I am considering starting a small research project on the the subject of "luck in sport".
It seems clear to me that in some sports, the better team almost always wins whereas in others a significant amount of luck is involved - particularly where balls can bounce randomly, and scores are low and subject to probability rather than statistics.
This can potentially be measured with an arguable amount of accuracy on a sport-by-sport basis, and sports then compared to see which involve the most/least luck in who wins the game.
The basic strategy is to use the half time result to break each game into two half games. Each half is played by the same people, at almost the same time, and both sides have the same basic strategy in both halves to maximise their points and minimise the opponent's points. Games with very little luck should have the side which wins the game winning both halves; conversely games with lots of luck will see results where a side wins only a single half but still wins the match. The winners of half games and winners of full games can be correlated and a numeric index of luck produced on a sport by sport basis.
Most people believe in the role of luck in sports, but as far as I can see nobody has tried to quantify this, and there does seem to be this mechanism to do so. It will involve looking at and data entering (in some manner) lots of historical sporting results. It will also require some knowledge of the sports to collect the information in a manner which eliminates systemic differences. For example in cricket, games where one side "declares" (voluntarily stops batting to save time) would need to be eliminated.
I don't know where this would go, maybe a web page, could be of interest to people who like to argue about sports, or people who bet on them.
Does anybody have:
(a) Any thoughts
(b) Any ideas on where to get the statistics (remember we need half time scores) hopefully as data files
(c) Any wish to become involved ?
Peter Webb wrote:
>It seems clear to me that in some sports, the better team
>almost always wins whereas in others a significant amount of
>luck is involved - particularly where balls can bounce
>randomly, and scores are low and subject to probability rather
>than statistics.
>This can potentially be measured with an arguable amount of
>accuracy on a sport-by-sport basis, and sports then compared
>to see which involve the most/least luck in who wins the game.
>The basic strategy is to use the half time result to break >each game into two half games. Each half is played by the same
>people, at almost the same time, and both sides have the same >basic strategy in both halves to maximise their points and >minimise the opponent's points. Games with very little luck >should have the side which wins the game winning both halves;
>conversely games with lots of luck will see results where a >side wins only a single half but still wins the match. The >winners of half games and winners of full games can be >correlated and a numeric index of luck produced on a sport by
>sport basis.
I think you need 3 components, not 2 ...
(1) skill
(2) luck
(3) the human element
For teams with approximately equal skill, the human element, not
luck, will often be the key secondary factor.
I'll outline two categories of situations for which the human
element may be the key factor ...
(1) Strategic Adjustment
Team A's chosen strategy may take team B by surprise, but
by the second half, the surprise has worn off and team B has
made appropriate adjustments.
Or, for multi-player team games, perhaps some player on team B is not playing well in the first half, so that player is replaced in the second half, and then all is well for team B.
(2) The Emotion Factor
Suppose Team A wins the first half by a large margin. In the
second half, it's hard for team A to psyche themselves up for
maximum output. Thus, team A will tend to "coast", riding their huge lead. At the same time, provided team A's lead is not too much to overcome, team B may be psyched to play at absolute maximum skill and power, thus potentially recovering some or all of the initial score deficit.
On the other hand, suppose team A gets a huge, essentially
unrecoverable lead in the first half. Then, in the second half, team B may have lost the heart to fight, so gets crushed even more.
Alternatively, for the huge, unrecoverable lead scenario, the
coach may make some substitutions to try some untested players. It's a good time to experiment since the game is lost anyway.
Thus, with team B using their "B team", the second half may be even worse.
Bottom line -- I think the human element dominates the luck element, and would be hard, perhaps impossible, to filter out.
> Peter Webb wrote:
> >It seems clear to me that in some sports, the better team
> >almost always wins whereas in others a significant amount of
> >luck is involved - particularly where balls can bounce
> >randomly, and scores are low and subject to probability rather
> >than statistics.
> >This can potentially be measured with an arguable amount of
> >accuracy on a sport-by-sport basis, and sports then compared
> >to see which involve the most/least luck in who wins the game.
> >The basic strategy is to use the half time result to break
> >each game into two half games. Each half is played by the same
> >people, at almost the same time, and both sides have the same
> >basic strategy in both halves to maximise their points and
> >minimise the opponent's points. Games with very little luck
> >should have the side which wins the game winning both halves;
> >conversely games with lots of luck will see results where a
> >side wins only a single half but still wins the match. The
> >winners of half games and winners of full games can be
> >correlated and a numeric index of luck produced on a sport by
> >sport basis.
> I think you need 3 components, not 2 ...
> (1) skill
> (2) luck
> (3) the human element
> For teams with approximately equal skill, the human element, not
> luck, will often be the key secondary factor.
> I'll outline two categories of situations for which the human
> element may be the key factor ...
> (1) Strategic Adjustment
> Team A's chosen strategy may take team B by surprise, but
> by the second half, the surprise has worn off and team B has
> made appropriate adjustments.
> Or, for multi-player team games, perhaps some player on team B
> is not playing well in the first half, so that player is
> replaced in the second half, and then all is well for team B.
> (2) The Emotion Factor
> Suppose Team A wins the first half by a large margin. In the
> second half, it's hard for team A to psyche themselves up for
> maximum output. Thus, team A will tend to "coast", riding their
> huge lead. At the same time, provided team A's lead is not too
> much to overcome, team B may be psyched to play at absolute
> maximum skill and power, thus potentially recovering some or
> all of the initial score deficit.
> On the other hand, suppose team A gets a huge, essentially
> unrecoverable lead in the first half. Then, in the second
> half, team B may have lost the heart to fight, so gets crushed
> even more.
> Alternatively, for the huge, unrecoverable lead scenario, the
> coach may make some substitutions to try some untested players.
> It's a good time to experiment since the game is lost anyway.
> Thus, with team B using their "B team", the second half may be
> even worse.
> Bottom line -- I think the human element dominates the luck
> element, and would be hard, perhaps impossible, to filter out.
>>It seems clear to me that in some sports, the better team
>>almost always wins whereas in others a significant amount of
>>luck is involved - particularly where balls can bounce
>>randomly, and scores are low and subject to probability rather
>>than statistics.
>>This can potentially be measured with an arguable amount of
>>accuracy on a sport-by-sport basis, and sports then compared
>>to see which involve the most/least luck in who wins the game.
>>The basic strategy is to use the half time result to break
>>each game into two half games. Each half is played by the same
>>people, at almost the same time, and both sides have the same
>>basic strategy in both halves to maximise their points and
>>minimise the opponent's points. Games with very little luck
>>should have the side which wins the game winning both halves;
>>conversely games with lots of luck will see results where a
>>side wins only a single half but still wins the match. The
>>winners of half games and winners of full games can be
>>correlated and a numeric index of luck produced on a sport by
>>sport basis.
> I think you need 3 components, not 2 ...
> (1) skill
> (2) luck
> (3) the human element
> For teams with approximately equal skill, the human element, not
> luck, will often be the key secondary factor.
> I'll outline two categories of situations for which the human
> element may be the key factor ...
> (1) Strategic Adjustment
> Team A's chosen strategy may take team B by surprise, but
> by the second half, the surprise has worn off and team B has
> made appropriate adjustments.
> Or, for multi-player team games, perhaps some player on team B
> is not playing well in the first half, so that player is
> replaced in the second half, and then all is well for team B.
> (2) The Emotion Factor
> Suppose Team A wins the first half by a large margin. In the
> second half, it's hard for team A to psyche themselves up for
> maximum output. Thus, team A will tend to "coast", riding their
> huge lead. At the same time, provided team A's lead is not too
> much to overcome, team B may be psyched to play at absolute
> maximum skill and power, thus potentially recovering some or
> all of the initial score deficit.
> On the other hand, suppose team A gets a huge, essentially
> unrecoverable lead in the first half. Then, in the second
> half, team B may have lost the heart to fight, so gets crushed
> even more.
> Alternatively, for the huge, unrecoverable lead scenario, the
> coach may make some substitutions to try some untested players.
> It's a good time to experiment since the game is lost anyway.
> Thus, with team B using their "B team", the second half may be
> even worse.
> Bottom line -- I think the human element dominates the luck
> element, and would be hard, perhaps impossible, to filter out.
> quasi
Most of those variables you list are in fact just luck. A team is lucky if it makes a good substitution, or unlucky if it gets an injury. We are trying to measure luck, the random component; you have mostly just listed where it shows up.
> The basic strategy is to use the half time result to break each game into
> two half games. Each half is played by the same people, at almost the same
> time, and both sides have the same basic strategy in both halves to maximise
> their points and minimise the opponent's points. Games with very little luck
> should have the side which wins the game winning both halves; conversely
> games with lots of luck will see results where a side wins only a single
> half but still wins the match.
I should begin by remarking that I know nothing about sport, but it
seems possible to me that:
i) a team doing badly at half time may be motivated to do better in the
second half (and may therefore actually do better); but also
ii) a team doing badly at half time may become disillusioned and
therefore do even worse in the second half.
Sports scientists surely include psychologists among their number who
have looked in to this.
-- The animated figures stand Adorning every public street And seem to breathe in stone, or Move their marble feet.
Peter Webb wrote:
>quasi wrote:
>>Peter Webb wrote:
>>>It seems clear to me that in some sports, the better team
>>>almost always wins whereas in others a significant amount of
>>>luck is involved - particularly where balls can bounce
>>>randomly, and scores are low and subject to probability rather
>>>than statistics.
>>>This can potentially be measured with an arguable amount of
>>>accuracy on a sport-by-sport basis, and sports then compared
>>>to see which involve the most/least luck in who wins the game.
>>>The basic strategy is to use the half time result to break
>>>each game into two half games. Each half is played by the same
>>>people, at almost the same time, and both sides have the same
>>>basic strategy in both halves to maximise their points and
>>>minimise the opponent's points. Games with very little luck
>>>should have the side which wins the game winning both halves;
>>>conversely games with lots of luck will see results where a
>>>side wins only a single half but still wins the match. The
>>>winners of half games and winners of full games can be
>>>correlated and a numeric index of luck produced on a sport by
>>>sport basis.
>> I think you need 3 components, not 2 ...
>> (1) skill
>> (2) luck
>> (3) the human element
>> For teams with approximately equal skill, the human element, not
>> luck, will often be the key secondary factor.
>> I'll outline two categories of situations for which the human
>> element may be the key factor ...
>> (1) Strategic Adjustment
>> Team A's chosen strategy may take team B by surprise, but
>> by the second half, the surprise has worn off and team B has
>> made appropriate adjustments.
>> Or, for multi-player team games, perhaps some player on team B
>> is not playing well in the first half, so that player is
>> replaced in the second half, and then all is well for team B.
>> (2) The Emotion Factor
>> Suppose Team A wins the first half by a large margin. In the
>> second half, it's hard for team A to psyche themselves up for
>> maximum output. Thus, team A will tend to "coast", riding their
>> huge lead. At the same time, provided team A's lead is not too
>> much to overcome, team B may be psyched to play at absolute
>> maximum skill and power, thus potentially recovering some or
>> all of the initial score deficit.
>> On the other hand, suppose team A gets a huge, essentially
>> unrecoverable lead in the first half. Then, in the second
>> half, team B may have lost the heart to fight, so gets crushed
>> even more.
>> Alternatively, for the huge, unrecoverable lead scenario, the
>> coach may make some substitutions to try some untested players.
>> It's a good time to experiment since the game is lost anyway.
>> Thus, with team B using their "B team", the second half may be
>> even worse.
>> Bottom line -- I think the human element dominates the luck
>> element, and would be hard, perhaps impossible, to filter out.
>Most of those variables you list are in fact just luck.
No, not really.
Strategic adjustment is not luck.
>A team is lucky if it makes a good substitution,
It's only common sense to replace a pitcher who, on a given
day, can't throw a strike, or to replace a basketball player who,
for some reason (pain, hangover, tiredness, whatever) can't make a shot.
I wouldn't call the score improvement resulting from such a
substitution luck.
>We are trying to measure luck, the random component; you >have mostly just listed where it shows up.
The human element allows a team to _adapt_ to the situation. It's a _function_ of the situation and, unlike luck, is both
controllable and predictable.
>> The basic strategy is to use the half time result to break each game into
>> two half games. Each half is played by the same people, at almost the same
>> time, and both sides have the same basic strategy in both halves to maximise
>> their points and minimise the opponent's points. Games with very little luck
>> should have the side which wins the game winning both halves; conversely
>> games with lots of luck will see results where a side wins only a single
>> half but still wins the match.
> I should begin by remarking that I know nothing about sport, but it
> seems possible to me that:
> i) a team doing badly at half time may be motivated to do better in the
> second half (and may therefore actually do better); but also
> ii) a team doing badly at half time may become disillusioned and
> therefore do even worse in the second half.
> Sports scientists surely include psychologists among their number who
> have looked in to this.
There's a simple model for some sports where for each half-game,
team A is assumed to score a number of points n_A which
follows a Poisson distribution of parameter mu_A (the mean
number of points scored), and team B analogously scores
a number of points n_B ~ Poisson(mu_B) .
Then n_A - n_B , the "point spread", follows a so-called
Skellam distribution.
Assuming mu_A > 0, mu_B > 0 , then for any integer m,
Prob[n_A - n_B = m] > 0 (any point spread is possible
in this very simple model).
I must add that it's assumed that the random variables
n_A and n_B, both Poisson, are independent r.v.s .
In the References section of that Wikipedia page,
they refer to the article below on sports and
Poisson distributions:
Karlis, D. and Ntzoufras, I. (2003) "Analysis of sports data using bivariate Poisson models". Journal of the Royal Statistical Society: Series D (The Statistician), 52 (3), 381 393. doi:10.1111/1467-9884.00366
In hockey, some players get injured. But is it just luck?
What if a player gets into fights a lot or skates too fast?
> On 06/13/2012 10:45 AM, Frederick Williams wrote:
> > Peter Webb wrote:
> >> [...]
> >> The basic strategy is to use the half time result to break each game into
> >> two half games. Each half is played by the same people, at almost the same
> >> time, and both sides have the same basic strategy in both halves to maximise
> >> their points and minimise the opponent's points. Games with very little luck
> >> should have the side which wins the game winning both halves; conversely
> >> games with lots of luck will see results where a side wins only a single
> >> half but still wins the match.
> > I should begin by remarking that I know nothing about sport, but it
> > seems possible to me that:
> > i) a team doing badly at half time may be motivated to do better in the
> > second half (and may therefore actually do better); but also
> > ii) a team doing badly at half time may become disillusioned and
> > therefore do even worse in the second half.
> > Sports scientists surely include psychologists among their number who
> > have looked in to this.
> There's a simple model for some sports where for each half-game,
> team A is assumed to score a number of points n_A which
> follows a Poisson distribution of parameter mu_A (the mean
> number of points scored), and team B analogously scores
> a number of points n_B ~ Poisson(mu_B) .
> Then n_A - n_B , the "point spread", follows a so-called
> Skellam distribution.
> Assuming mu_A > 0, mu_B > 0 , then for any integer m,
> Prob[n_A - n_B = m] > 0 (any point spread is possible
> in this very simple model).
> I must add that it's assumed that the random variables
> n_A and n_B, both Poisson, are independent r.v.s .
> In the References section of that Wikipedia page,
> they refer to the article below on sports and
> Poisson distributions:
> Karlis, D. and Ntzoufras, I. (2003) "Analysis of sports data using
> bivariate Poisson models". Journal of the Royal Statistical Society:
> Series D (The Statistician), 52 (3), 381–393. doi:10.1111/1467-9884.00366
> In hockey, some players get injured. But is it just luck?
> What if a player gets into fights a lot or skates too fast?
> Dave
Luck might be better described as inconsistent over several matches
between the same opponents.
e.g. in BOXING
TYSON beats ROCKY
ROCKY beats ALI
would have a high incidence of consistent results in rematches.
TYSON beats ROCKY
ROCKY beats ALI
TYSON beats ROCKY
ROCKY beats ALI
Maybe there are less variables in a 1 on 1 sport for luck to generate
from.
Whereas in Aussie Rules Football the results flip back and forth more
like tossing a coin.
Incidentally I went to the fitness shop last week to get some boxing
mitts, but came out with a pair of MMA Gloves.. Put your face in
front of one of those "mitts" and you won't be having much luck for a
long time!
> On Jun 14, 7:27 am, David Bernier<david...@videotron.ca> wrote:
>> On 06/13/2012 10:45 AM, Frederick Williams wrote:
>>> Peter Webb wrote:
>>>> [...]
>>>> The basic strategy is to use the half time result to break each game into
>>>> two half games. Each half is played by the same people, at almost the same
>>>> time, and both sides have the same basic strategy in both halves to maximise
>>>> their points and minimise the opponent's points. Games with very little luck
>>>> should have the side which wins the game winning both halves; conversely
>>>> games with lots of luck will see results where a side wins only a single
>>>> half but still wins the match.
>>> I should begin by remarking that I know nothing about sport, but it
>>> seems possible to me that:
>>> i) a team doing badly at half time may be motivated to do better in the
>>> second half (and may therefore actually do better); but also
>>> ii) a team doing badly at half time may become disillusioned and
>>> therefore do even worse in the second half.
>>> Sports scientists surely include psychologists among their number who
>>> have looked in to this.
>> There's a simple model for some sports where for each half-game,
>> team A is assumed to score a number of points n_A which
>> follows a Poisson distribution of parameter mu_A (the mean
>> number of points scored), and team B analogously scores
>> a number of points n_B ~ Poisson(mu_B) .
>> Then n_A - n_B , the "point spread", follows a so-called
>> Skellam distribution.
>> Assuming mu_A> 0, mu_B> 0 , then for any integer m,
>> Prob[n_A - n_B = m]> 0 (any point spread is possible
>> in this very simple model).
>> I must add that it's assumed that the random variables
>> n_A and n_B, both Poisson, are independent r.v.s .
>> In the References section of that Wikipedia page,
>> they refer to the article below on sports and
>> Poisson distributions:
>> Karlis, D. and Ntzoufras, I. (2003) "Analysis of sports data using
>> bivariate Poisson models". Journal of the Royal Statistical Society:
>> Series D (The Statistician), 52 (3), 381 393. doi:10.1111/1467-9884.00366
>> In hockey, some players get injured. But is it just luck?
>> What if a player gets into fights a lot or skates too fast?
>> Dave
> Luck might be better described as inconsistent over several matches
> between the same opponents.
> e.g. in BOXING
> TYSON beats ROCKY
> ROCKY beats ALI
> would have a high incidence of consistent results in rematches.
> TYSON beats ROCKY
> ROCKY beats ALI
> TYSON beats ROCKY
> ROCKY beats ALI
> Maybe there are less variables in a 1 on 1 sport for luck to generate
> from.
> Whereas in Aussie Rules Football the results flip back and forth more
> like tossing a coin.
> Incidentally I went to the fitness shop last week to get some boxing
> mitts, but came out with a pair of MMA Gloves.. Put your face in
> front of one of those "mitts" and you won't be having much luck for a
> long time!
> Herc
Yeah, well boxing can break the brain ...
How about:
"Modelling Association Football Scores and Inefficiencies in the Football Betting Market", by Mark J. Dixon and Stuart G. Coles.
In article <jra04d$jv...@news.albasani.net>,
"Peter Webb" <r.peter.webb...@gmail.com> wrote:
> Most of those variables you list are in fact just luck. A team is lucky if > it makes a good substitution, or unlucky if it gets an injury. We are trying > to measure luck, the random component; you have mostly just listed where it > shows up.
Sure, luck means a lot in football. Not having a good quarterback is bad luck.
--Don Shula
>I am considering starting a small research project on the the subject of >"luck in sport".
> It seems clear to me that in some sports, the better team almost always > wins whereas in others a significant amount of luck is involved - > particularly where balls can bounce randomly, and scores are low and > subject to probability rather than statistics.
> This can potentially be measured with an arguable amount of accuracy on a > sport-by-sport basis, and sports then compared to see which involve the > most/least luck in who wins the game.
> The basic strategy is to use the half time result to break each game into > two half games. Each half is played by the same people, at almost the same > time, and both sides have the same basic strategy in both halves to > maximise their points and minimise the opponent's points. Games with very > little luck should have the side which wins the game winning both halves; > conversely games with lots of luck will see results where a side wins only > a single half but still wins the match. The winners of half games and > winners of full games can be correlated and a numeric index of luck > produced on a sport by sport basis.
I think there is a huge problem with this analysis. Teams are not trying to win half-games, but whole games. If a team has a 30 point lead at the end of the first half, they will not play a strategy that necessarily maximizes their chance of winning the second half. They will (try to) play a strategy that minimizes their chance of losing the second half by more than 29 points. Similarly, their opponent will be playing not to try to win the second half, but to try to win the second half by at least 30 points. Differences in correlation of halves and games won between two sports may reflect the effects of this kind of strategizing being more pronounced in one than in the other.
> Most people believe in the role of luck in sports, but as far as I can see > nobody has tried to quantify this, and there does seem to be this > mechanism to do so. It will involve looking at and data entering (in some > manner) lots of historical sporting results. It will also require some > knowledge of the sports to collect the information in a manner which > eliminates systemic differences. For example in cricket, games where one > side "declares" (voluntarily stops batting to save time) would need to be > eliminated.
> I don't know where this would go, maybe a web page, could be of interest > to people who like to argue about sports, or people who bet on them.
> Does anybody have:
> (a) Any thoughts
> (b) Any ideas on where to get the statistics (remember we need half time > scores) hopefully as data files
> (c) Any wish to become involved ?
> "Peter Webb" <r.peter.webb...@gmail.com> wrote in message
> >I am considering starting a small research project on the the subject of
> >"luck in sport".
> > It seems clear to me that in some sports, the better team almost always
> > wins whereas in others a significant amount of luck is involved -
> > particularly where balls can bounce randomly, and scores are low and
> > subject to probability rather than statistics.
> > This can potentially be measured with an arguable amount of accuracy on a
> > sport-by-sport basis, and sports then compared to see which involve the
> > most/least luck in who wins the game.
> > The basic strategy is to use the half time result to break each game into
> > two half games. Each half is played by the same people, at almost the same
> > time, and both sides have the same basic strategy in both halves to
> > maximise their points and minimise the opponent's points. Games with very
> > little luck should have the side which wins the game winning both halves;
> > conversely games with lots of luck will see results where a side wins only
> > a single half but still wins the match. The winners of half games and
> > winners of full games can be correlated and a numeric index of luck
> > produced on a sport by sport basis.
> I think there is a huge problem with this analysis. Teams are not trying to
> win half-games, but whole games. If a team has a 30 point lead at the end of
> the first half, they will not play a strategy that necessarily maximizes
> their chance of winning the second half. They will (try to) play a strategy
> that minimizes their chance of losing the second half by more than 29
> points. Similarly, their opponent will be playing not to try to win the
> second half, but to try to win the second half by at least 30 points.
> Differences in correlation of halves and games won between two sports may
> reflect the effects of this kind of strategizing being more pronounced in
> one than in the other.
if there's a high margin then a strategy towards a low scoring game
for each side might be used by the leading team.
But you might still be able to determine factors like:
does the bounce of an oval shaped ball compared to a round ball
randomize the chances of winning?
does a zero strategy game, eg. 10 pin bowling where a player's game
environment is determined only by his own play increase consistent
winning streaks?
On Jun 16, 4:26 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> does a zero strategy game, eg. 10 pin bowling where a player's game
> environment is determined only by his own play increase consistent
> winning streaks?
technically you might opt out of going for a difficult split with the
pins if you only needed 1 pin to win a match!
> I am considering starting a small research project on the the subject of
> "luck in sport".
> It seems clear to me that in some sports, the better team almost always wins
> whereas in others a significant amount of luck is involved - particularly
> where balls can bounce randomly, and scores are low and subject to
> probability rather than statistics.
> This can potentially be measured with an arguable amount of accuracy on a
> sport-by-sport basis, and sports then compared to see which involve the
> most/least luck in who wins the game.
> The basic strategy is to use the half time result to break each game into
> two half games. Each half is played by the same people, at almost the same
> time, and both sides have the same basic strategy in both halves to maximise
> their points and minimise the opponent's points. Games with very little luck
> should have the side which wins the game winning both halves; conversely
> games with lots of luck will see results where a side wins only a single
> half but still wins the match. The winners of half games and winners of full
> games can be correlated and a numeric index of luck produced on a sport by
> sport basis.
> Most people believe in the role of luck in sports, but as far as I can see
> nobody has tried to quantify this, and there does seem to be this mechanism
> to do so. It will involve looking at and data entering (in some manner) lots
> of historical sporting results. It will also require some knowledge of the
> sports to collect the information in a manner which eliminates systemic
> differences. For example in cricket, games where one side "declares"
> (voluntarily stops batting to save time) would need to be eliminated.
> I don't know where this would go, maybe a web page, could be of interest to
> people who like to argue about sports, or people who bet on them.
> Does anybody have:
> (a) Any thoughts
> (b) Any ideas on where to get the statistics (remember we need half time
> scores) hopefully as data files
> (c) Any wish to become involved ?
> Peter Webb
Somewhat of a lost cause.
Even if all he variables are accounted for (unlikely), unless they are
quantifiable, the exercise becomes one of mysticism.
