Statistically predicting the number one selling Christmas toy

Features

  • Author: Dr John Fry
  • Date: 21 Dec 2015

There is enduring interest in the media over what will be the number one selling toy this Christmas. The toys of one’s childhood have a certain almost romantic charm about them. As a simple illustration of this the website [1] lists a “hall of fame” of around 30 years of the best selling Christmas toy. Past “winners” include transformers Optimus Prime (1985), Teenage Mutant Ninja Turtles (1990), Pogs (1995), Teksta the robotic dog (2000), the relaunched Tamagotchi (2005) and the Jet Pack Buzz Lightyear (2010). As further evidence of the widespread fascination with toys a list of the projected 50 top-selling toys for this Christmas has also been produced [2].

thumbnail image: Statistically predicting the number one selling Christmas toy

However, the issue of the number one selling Christmas toy is not mere child’s play. The retail value of the UK toy industry has been valued as highly as £6.3bn in 2014 [3] with various commentators labelling 2014 as the best for the UK toy industry since 2010 [4]. With around 90% of children’s toys linked to films and television shows [5] the UK toy industry had high hopes for 2015 with the scheduled release of news films in the Star Wars and Jurassic Park franchises on top of recent signs of growth in the industry. Other bestselling toys this year including Disney’s Frozen Sing-a-long Elsa and Thunderbirds interactive Tracy Island reinforce the link with film and television. All this occurs against the backdrop of Christmas – a highly important time for the UK’s wider retail industry, which targets the “golden quarter” of October to December as the time to make most profit, and the pre-Christmas shopping season that peaks from around mid-November onwards [6].

Whilst once again we feel the “force” of Star Wars, with the new game predicted to sell very well, established titles like Call of Duty, Fifa and Tomb Raider continue to make their presence felt. The suggestion appears to be that there are important differences with film and television titles facing a harder battle to penetrate the video games market compared to the wider toys market.

How can we assess the probability of being the number one selling Christmas toy? One simple way of doing this is to look at bookmakers’ odds. The website for UK bookmaker William Hill [7] lays odds for the number one selling Christmas toy. The underlying probabilities associated with the quoted odds can be calculated as follows. According to William Hill, the odds of the Star Wars lightsabre being the number one selling Christmas toy are 4/1. This means that the implied probability can be calculated by setting 1-p/p=4/1 giving p=0.2. We can continue in this way and calculate the implied probability for the remaining toys in the list. However, once we do this we do not achieve a proper probability distribution: If we add up all the probabilities in the list the total, p total say, does not equal 1. In fact the probabilities add up to more than 1 – roughly 1.4. This does not mean that the bookmakers are incoherent nor does it mean that the bookmakers can be systematically exploited. In this case, this reflects the bookmakers own margin for error and the way in which bookmakers can continue to make a profit in such a thin market.

The best estimate of the probability is given by p/ p total i.e. our initial estimate of the implied probability divided by the sum of all the other probabilities. This simple procedure has a fancy name – renormalisation. The full list of results obtained in this way is shown below in Table 1. Interestingly, by adding up all the probabilities in the table, it seems that there is a roughly one in three chance (p=0.159+0.100+0.072=0.331) that the Star Wars franchise will produce the number one selling Christmas toy – again reinforcing the dominance of film and television in the UK toy market.

Rank Toy Probability of being number one seller
1. Star Wars Bladebuilders Jedi Master lightsabre 0.159
2. Pie Face from Hasbro 0.113
3=. Disney Frozen Sing-a-long Elsa 0.100
Star Wars Kylo Ren's Command Shuttle 0.100
5. Star Wars: The Force Awakens Millennium Falcon 0.072
5. Star Wars: The Force Awakens Millenium Falcon 0.066
6=. City Deep Sea Exploration Vessel from LEGO 0.066
Toot Toot Busy Sounds Discovery Home 0.066
Thunderbirds Interactive Tracy Island 0.066
Little Live Pets Cleverkeet 0.066
Shopkins Food Fair - Scoops Ice Cream Truck 0.066
Paw Patrol Paw Patroller 0.066
12. IDO3D Deluxe Design Studio 0.057

Table 1: Estimated probability of being the number one selling Christmas toySeveral websites (betbreakingnews.com, betfair and paddypower) also quote odds for the related category of the number one selling Christmas video game.

Several websites (betbreakingnews.com, betfair and paddypower) also quote odds for the related category of the number one selling Christmas video game. Here the market appears a little more developed. Implied probabilities can be calculated for each website in the same way as before. Once again we have to do a substantial amount of renormalisation to obtain proper probability distributions that add up to 1 – again reflecting some of the considerable uncertainties involved and the thinness of the market. Finally, overall probabilities obtained can be calculated by taking an average over all three websites. The full results obtained are shown below in Table 2. Whilst once again we feel the “force” of Star Wars, with the new game predicted to sell very well, established titles like Call of Duty, Fifa and Tomb Raider continue to make their presence felt. The suggestion appears to be that there are important differences with film and television titles facing a harder battle to penetrate the video games market compared to the wider toys market.

Rank Video Game Probability of being number one seller
1. Call of Duty - Black Ops III 0.306
2. Star Wars Battlefront 0.228
3. Fifa 16 0.165
4. Fallout 4 0.142
5. Rise of the Tomb Raider 0.054
6. Assassins Creed Syndicate 0.038
7. Grand Theft Auto V 0.019
8. Guitar Hero Live 0.014
9=. Destiny - The Taken King 0.009
Metal Gear Solid V - The Phantom Pain 0.009
11=. Pro Evolution Soccer 2016 0.007
Unchartered - The Nathan Drake Collection 0.007

Table 2: Estimated probability of being the number one selling Christmas video game

The Christmas market for toys and video games is both big business and also of wider interest – to the extent to which people are prepared to place bets and to lay odds. The number one selling Christmas toy also has a rich history [1]. The influence of films and television upon children’s toys is well documented and there appears to be a good chance (roughly 33.1%) that the new Star Wars film will give rise to the number one selling Christmas toy. However, the video games market appears markedly different to the wider toy market and though the new Star Wars game is predicted to sell highly, it is probably less likely to displace well established rivals at the top of the sales charts.

Acknowledgements

The author would like to acknowledge helpful comments from an anonymous reviewer. The usual disclaimer applies.

References

[1] Here are 30 years of the number one selling toys at Christmas - can you spot your favourite? Mirror Website.
http://www.mirror.co.uk/news/world-news/here-30-years-number one selling-toys-6500570     
[2] Top Toys: The 50 toys predicted to fly off the shelves this Christmas as parents are offered to 'reserve' favourites so children won't miss out
http://www.dailymail.co.uk/news/article-2205468/Top-Toys-The-50-toys-predicted-fly-shelves-Christmas-parents-offered-reserve-favourites-children-wont-miss-out.html  
[3] Davidson, L. (2015) Telegraph website.
http://www.telegraph.co.uk/finance/newsbysector/retailandconsumer/11681976/Frozen-Lego-and-video-games-boost-the-struggling-UK-toy-sector-to-staggering-growth.html  
[4] Sabharwal, V. (2015) 2014: best performance since 2010 for British toy market. Retail Gazette Website.
http://www.retailgazette.co.uk/blog/2015/01/12114-2014-best-performance-since-2010-for-british-toy-market  
[5] Top children's toys for Christmas 2015: Must haves and where to buy them cheapest. Mirror Website.
http://www.mirror.co.uk/news/uk-news/top-childrens-toys-christmas-2015-5927503  
[6] The economics of Christmas. Wikipedia.
https://en.wikipedia.org/wiki/Economics_of_Christmas  
[7] Star Wars set to top toy charts as well as the movie charts. William Hill website.
http://www.williamhillplc.com/media/newsroom/media-releases/2015/star-wars-set-to-top-toy-charts-as-well-as-movie-chart/

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