Modelling the High and Low Offers in The Chase Australia
/Previously, we’ve investigated the relative performance of the Chasers on the Australian and UK versions of the show using data from this Google document from James Spencer for the Australian data, and from this website for the UK data.
James, to celebrate the 1,000th episode of The Chase Australia, has recently added contestant-by-contestant data to his Google document, which allows us to investigate another topic I’ve long been interested in: how predictable are the Chasers’ high and low offers?
THE DATA
We have data for 939 episodes, from which we’ll exclude:
any episode where there were only two contestants (9 episodes)
any episode that aired on a Sunday (3 episodes - these episodes look qualitatively different)
any episode where the high or low offers are not available in the data (1 episode)
That leaves us with data for 3,704 contestants from 926 episodes.
BUILDING A PREDICTIVE MODEL
For today’s blog I’m going to build simple linear regressions. As potential explanatory variables, we’ll include:
The Chaser name
The Year in which the episode aired (treated as a categorical variable)
The Day of the Week on which the episode aired (treated as a categorical variable)
The Seat Number of the contestant in question (1 to 4, treated as a categorical variable)
The Cash Builder Amount that the contestant earned (in dollars)
The Number of Players who were already home before this contestant was up (0 to 3)
The Amount of Money already banked by earlier contestants (in dollars)
We’ll split the available data 70/30 into a training and a test set, and then fit two models to the training data, one with the High Offer as the target, and one with the Low Offer as the target.
THE HIGH OFFER MODEL
The fitted model for the High Offer is summarised at right and can be interpreted as follows:
The expected High Offer for a contestant in Seat 1 who registered $0 in his or her Cash Builder facing Anne Hegerty in an episode that aired on a Friday in 2015 is just over $9,000
Contestants facing Cheryl, Matt, or Brydon could expect to be offered about $1,100 to $1,400 less, facing Issa about $600 less, facing Mark about $70 more, and facing Shaun about $200 more
Contestants in Seat 2 could expect a High Offer just over $4,000 higher, in Seat 3, just over $8,000 higher, and in Seat 4, almost $14,000 higher
For every additional contestant who was already back home at the time the contestant in question was made the offer, the High Offer is expected to increase by about $1,200.
However, for every $1,000 those back home contestants had banked, the High Offer is expected to decrease by about $120. So, if there’s already one contestant back home who banked $10,000, the nett effect of this and the previous factor is zero (ie 10 x $120 - $1,200)
As we would expect, better Cash Builder performances are rewarded by bigger High Offers. For every additional one question answered correctly (ie $2,000 more in the Cash Builder), the expected High Offer increases by about $3400
The airing year and day have a significant influence on the size of the High Offer. Relative to 2015, the High Offer increased by between about $8,250 (2018) and $12,500 (2017).
Relative to shows that aired on a Friday, shows that aired on other weekdays had High Offers that, on average, ranged from about $4,000 (Mon, Tue and Wed) to $5,000 (Thu) lower.
This model explains about two-thirds of the variability in High Offer amounts in the training set. As one piece of evidence that this model is not overfit, it also explains about 60% of the variability in High Offer amounts in the test set.
We can make a quantitative assessment of the relative importance of each of the variables in this model by creating a variable importance plot, which we do below.
It shows that, by far, the contestant’s Cash Builder amount is the most important variable in the model for predicting the High Offer a contestant might expect to receive, followed by whether or not he or she was sitting in Seat 4, then by whether or not he or she was in a show that aired in 2017 or 2019.
THE LOW OFFER MODEL
The fitted model for the Low Offer is summarised at right and can be interpreted as follows:
The expected Low Offer for a contestant in Seat 1 who registered $0 in his or her Cash Builder facing Anne Hegerty in an episode that aired on a Friday in 2015 is just under $3,000
Contestants facing any other of the Chasers could expect to be offered about $200 to $400 less
Contestants in Seat 2 or Seat 3 could expect a Low Offer only about $100 to $200 higher, and in Seat 4 barely $25 higher
For every additional contestant who was already back home at the time the contestant in question was made the offer, the Low Offer is expected to decrease by about $30
There is virtually no adjustment in the expected Low Offer based on the amount already banked by previous contestants
Again, better Cash Builder performances are rewarded by bigger Low Offers. For every additional one question answered correctly (ie extra $2,000 in the Cash Builder), the expected Low Offer increases by about $400.
The airing year and day also have a significant influence on the size of the Low Offer. Relative to 2015, the Low Offer decreased by around $2,100 to $2,400.
Relative to shows that aired on a Friday, shows that aired on other weekdays had Low Offers that, on average, ranged from about $60 to $300 lower.
This model explains about 54% of the variability in Low Offer amounts in the training set, and about 54% of the variability in Low Offer amounts in the test set.
Here, too, we can produce a variable importance plot.
Once again, the size of the contestant’s Cash Builder emerges as the most important variable, but with the year of airing filling the spots from 2nd to 7th.
SUMMARY AND CONCLUSION
It is possible to build simple linear models that explain a significant proportion of the variability in High Offers and Low Offers in the Australian version of The Chase.
Those models reveal that:
A contestant’s Cash Builder amount has the largest impact on the High and Low offers he or she receives
Seat Number also has a relatively large and important influence on the expected High Offer a player receives
There is some variability across the Chasers in terms of the High Offers they make in a given situation, but less variability in the Low Offers they make
There has been considerable variability in both the High and Low offers made across the years. In particular, there was a substantial increase in High Offers and decrease in Low Offers after the 2015 season
Whether or not a show aired on a Friday had a substantial effect on the expected size of the High Offer
