The Chase Australia : What's in a Name Gender?
/For today’s blog we’re returning to analyse this Google document from James Spencer, which covers the entire history of Andrew O’Keefe’s reign as host from late 2015 to mid-2021, with the intention of understanding what, if anything the name gender composition of a team tells us about their likely performance.
To do this, we need to attach name genders to each of the contestant names in the document, which we do, firstly, using Derek Howard’s Gender by Name database. That leaves a number of names ungendered - including a surprising number of Bec’s and Lachie’s - which we manually gender by conducting web searches, tip-toeing through the minefield of pseudo-informative baby name websites that are out there. We then set a name’s name-gender to Male if the male probability assigned to it is 75% or more, and to Female if the male probability is 25% or less. On inspection, a few names from the Howard tool have been mis-name gendered in my opinion, so, as a final step, I alter them.
In the end, of the 3,708 contestants from the 927 episodes not aired on a Sunday and with exactly 4 contestants, only 99 cannot be name-gendered. Those 99 are spread across 95 different episodes.
WHO SITS WHERE?
There have been slightly more contestants with male-gendered names (which, for brevity, I’ll just call males from here onwards) than with female-gendered names (henceforth females), and females have been disproportionately placed in Seats 3 and 4.
For any given Seat Number, males tend to record higher Cash Builders than females, though the effect size ranges from only about $450 to $900. Bootstrapped confidence intervals for the difference between average male and female Cash Builder amounts by Seat Number suggest that these differences are all non-zero except, perhaps, for Seat 4.
The same is true for the Amount Contributed, where males, on average, put about $600 to $1,500 more into the Prize Fund, depending on which Seat we look at. Again the bootstraps for male v female differences suggest that all are likely non zero, except for Seat 4.
(Technical note: the bootstrap estimates are made by creating new samples of the same size as the actual data by sampling from the original data with replacement. We then calculate the difference between the means of these new samples, and repeat the process 10,000 times. In essence, we assume that the observed values of, say, Cash Builder amounts from males in Seat 1 is an unbiased sample of the universe of such amounts, and then proceed to create new samples from those observations as if they were the population. The first time I ever used bootstraps was back in the late 1980s as part of my Honours thesis).
CHOOSING AN OFFER AND GETTING HOME
In terms of Offer selection, the table below reveals that:
Males and females from Seat 1 have a similar profile of Offer choices, including taking the Middle offer about 91% of the time
Females in Seat 2 are twice as likely to take the Low Offer as males in Seat 2, though still only do so about 1 time in 10
Males and females from Seat 3 have broadly similar profiles of Offer choices, including taking the Middle Offer slightly less than 90% of the time
Females from Seat 4 take the Low Offer about 1 time in 6 compared to 1 time in 11 for males in Seat 4
Overall, females take the Low Offer about 10% of the time and the High Offer about 5% of the time, while males take the Low Offer only 7% of the time and the High Offer 6% of the time
Although we need to exercise some caution because of the small sample sizes in some cases, we do see some differences in the rates at which males versus females get home after having chosen an Offer:
In Seat 1, males taking the High Offer have contributed to the Prize Fund almost 40% of the time (6 of 16 have done so) while less than 10% of females have done so (1 of 12). Conversely, almost 85% of females have landed the Low Offer from this Seat, compared to less than 65% of males
Seat 2 shows higher conversion rates for males and for females, especially for those taking other than the Middle Offer. Almost half the males taking the High Offer (15 of 31) have contributed to the Prize Fund
Seat 3 sees particularly high conversion rates for those taking the Low Offer, but also reasonable success rates for those taking the High Offer (7 of 24 for males, and 5 of 26 for females)
Seat 4 represents the best conversion rate for females taking the High Offer (almost 40%, which is 11 from 28) and also the second-highest conversion rate for females taking the Low Offer
Overall, females have about a 5% point higher conversion rate than males when taking the Low Offer, but a 3% point lower conversion rate when taking the Middle Offer, and a 10% point lower conversion rate when taking the High Offer. All told, about 62% of females contribute to the Prize Fund, and 63% of males do likewise.
GENDER COMPOSITION OF THE ORIGINAL TEAM
The Chase producers have a fairly clear preference for teams with two females and two males since that has been the composition in 638 of the 832 episodes (about 77%) where all four contestants have been name-gendered.
Looking across all possible gender compositions (ie, the sub totals in the table) we find that:
The highest win rate (31%) has been achieved by teams with 3 females and 1 male, although such teams have competed in only 59 episodes. Next best are the 31 all-male teams with 29%
The 10 all-female teams have done best at getting contestants through to the Final Chase, while the 31 all-male teams have done next best. That has helped these two combinations set the highest average Prize Funds
The all-male teams have the highest average team Winnings, ahead of the teams with 3 females and 1 male
In the columns on the righthand side of this table we compare the winning rate and winnings performance of different team compositions to that for teams with 2 females and 2 males. We see that:
All-female teams tend to win less often and win less money, although the bootstrapped confidence intervals suggest that we can’t be too certain that this observed result isn’t down to chance
Teams with 3 females and 1 male tend to win more often and win more money, although, again, the bootstrapped confidence intervals suggest that we can’t be too certain that this observed result isn’t down to chance
Teams with 1 female and 3 males tend to win very slightly less often and win less money, although, here too, the bootstrapped confidence intervals suggest that we can’t be too certain that this observed result isn’t down to chance
All-male teams tend to win more often and win more money, although the bootstrapped confidence intervals here especially suggest that we can’t be too certain that this observed result isn’t down to chance
The main message here about these comparisons is that we don’t really have enough data yet, given the levels of variability we’ve witnessed, to make any confident assertions about which team composition is likely to be more successful than any other.
GENDER COMPOSITION OF THE FINAL TEAM
The gender balance that we see in original teams broadly persists in the composition of final teams, with:
101 of 132 (77%) final teams of size four comprising 2 females and 2 males
276 of 304 (91%) final teams of size three including at least 1 female and 1 male
166 of 288 (58%) final teams of size two comprising 1 female and 1 male
We see, as we would expect, that larger final teams tend to have higher win percentages but, within teams of the same size we have:
Two female / One male teams outperforming Two male / One female teams in terms of win percentage, pushback conversion, and mean winnings
Two female / No male teams outperforming Two male / No female teams in terms of win percentage, pushback conversion, and mean winnings (although the sample sizes are much smaller here)
Sole female teams outperforming solo male teams in terms of win percentage and mean winnings (but not pushback conversion)
This would suggest that female-heavy teams perhaps do slightly better than male-heavy teams in Final Chase, To investigate this further and attempt to obviate some of the sample size issues, in the following table we group some of these final team compositions based solely on their gender mix and create bootstrap confidence intervals to allow us to assess if the effect sizes we’re seeing are likely to truly be non-zero.
Regrettably, sample size issues still confound us, but we find that:
For four-person final teams:
Majority female teams tend to do worse than balanced teams, although we can’t discount that the true differences are zero
Majority male teams tend to do better than balanced teams, although we can’t discount that the true differences are zero
Majority male teams tend to do particularly better than majority female teams, although we can’t discount that the true differences are zero
For three-person final teams:
Majority male teams tend to do worse than majority female teams, although we can’t discount that the true differences are zero
For two-person final teams:
Majority female teams tend to do better than balanced teams, although we can’t discount that the true differences are zero
Majority male teams tend to do better than balanced teams, although we can’t discount that the true differences are zero
Majority male teams tend to do worse than majority female teams, although we can’t discount that the true differences are zero
For one-person final teams:
Male solo teams tend to do worse than female solo teams, although we can’t discount that the true differences are zero
SUMMARY AND CONCLUSION
Not for the first time have I performed an analysis and wished for a little more data, but that is what is preventing us from making firmer conclusions here.
Nonetheless, I think we can say the following:
Females are definitely slightly more likely to be positioned in Seats 3 or 4
Males, especially in Seats 1 to 3, have higher Cash Builders and contribute more to the Prize Fund than do females from the same Seats. The effect sizes are relatively small, however (less than half a question in the Cash Builder and only about $1,000 to $1,500 in the Prize Fund)
Given the Seat they are in, males and females make meaningfully different Offer choices but ultimately get home at about the same rate
It’s hard to be definitive about the effects of original team composition on a team’s performance, although those with more females seem to do slightly better than original teams with more males in terms of winnings. Again, though, the effect size is small
Similarly, it’s hard to be definitive about the effects of the final team composition, but it seems that, in four-person final teams, male-dominated ones do slightly better generally (although there aren’t that many) and, in smaller final teams, female-dominated ones do slightly better
I’ll finish with one final set of statistics, which I think highlights the overall small effect of name gender on success on The Chase:
About 18% of all females can expect to walk away with some money
About 18% of all males can expect to walk away with some money
Females can expect to walk away with $2,282
Males can expect to walk away with $2,254
