Astor32053.84
1965Stormvogel320303.85
1966Fidelis48394.36
1967Pen Duick III44104.17
1968Ondine II430205.26
1970Buccaneer31463.59
1971Kialoa312463.53
1972American Eagle34423.20
1973Helsal31323.06
1974Ondine III313513.58
1975Kialoa214362.61
1976Ballyhoo37593.33
1977Kialoa II310143.43
1978Apollo42234.10
1979Bumblebee IV31453.07
1980 New Zealand218452.78
1981Vengeance3 22303.94
1982Condor of Bermuda30593.04
1983Condor30503.03
1984New Zealand311213.47
1985Apollo34323.19
1986Condor of Bermuda223262.98
1987Sovereign221582.92
1988Ragamuffin315293.65
1989Drumbeat36213.26
1990Ragamuffin22152.88
1991Brindabella31143.05
1992New Zealand Endeavour2 1192.80
1993Ninety Seven40544.04
1994Tasmania217482.74
1995Sayonara30533.04
1996Morning Glory21472.59
1997Brindabella223372.98
1998Sayonara2203.52.84
1999Nokia119481.83
2000Nicorette21422.58
2001Assa Abloy220462.87
2002Alfa Romeo24582.21
2003Skandia215142.63
2004Nicorette21612.67
2005Wild Oats XI118401.78
2006Wild Oats XI28532.37
2007Wild Oats XI121251.89
2008Wild Oats XI120341.86
2009Alfa Romeo II2922.38
2010Wild Oats XI27372.32
2011Investec Loyal26142.26