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Who will win the game?...
Story
You are in the office pool, currently betting on the outcome of next week's
basketball game between the
MallRats and the
Chinooks.
You have to decide which team will win, then bet on that team. Of
course, you could just guess, or flip a coin. Here we present
a way that (typically) will do better: by using observations about the
past performance of the teams. That is...
You've been tracking the MallRats over the season, and recorded various
information about the previous games.
In addition to the obvious logistics about each game:
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the name of the opponent
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was the game at Home or Away, and
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was the starting time 5pm, 7pm or 9pm.
you also note some of the "coaching decisions":
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Did Fantastic Fred (FF) start the game; or come in off the bench
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Did Joe play center (in the MallRat offense), or did he play
power forward.
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Did Joe guard the opponent's center, as opposed to one of
the opponent's forwards.
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You also note whether that opponent's center was tall (over 6'9") or not,
Finally, you record
The results are shown below:
Where |
When |
Fred Starts |
Joe offense |
Joe defense |
Opp C |
OutCome |
Home |
7pm |
Yes |
Center |
Forward |
Tall |
Won |
Home |
7pm |
Yes |
Forward |
Center |
Short |
Won |
Away |
7pm |
Yes |
Forward |
Forward |
Tall |
Won |
Home |
5pm |
No |
Forward |
Center |
Tall |
Lost |
Away |
9pm |
Yes |
Forward |
Forward |
Short |
Lost |
Away |
7pm |
No |
Center |
Forward |
Tall |
Won |
Home |
7pm |
No |
Forward |
Center |
Tall |
Lost |
Home |
7pm |
Yes |
Center |
Center |
Talls |
Won |
Away |
7pm |
Yes |
Center |
Center |
Short |
Won |
Home |
9pm |
No |
Forward |
Center |
Short |
Lost |
Away |
7pm |
No |
Forward |
Forward |
Short |
Lost |
Away |
5pm |
No |
Center |
Forward |
Tall |
Won |
Home |
7pm |
No |
Center |
Center |
Tall |
Lost |
Home |
9pm |
No |
Forward |
Forward |
Short |
Lost |
Away |
9pm |
Yes |
Center |
Forward |
Short |
Lost |
Home |
7pm |
Yes |
Center |
Center |
Short |
Won |
Home |
7pm |
Yes |
Center |
Forward |
Short |
Won |
Home |
5pm |
No |
Forward |
Center |
Short |
Lost |
Home |
7pm |
Yes |
Center |
Forward |
Tall |
Won |
Away |
5pm |
No |
Center |
Center |
Tall |
Lost |
You know, from various reliable sources, that this championship game
will be away (not on the MallRat court), at 9pm, that Fantastic Fred will not start, and
that Joe will play center on offense, but will not defend the Chinook's 7'1"
center.
That is, you know:
Where |
When |
Fred Starts |
Joe offense |
Joe defense |
Opp C |
Outcome |
Away |
9pm |
No |
Center |
Forward |
Tall |
?? |
What you don't know, of course, is who will win this game.
Of course, it is reasonable to assume that this future game will resemble the
past games. Note, however, there are no previous games that match these
specific values -- ie, no previous game was exactly
[Where=Away, When=9pm, FredStarts=No,
JoeOffense=Center, JoeDefends=Forward, OppC=Tall].
We therefore need to generalize -- by using the known examples to infer
the likely outcome of this new situation.
But how?
Your turn
Who do you think will win? ... and why?
Note that the MallRats have split their previous 20 games --- winning
10 and losing 10. So this "overall statistic" does not help.
Similarly, they are 4-and-4 on away games -- which also does not help.
However, they have lost all 4 of their previous 9pm games, which suggests
they will lose this upcoming 9pm game.
They have also lost 6 of the 8 games when Fred did not start.
However, they are 8-Wins-and-3-Losses when Joe plays center on offense,
which suggests they will win this game;
and they are [6W, 4L] when the opposing center is over 7'.
Or perhaps we should consider some combination:
perhaps Joe does a good job defending tall centers, or whatever...
So, if you were going to place a bet,
would you bet that the MallRats will win, or not?
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