Age, Gender and Performance on the UK Chase
/In the most recent blog post here, we analysed the performance of contestants on the UK Chase based on inferring their gender from their first names.
It turns out that the incredibly diligent website owner of OneQuestionShootout has the actual gender data for over 9,000 contestants, as well as their age and occupation. He’s been kind enough to give me access to that treasure trove of data, and today we’ll take our first look at it to investigate two main questions:
How does contestant performance and behaviour vary based on a contestant’s age and gender? We’ll look at performance based on the average Cash Builder amount accrued, the likelihood of getting home, the average amount contributed to the Prize Fund, and the average Contestant Winnings. We’ll also look at the propensity to take the Low, Middle, or High offer, which obviously has a big influence on how Cash Builder amounts are converted into team and individual winnings
What is the optimal mix of ages across the four people in a team?
CONTESTANT PERFORMANCE AND BEHAVIOUR BY AGE AND GENDER
Perhaps the purest measure of a contestant’s knowledge is what he or she accrues in the Cash Builder, and that is what we will analyse firstly.
That analysis is summarised in the chart below but, before getting into what we can glean from this chart, here’s a quick explanation of what’s here, much of which will be helpful in interpreting other of the charts in this blog. Each dot represents the average Cash Builder amount accrued by contestants of a given age and gender with contestants getting older as we move from left to right and accruing larger amounts as we move up the chart. The size of the dot reflects how many contestants it represents. The larger the dot, the more contestants there have been of that age and gender.
The lines are a smoothed representation of the relationship between age and average Cash Builder amount for a given gender - blue for males, and red for females - and the shaded band either side of the line gives an idea of how much statistical variability there is in the estimate of that line. Narrow bands mean that we are more confident about roughly where the line should be. Wide bands mean that we have less idea - often because we have relatively few contestants on which to base our estimates, for example for older contestants.
CASH BUILDER
From this chart we can conclude that:
For a given age, on average, males tend to do better in the Cash Builder than females (about £500 to £600 up to age 50)
There is an inverse-U shaped relationship between age and average Cash Builder amount
The peak age for males and females seems to be around 50 years of age, which is presumably when knowledge, and the ability to recall it under pressure, peaks
Male performance seems to fall off after the peak more rapidly than does female performance
GETTING HOME
It’s one thing to have a scorching Cash Builder performance, but it’s all for nought if the Contestant doesn’t get home to contribute to the Prize Fund and participate in the Final Chase.
Probability of Getting Home
In this next chart we simply calculate the proportion of all contestants of a given age and gender who successfully got back to their chair, regardless of the Cash Builder they accrued, or the offer they chose or its pound amount.
From this chart we can see that:
For males, the probability of getting home is fixed at about 70% from age 40 onwards. Before that it tends to increase linearly with age starting at about maybe 45% for 18 year-olds
For females, the probability of getting home tends to increase linearly with age starting at about maybe 50% for 18 year-olds and getting up to about 65% for 60 year-olds. After that age there seems to be a sharp decline in the rate of getting home - sharper than for the men, but the sample size is fairly small.
Comparing this chart to the last reveals that the variability Cash Builder performance across ages that we saw earlier is much more pronounced than the variability of the probability of contestants getting home across ages.
Choosing the Low, Medium or High Offer
One obvious potential source of these differences in the rates of getting home is differential proclivities to take Low, Medium, or High offers.
What we can see about that from this chart is that:
For any given age (except maybe for the very oldest Contestants), females are more likely to take the Low offer than are males
For any given age (again except maybe for the very oldest Contestants), males are more likely to take the High offer than are females
In absolute terms, males and females are most likely to take the Middle Offer regardless of age and seem to take it at much the same rate for a given age
For females and for males, the rate of taking the Low offer is highest amongst the youngest and the oldest, and roughly plateaus between the ages of 40 and 60 (although still falling a little with age for males in that age range)
For females and males, the rate of taking the High offer increases roughly linearly with age with quite an inflexion point around 65 years of age
Getting Home after Choosing an Offer
Just as average Cash Builder amount could serve as a measure of performance in the initial part of the game, getting home once we adjust for the risk taken because of the offer chosen can serve as a (risk-adjusted) measure of performance in the Contestant v Chaser part of the game.
What we see here is that:
Overall, the probability of getting home is highest for those who take the Low offer, and lowest for those who take the High offer. I doubt there’ll be any consideration of a Nobel Prize for affirming this, although the size of differences are interesting (Females: Low offer 71%, Middle offer 59%, High offer 36%. Males: Low offer 76%, Middle offer 64%, High offer 43%)
We see a similar inverted-U shape in this performance metric for those taking the Middle and High offers (and maybe Low offers if you squint a bit), much as we did when we analysed Cash Builder performance
For those taking the Middle offer, performance now seems to peak at about 50 years of age for males, and 60 years of age for females.
Contributing to the Prize Fund
If we take a team - rather than an individual - perspective of performance, the most appropriate measure at the point in the game just after the Contestant v Chaser contests is how much money the contestant banked for the team.
We find that:
For any given age, males tend to end up contributing more to the Prize Fund, on average, than do females
For males and females, contribution tends to rise roughly linearly with age, peaking at around age 60, and falling off a little after that, possibly more for males than for females but with our usual small-sample caveat
Whilst we do see the by now familiar inverse-U shape here, it seems to be less concave than what we’ve seen earlier in many of the charts, perhaps here because of the greater proclivity of the the middle- and older-aged to take the High offer and the younger contestants greater proclivity to take the Low offer.
Taking Money Home
The final individual performance metric we’ll analyse today is the average amount that contestants of different ages and genders have taken home.
What we see here is that:
Average winnings are relatively constant for males of all ages, though perhaps slightly larger for those aged 30 and above
Average winnings are fairly flat up to about age 30 and then rise with age from about 30 to 60 for females
For any given age below about 60, males, on average, win more money than dp females of the same age
Overall, the average male contestant takes home £1,383 and the average female contestant £1,180, or about 15% less.
So, despite an initial difference in Cash Builders between the genders amounting to about £500 or £600, that translates into a take-home difference of less than one-half or one-third of that.
ON FOR YOUNG AND OLD?
It seems then that the best Contestant, considered individually, would be someone in the age range 45 to 60, but would the best team comprise four such contestants, or would such a team lack important pieces of knowledge, say in terms of current celebrities or music?
To investigate this we first group contestants into age categories, ignoring gender. The age categories used are:
20 to 35
36 to 45
46 to 60
Over 60
These are loosely based on the performance results from earlier charts.
We then create an “Age Mix” variable, which is simply the count of contestants in a team that fall into each of these age ranges. So, for example, a team comprising four contestants from the 46 to 60 age range would have an Age Mix variable of 0040 since there are four contestants in the third range and none in the first, second, or fourth.
By keeping the number of age ranges to a minimum, we ensure that we obtain a number of age mixes that have occurred in a significant number of episodes.
We find here that:
The best observed mix - determined based on average total team winnings - has two contestants under 36, one in the 46 to 60 age range, and one aged over 60. It wins 26% of the time and yields an average of £5,634 per team
Next best is a team with two contestants under 36, one in the 36 to 45 age range, and one aged over 60. It wins 21% of the time and yields an average of £5,561 per team
The two next best teams have two contestants from the prime 46 to 60 age range and produce around £5,250 winnings per episode. Their winning rates are quite different at 19% and 24% from which we can infer that their average final Prize Funds differ by about 15 to 20%.
It’s important to point out that missing from this chart because they have occurred so rarely are two mixes that include three contestants from the 46 to 60 age group. They are:
0130: 5 episodes. Average Team Winnings £21,400
1030: 14 episodes. Average Team Winnings £6,100
Combined they represent 19 episodes with an average Team Winning of over £10,000. So it might well be then that stuffing your team full of 46 to 60 year olds is the optimal strategy, but we are lacking sufficient data to test this.
More generally, it’s clear that the producers pay careful attention to the age mix in assembling the contestants for an episode because:
No episode has ever had all four contestants from the same age range
No episode has ever had three of the four contestants from the over 60 age range
Only 19 episodes (as outlined above) have had three of the four contestants from the 46 to 60 age range
Only 3 episodes have had three of the four contestants from the 36 to 45 age range
Only 22 episodes have had three of the four contestants from the 20 to 35 age range
No episode has ever had all four contestants aged over 45
Only 20 episodes have had all four contestants aged 45 or under
SUMMARY AND CONCLUSION
It’s clear that individual performance and behaviour on the UK Chase vary with the age and gender of a contestant.
Younger contestants tend to accrue smaller Cash Builders and are more likely to take the Low offer
They are, nonetheless, least likely to get home and therefore tend to contribute least to the Prize Fund
Those aged 46 to 60 tend to accrue the largest Cash Builders. They are also most likely to get home once you adjust for the chosen offer, and tend to contribute the largest amounts to the Prize Fund
When it comes to taking money home, however, we see relatively little variation with age, though a little more with females than males.
Females, generaly speaking:
Accrue slightly smaller Cash Builders at any given age (mostly around half a question’s worth)
Contribute less, on average, to the Prize Fund
Take home less, on average, in prizemoney
It’s less clear what the perfect age mix of a team might be, partly because the UK Chase producers strive to prevent strong age imbalances, which means, for example, that there has never been a team full of contetsnats from the 46 to 60 age range, or even all aged over 45.
IN THE FUTURE
I am planning to do something with the occupation data eventually, but still need to find a good R package that will convert job titles into occupations for some occupation schema like OSCA. I’ve tried the LabourR pakage, but it doesn’t seem to do a satisfactory job. Please let me know if you are aware of a better package.
Doubtless, there’ll be more I can do with the age and gender data too, and I’ve also been provided with the question-by-question Final Chase progress data, so there might be something with that.
Your questions and suggestions for any further analyses are welcomed, too.
