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Name(s) _____________________________
BA 368: Business Analytics Case 1, Part 1
Goal: Estimate the probability that the Denver Broncos beat the Carolina Panther on Thursday 9/8/16.
(And in general, estimate this probability for any game given the point spread.)
The Broncos are underdogs in Thursday’s game, but they certainly have a chance to emerge victorious.
How would you estimate their chances, understanding that either team can win?
1) Combine that data for years 2008 – 2011 from the Excel file on the course webpage.
2) Sort the data by point spread, but only consider one half of the data. Think carefully about what
to do with the “Pick ‘em” games.
3) Determine whether the favorite actually won the game (not beat the spread) for each data
point. See the hint online for how to do this. The best way to do this is by using the PivotTable
function in MS Excel. If you don’t know how to do this, ask me or a classmate for help. If you do
know how to do this, please share your expertise with your classmates.
Now, use this data to make some estimates:
A. i) What proportion of 3 point favorites actually won?
ii) Is this a good estimate for the probability that a future 3 point favorite will win?
B. Repeat A. for 7 point favorites.
C. Repeat A. for 14 point favorites.
D. Does the trend make sense? Do higher favorites have a better chance of winning?
E. The Broncos are currently a _____ point underdog in the game. According to your results, what
percent of the time to _____ point underdogs win?
F. Now, consider something weird: Look at the win probabilities for point spreads ranging from 3
to 6. Shouldn’t these be increasing? But they’re not. The problem here is small sample sizes.
For example, at the 4.5 mark, you should have n = 35 and at the 5 mark, you should have n =37.
But the win probability for 4.5 is quite a bit higher than for 5 (which is barely over 50%!). With
small samples, things don’t always work out exactly the way you expect them to. To understand
this better, determine a 95% confidence interval for the true win probabilities for point spreads
of 4.5 and 5. This is something you learned in statistics and have likely forgotten by now – ask
me for help if you need it. Interpret what these intervals mean.
G. Now, graph the point spreads (ranging from 0 to the max) versus the win probabilities and then
fit a linear regression line to the data. Determine and interpret the equation of the line and the
coefficient of determination. Print out the graph with the line on it. How much does the
probability of winning the game increase for every additional unit of point spread?
H. Use Excel to try to fit a better curve (than linear) to the data. Next week we will develop our
own function that should fit very well in class.
I. {Extra Credit} Repeat what you did in G. above, but now there are a lot more data points. For
example, the point spread of 10 isn’t just one point with probability 79%, it’s actually n = 29
points at point spread 10 with probability 79%. Use all 1068 data points.
Deliverable: Type up all of your results into a clear document that addresses each part above.
The due date will be sometime next week and will depend on the class’s progress and overall
level of effort.