Report Modelling Basic Course b1.2
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Summary
This report will investigate how a share & win campaign can reach the most people via Facebook. When the campaign is seen, it can be shared and thus seen by more Facebook-users. To increase the number of shares, the model will investigate what the value of the prize should be. At the end, the model will optimize the value of the prize, in order to reach the most people via Facebook for which the ratio: ‘money spent / reached person’ is minimum.
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Content Definition phase
1. Context 2. Problem Definition & Purpose 3. Sub-questions
Conceptualization phase
4. Concept, properties, values and relations
Formalization phase
5. Quantities and their relationships 6. Approximations and assumptions 7. Derivations 8. Special cases 9. Estimates
Execution phase
10. Rephrase the problem statement in formal terms 11 Calculations/Implementation/Simulation 12. Validation and Verification; Accuracy and Precision
Conclusion phase
13. Presentation and Interpretation
Reflections and discussions 14. 15. 16. 17.
Discussion after the Conceptual Model Discussion after the Formal Model Discussion after the Result Discussion after the Solution of the Initial Problem
Reflection on the assignment
18. Extension 19. necessity for improvement 20. possibilities for improvement 21. What aspects of your work are you proud of? 22. What have you learned?
Appendices
23. Used Literature 24. List of definitions 25. List of illustrations
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1. Context
Advertising of goods and services on the internet is booming. One of the advertising strategies is called epidemic marketing. In this strategy people share an advertising message with others and the advertiser uses the social network of the receivers. The infection is initiated by a deliberate choice of a population of initial senders.
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We want to advertise Nike sports shoes to runners. In order to reach as many runners as possible we will use a campaign on social network Facebook. We will set up a so-called share & win action, which is based on the principle that people can share posts on Facebook. Anyone who shares the advertisement, will have a chance to win a new Nike Running Kit advertised. The initial group for this campaign will be the followers of the ‘Nike Running Nederland’ Facebook page. When the campaign is being shared, the friends of the “sharer” get to see the campaign.
These newly reached people do not have to follow Nike Netherlands in order to see the campaign. The newly reached people can in their turn also share the campaign, and have a chance to win a new Nike Running Kit. Our model will optimize the reach of the campaign, for the minimum costs per person reached. The ratio between costs (value of the Nike Running Kit) of the campaign and the reach of the campaign should be as low as possible.
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2. Problem Definition & Purpose
Problem definition
For what value of the prize does Nike spend the less costs per reached person, in order to minimize the costs per reached person.
Problem owner
Nike is the problem owner. Nike wants to show their campaign to a maximum amount of people. How will Nike reach as many people as possible with this advertisement, and what should be the value of the price in the campaign?
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Stakeholders
Nike is the company who is going to run the campaign.
Nike
Facebook is the social platform on which we want to place our advertisement.
Facebook users who liked the page of ‘Nike Running Nederland’ are the initial group, the group of people who are going to see the campaign first. If these Facebook users think the campaign is attractive, they will share it and pass it on on Facebook. Facebook users, who liked the Nike page
This is the group of Facebook users who will potentially see the Nike campaign on their Facebook wall.
Facebook users, friends
Everybody on Facebook. Nike introduces a new Running Kit. Everyone is the target group as Nike targets both people who are already runners, and people they would like to convince to start with running. Target group
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3. Sub-questions
How valuable must the prize that you can win be? What is the maximum reach the campaign will have after 12 days?
image 3.1
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4. Concept, properties, values and relations
image 4.1
The campaign exists of a prize that is advertised and can be won. The campaign is going to be advertised to the initial group at first, which consists of the followers of the Nike Running Nederland Facebook page. The price has a certain value, which influences the chance of winning a price
when sharing. This will influence how many of the Facebook users, who will see the advertisement, are actually going to share the campaign. Every time someone shares the ad, part of their friends will see it on their timelines on Facebook. This is the reach.
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5. Quantities and their relationships
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Relation
Category
Dimensions
Assumptions
Ratio = Value / Reach
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[€]/[people] = [€] / [people]
The only costs are the cost for the prizes which nike is handing out the the winners of the share campaign
valueOfPrize = {40...500} [€]
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[€]
We assume that the value of the prize ranges from a minimum of 40 euros to a maximum of 500
Reach = ((avgNuSeen*sharePer1)^(i+1)/ (AvgNuSeen*sharePer1))*initGroup*seePer
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[people]=(([people]* [naturalNumber]1)^([naturalNumber]+1))/ ([people]* [natualNumber]-1))* [people]* [naturalNumber]
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avgNuSeen
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[people]
We have decided that the average number of fiends who are going to see the campaign is 5
sharePer
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[naturalNumber]
We assume that the sharePer has a maximum value of 85%
i
1
[naturalNumber]
We have chosen that the number of iterations is 4
seePer = 0.70
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[naturalNumber]
We have assumed that on average 70% of the Facebookfriends/followers will see the campaign, as they will check their Facebook feed and page
initialGroup = 73.037
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[people]
The initial group are only the Facebooklikers of the Nike NL Facebookpage
6. Approximations and assumptions We exclude word of mouth and other forms of communication from our model, because we want to focus on the widest possible audience reach, by only using Facebook.
We assume the following:
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For every person who shares the campaign, 5 people will see it. They haven’t seen the campaign before.
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70% of the initial group (i.e. the followers of Nike Running Nederland) will see the campaign when it’s first shared on this Facebook page.
4 Nobody will see the campaign if someone has only liked it, but has not shared it.
15% of all Facebook users will never participate in Share & Win, out of principles.
5 The only costs that are being made, is the price of the prize given away
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7. Derivations Definition
Explanations
Value
initialGroup
Number of people who have 73037 liked the Facebook-page Nike Running Nederland and see the campaign
valueOfPrize = seePercentage
Percentage of people who sees the campaign, we have estimated this number to be 70% of that person’s friends/ followers
0.7
avgNuSeen
Average number of friends who see and share the campaign
5
i
Iterations
4
value
Value and cost of one prize
Maximum value is â‚Ź500
sharePer
The percentage of people that 1500/(value*17+1500) will share when they see it, with a maximum of 85%
reach
Number of people that will see the Nike campaign eventually
ratio
How much money is going to be spend per person
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[
8. Special cases
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2 The reach can not be 0, otherwise the campaign would not reach anyone.
The initial group and the see percentage
are
not allowed
to be 0. If this were the case, the campaign would not reach anyone.
3 The price can not be 0, as then no one would share the campaign.
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9. Estimates
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2 We assume that the duration of the campaign is lasting until 12 days. We assume that one iteration takes 3 days.
The initial group= 73037 This is the number of people who have liked the Facebook-page Nike Running Nederland. These people are all runners.
3 Value of the prize: {10,- ‌ 500,-} ₏
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10. Rephrase the problem statement in formal terms
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11. Calculations/ Implementation/Simulation
image 11.1
Using a graphical calculator we found a minimum of 1.125e^-4 [â‚Ź/reached person] at a value for the prize of â‚Ź406,31.
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That means that with this prize the campaign will reach 1/1.125 E-4*406,31=3.611 million people.
12. Validation and Verification; Accuracy and Precision We don’t think this model is extremely accurate, because we didn’t know all the values for sure. We do however think that the model has a potential to be very accurate with the right amount of research. Unfortunately we did not have enough time or resources to conduct this research. The sources of these uncertainties are mainly the avgNuSeen and the sharePer, as we have not researched
them, but have chosen a value/curve that seemed reasonable and gave a plausible result. The model is not accurate enough to solve this problem now, but like we said it does have the potential to be so with some more extensive research.
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13. Presentation and Interpretation
For the representation of our results we have chosen for a couple of graphs. Our purpose was to optimize, and this way the client can see where that optimum lays and what happens when they decide to have a smaller prize or want to make another change.
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As is visible in the graphs, the ideal value of the prize is â‚Ź406,31. This way you will reach 3.611 million people.
14. Discussion after the Conceptual Model
We exclude word of mouth and other forms of communication from our model, because we want to focus on the widest possible audience reach, by only using Facebook. Because our goal is to reach as many people as possible by getting a maximal amount of likes and shares, we have exluded word of mouth advertisement. Besides that, word of mouth advertisement is calculable. However, with more time we could try to include it in our model.
We assume that if one person sees the campaign through different friends: the percentage is still valid. We made tis assumption in order to minimize the number of values. You can combine values that don’t change and are in the same formula with each other.
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15. Discussion after the Formal Model The numbers 1500 en 17 in the formula for sharePer have been chosen like this because this resulted in a formula with a clear minimum. Furthermore, these values gave a realistic result, and had a percentage of 85% at value=â‚Ź500,which complies with the fact that we assumed that 15% of the people does not share out of principle.
image 15.1
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16. Discussion after the Result
The result of our model says something about the optimal value of the prize you can win. However, the value â‚Ź406,31 is not fully reliable since the formulas and values we used are not completely accurate. We made several assumptions to simplify our model and to make sure we would come to a result.
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17. Discussion after the Solution of the Initial Problem
We believe that we have, very roughly, given a plausible solution for the initial problem. With more time and more resources, we think our model could give an accurate answer to the initial problem.
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18. Extension
If we were allowed to continue working on this model for some more time, we would definitely make it more precise. So we would include more aspects, such as Facebook asking for money when you run a campaign on their website, and less
global assumptions. Due to the time we also have to delete elements from the model, to make it easier and doable in the time we had. With the extra time we could make the calculations more complex and have a more realistic model.
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19. necessity for improvement The purpose of our model is optimization, so the aspects that are important for the model are: genericity, scalability, convincingness and impact.
1 Genericity
the model is already quite generic, as it could apply to any similar campaign by changing the initial group and the value range.
3 Convincingness the convincingness is not that good, because we did not use values which were known we had to assume them and we derived the formulas ourselves, we did not use laws our set formulas.
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2 Scalability
if we want to scale up our model, we can easily scale up the value without doing an extra effort on the model. So the solving effort does not depend on value.
4 Impact
the impact is not that big, because we calculate the optimum ratio. And the company can use this as advice and not for example as decision, they can still change it.
20. possibilities for improvement
1 Convincingness
the assumptions should be further investigated and more precise. Such as the seePercentage, we assumed that it is 70%. This is an example of a quantity we should investigate further to make our model more convincing.
2 Impact
the way we could improve our model is to generate more impact on the results. We could better define a model with a decision purpose in order to generate a result with more impact. In that case the model is not optimizing the value of the winning prize, but advising the company on if they should run the campaign or not.
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21. What aspects of your work are you proud of? At the beginning of the course it was unimaginable for us that we could to create a working model. We did have some prior knowledge on Arduino, but we had not made a model from scratch before. So that now, 8 weeks later, we can present a working model that shows what the optimal value and amount of prices are, is something we are rather proud of. Of course there also smaller parts of the report we are proud of, such as the creation of the formulas. This was a difficult part of the assignment, and something we had to do a multiple times in order to get it right.
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Furthermore, it has been really changeling to make a very abstract assignment really concrete. This took us some time, but it has taught us how to think more abstractly and that this way abstract phenomena can be described in mathematics. So this is also something we think we should be proud of.
22. What have you learned?
During the course we have learned how to translate abstract problems to mathematics. This way everyone knows what you are talking about and this makes you able to communicate with other specialists (e.g. mathematicians, physicians, etc.). In our opinion this is necessary and very useful for a designer, as a designers have to communicate with all the other specialists on the team. Besides that we have learned how to make a model, we have learned how to keep it readable for other people. At simple as it seems, it proved to be rather difficult, as the modeller fully understands his/hers model. In the lectures and in the assignment we got to know the different stages of the modelling process, and how you go from one phase to the other. This structured approach to modelling makes it all a bit easier and has proved to be a very valuable.
Furthermore, we have learned that there are a lot of purposes for a model and how they differ from each other. We know also know that you can’t include too many properties, because otherwise you will get a state space explosion. The course gave us some tools to prevent this, but we, rather thankfully, didn’t need to use them. In lecture week 5 we learned that you have 4 categories of quantities, how they differ, and that you should not include too many category 2 quantities. These lessons were very useful for our model. In the last lecture weeks we were taught how you can check your model, what the differences are between verification and validation, and the differences between accuracy and precision. This knowledge led to us being able to check our model and all our future models.
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23. Used Literature
Nike Running Nederland. (n.d.). Retrieved February 26, 2015, from https://www.facebook.com/NikeRunningNederland?fref=ts
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24. List of definitions Definition
Explanation
initialGroup
Number of people who have liked the Facebook-page Nike Running Nederland and see the campaign
seePercentage
Percentage of people who sees the campaign, we have estimated this number to be 70% of that person’s friends/followers
AvgFriends
The average number of friends a Facebook-user has on Facebook
AvgNuSeen
averageNumber of friends who see and share the campaign
W = Winningchange
A percentage that says something about the winningChance of a pair of shoes
y
Cost of 1 price
W(y)
The ratio between the cost of 1 price divided by the maximum price
Reach
Number of people that will see the Nike campaign eventually
ratio
How much money is going to be spend per person
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25. List of illustrations
1 image 3.1 This is an example of a message that Nike could post on Facebook
image 4.1 The
visualisation
of
our
conceptual model
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image 15.1 image 11.1 This graph with x= value of price and y= money spent/ reached person shows a minimum.
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This graph with x= value of price and y= share percentage shows a maximum