Google Sheets

A Series 19 Google Sheets has been created by to track basic information on series of the information. Tabs include:

• Contestants: Information on the contestants, including their name, intials, URL to an image of them, and their seat number.
• Attempt-Tasks: Each contestants task attempt in each episode of the series. This is the most important dataset.
• MetaData: Data used for verification and quality purposes.

Data can be imported into R from Google Sheets via the package googlesheets4. For the purpose of our task in hand, only the Attempts-Tasks and Contestants are only required.

library(googlesheets4)
gs4_auth(email = "themedianduck@gmail.com")
gs_data_link <- "https://docs.google.com/spreadsheets/d/1DruoLL3X1HJAfUzE13_ZlAyXzshRvFHMCIVx9ncM6NI/edit?usp=sharing"

task_attempt_df <- range_read(gs_data_link, sheet = "Attempts-Tasks")

contestants_df <- range_read(gs_data_link, sheet = "Contestants")

A sample of the Attempts-Tasks tab can be found in Table 1.

Do You Want Me To Stop the Clock?

We have a way of estimating probability distribution for a contestant’s placement in a episode! Job done, stop the clock.

One advantage of the ORT approach is the simplicity and intuitive nature of it. It is grounded in reality as it is based on contestant’s placement in each episode. Consequently, it is simple to calculate (low computational power) and can be conveyed easily to others.

Figure 2: Stop the clock Alex!

The Drawback of the Backdraw

However, one potential drawback of the ORT approach is that if a contestant has not ended up in a particular place for a episode, our probability estimate of this event occurring is 0%.

Whilst this is true from the observations we have, it is potentially misleading to assign a probability of 0% with such definitiveness. It could be that this event has not occurred yet (but is still probable and possible), or is an extremely rare event (extremely rare is not the same as impossible).

One consequence of this approach is that at the beginning of the series when data is limited, many of the probabilities will be 0% since we have not observed that particular (contestant, placement ranking) combination. Consequently, the ORT estimated probabilities are likely not representative of what could occur later in the series.

What’s the Situation?

I’ll go into more detail in a later post of how these alternative timelines are simulated, and the generating the probability distribution of contestant placement within an episode. In short:

• The alternative timelines are generated through sampling and simulation based techniques.
• Sampling is performed (with replacement) on existing (contestant, task-attempt) data we have observed to date.
• Additional logic is then employed to group, re-rank and reassign points to contestants based on these samples.
• Once we have simulated these alternative timelines and outcomes, we can then estimate probabilities based on an equation similar to Equation (1).
  • However under MV, we would be considering all alternative timelines we have simulated for both the numerator and denominator, and not just episodes that have brodcasted and observed.

In the statistical literature, this approach is based on concepts concerning sampling (in particular Bootstrapping), and Monte Carlo simulation methods.

The Customised Inhaler Gang

Figure 3: Probability Distribution of a Contestant Placement within an Episode, based on the MultiVerse method.

Figure 4: Series Performance so far for Series 19.

Figure 5: Distribution of Contestant Task Performance.

Where Do we Go From Here?

One potential benefit of the MV approach is that we are likely able to produce distributions on series outcomes. For example:

• We are likely able to produce distributions on each contestants placement at the end of the series.
  • For example, the probability of Fatiha finishing in 5th place at the end of series, or Jason winning the series (how improbable is it, or is it simply impossible?).
• We are able to also produce distributions on each contestants series points.
  • For example, what is the probability of Jason scoring more than 140 points by the end of the series.

Figure 6: You have been warned of these plans…

However, the MV approach to estimate probability distributions of contestant ranking placements within an episode is by no means perfect. There are still some considerations and assumptions that needed to be expanded upon in the future. For example:

• Is 1000 alternate timelines (simulations) sufficient in obtaining the accurate, reliable probability distributions?
  • Ideally, sufficient simulations have been performed such that the distribution does not drastically between randomness settings.
  • A study of the number of simulations required to achieve a stable distribution is likely a topic for another post.
• The proposed MV method does not account for certain Taskmaster idiosyncrasies.
  • For example, we do not distinguish between solo and team tasks. Nor do we account for “5 points to the winner, 0 for everyone else” instances, or Series 18’s Joker mechanism.
• Greater care and understanding of how ties should be handled. In particular, we do not consider tie breakers when two or more contestants having the highest number of points at the end of the episode. The winner of these tie breakers is officially deemed the winner of the episode (they get to take home the prizes), but does not affect the series points.