How does mathematics help Yandex earn?
Yandex earns hundreds of millions of dollars a year, although our search is free. The main income we receive from advertising, connecting sellers with buyers. To do this well, we use complex algorithms created on the basis of mathematical statistics, probability theory, machine learning, game theory, and auction theory. The improvement of algorithms by only a few percent is an additional tens of millions of dollars a year. This lecture will show you how mathematics can work in advertising.
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There are several options for paying for the placement of advertisements on the Internet. The simplest and most profitable model for an advertising platform is CPM (cost-per-mille - cost per thousand impressions). It implies that the payment is solely for the display of ads on the pages of search results. At the same time, the site is not responsible for how well the advertisement was targeted, whether the users liked it, and whether the advertiser brought any profit. Accordingly, this model is not very profitable for an advertiser, and is not particularly popular.
Another model is CPA (cost-per-action). It implies that the advertiser pays only if he has achieved the desired result of the result, for example, the sale of a product or service.
For the advertiser, it is extremely profitable, because he pays only in the case of making a profit on his part. The advertising platform in this model may have some difficulties. After all, even if the advertisement was correctly targeted, the user became interested in the product or service and went to the advertiser's site, it is not at all necessary that the purchase be made immediately. The user can return later, or make an order by phone.
The third model is PPC (pay-per-click), pay per click. It can be said that this is some golden mean, equally beneficial for both the site and the advertiser. The advertiser can be confident that his ads will be shown to users who may potentially be interested in them, and the site avoids the difficulty of fixing the conversion. It is this model that is mainly used in Yandex.
In Yandex, the main advertising targeting is based on the user's request. Suppose a user entered a query [plastic windows in Rostov]. When submitting an ad, advertisers indicate for which keywords in the request they would like to show it, and for which - not. But even in this case, it may turn out that there are too many candidates for the show, from among which it is necessary to select the most suitable.
Suppose we have one advertising space on the issue page. Based on the request, we have compiled a list of candidates for the show and selected from them the three best ads. The first has already been demonstrated 1,000 times, and gained 100 clicks. The second was shown 500 times and also collected 100 clicks. And on the third clicked 300 times for 10,000 hits. If we estimate the probability of clicks, it will be 10%, 20% and 3% for each of the ads, respectively. Obviously, the second ad is the most effective for the user-entered query Those. provided that all three advertisers pay the same amount per click, then the second ad will be the most profitable.
But the rate per click may be different. Suppose that the first advertiser set the pay per click to $ 0.3, the second $ 0.1, and the third $ 2. In this case, the profitability of placing each of the ads varies. Multiplying the probability of a click on a bet, we get the following amounts: for 1000 impressions of the first ad, the site will earn $ 30, the second $ 20 and the third $ 60. Accordingly, the display of the third announcement becomes more profitable. This is a very simplified model, but it allows you to understand how everything works.
How to determine how much money to take per click? After all, the profit from it for each advertiser may be different. The most obvious option is to arrange an auction, then it will become clear how much advertisers are willing to pay for displaying an ad on request with certain keywords. However, the usual auction, in which competitors increase the price and in the end, who offered the highest, pays it, because of some features of the system, it turns out to be disadvantageous to both parties. Therefore, an auction of the second price is used, where the highest bidder also wins, but he pays as much as the previous participant offered.
Usually the advertiser represents approximately how much each click on an ad is to him. If we accept the value of a click for v, and the bid for b, then b must always be less than or equal to v, because otherwise the click will not bring any benefit to the advertiser. The most profitable strategy for advertisers in such an auction is to honestly set the value of b to the value of v. This is not difficult to prove with the theory of auctions.
For example, two advertisers compete for placing ads on one of the ad slots. One of them is betting b, and the second is betting b '. The price that the winner will pay in the end is denoted as c, and it will definitely be less than the value b set by him, because its value is taken from the stake of the loser. The winner’s profit (denoted by s) can be calculated using the formula s = p (v - c), where p is the probability of clicking on an ad when it is shown. Now we prove that it is most advantageous to set b equal to v. We don’t determine what to put b> v to the advertiser initially, so we’ll consider the course of events with b <v. If b 'is greater than v, then the participant who has placed b loses and does not receive any profit. In this case, there is simply no opportunity to win a player with a bet b, since b cannot be greater than v.
And if b 'is less than v, but greater than b, then the first participant loses again, although he had the opportunity to win from him, set b to v. If b is greater than b ', but less than v, then all the same, c will be equal to b', as if b were equal to v. Thus, when b <v, the probability of winning an auction is less, and the final price as a result of winning will still be equal to b '.
After attending a lecture, you will also find out why in such a seemingly simple matter, as advertising, you need such complex things as machine learning and distributed computing.
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What do advertisers pay for?
There are several options for paying for the placement of advertisements on the Internet. The simplest and most profitable model for an advertising platform is CPM (cost-per-mille - cost per thousand impressions). It implies that the payment is solely for the display of ads on the pages of search results. At the same time, the site is not responsible for how well the advertisement was targeted, whether the users liked it, and whether the advertiser brought any profit. Accordingly, this model is not very profitable for an advertiser, and is not particularly popular.
Another model is CPA (cost-per-action). It implies that the advertiser pays only if he has achieved the desired result of the result, for example, the sale of a product or service.
For the advertiser, it is extremely profitable, because he pays only in the case of making a profit on his part. The advertising platform in this model may have some difficulties. After all, even if the advertisement was correctly targeted, the user became interested in the product or service and went to the advertiser's site, it is not at all necessary that the purchase be made immediately. The user can return later, or make an order by phone.
The third model is PPC (pay-per-click), pay per click. It can be said that this is some golden mean, equally beneficial for both the site and the advertiser. The advertiser can be confident that his ads will be shown to users who may potentially be interested in them, and the site avoids the difficulty of fixing the conversion. It is this model that is mainly used in Yandex.
How to select ads?
In Yandex, the main advertising targeting is based on the user's request. Suppose a user entered a query [plastic windows in Rostov]. When submitting an ad, advertisers indicate for which keywords in the request they would like to show it, and for which - not. But even in this case, it may turn out that there are too many candidates for the show, from among which it is necessary to select the most suitable.
What is better to show?
Suppose we have one advertising space on the issue page. Based on the request, we have compiled a list of candidates for the show and selected from them the three best ads. The first has already been demonstrated 1,000 times, and gained 100 clicks. The second was shown 500 times and also collected 100 clicks. And on the third clicked 300 times for 10,000 hits. If we estimate the probability of clicks, it will be 10%, 20% and 3% for each of the ads, respectively. Obviously, the second ad is the most effective for the user-entered query Those. provided that all three advertisers pay the same amount per click, then the second ad will be the most profitable.
But the rate per click may be different. Suppose that the first advertiser set the pay per click to $ 0.3, the second $ 0.1, and the third $ 2. In this case, the profitability of placing each of the ads varies. Multiplying the probability of a click on a bet, we get the following amounts: for 1000 impressions of the first ad, the site will earn $ 30, the second $ 20 and the third $ 60. Accordingly, the display of the third announcement becomes more profitable. This is a very simplified model, but it allows you to understand how everything works.
How much to write off?
How to determine how much money to take per click? After all, the profit from it for each advertiser may be different. The most obvious option is to arrange an auction, then it will become clear how much advertisers are willing to pay for displaying an ad on request with certain keywords. However, the usual auction, in which competitors increase the price and in the end, who offered the highest, pays it, because of some features of the system, it turns out to be disadvantageous to both parties. Therefore, an auction of the second price is used, where the highest bidder also wins, but he pays as much as the previous participant offered.
Usually the advertiser represents approximately how much each click on an ad is to him. If we accept the value of a click for v, and the bid for b, then b must always be less than or equal to v, because otherwise the click will not bring any benefit to the advertiser. The most profitable strategy for advertisers in such an auction is to honestly set the value of b to the value of v. This is not difficult to prove with the theory of auctions.
For example, two advertisers compete for placing ads on one of the ad slots. One of them is betting b, and the second is betting b '. The price that the winner will pay in the end is denoted as c, and it will definitely be less than the value b set by him, because its value is taken from the stake of the loser. The winner’s profit (denoted by s) can be calculated using the formula s = p (v - c), where p is the probability of clicking on an ad when it is shown. Now we prove that it is most advantageous to set b equal to v. We don’t determine what to put b> v to the advertiser initially, so we’ll consider the course of events with b <v. If b 'is greater than v, then the participant who has placed b loses and does not receive any profit. In this case, there is simply no opportunity to win a player with a bet b, since b cannot be greater than v.
And if b 'is less than v, but greater than b, then the first participant loses again, although he had the opportunity to win from him, set b to v. If b is greater than b ', but less than v, then all the same, c will be equal to b', as if b were equal to v. Thus, when b <v, the probability of winning an auction is less, and the final price as a result of winning will still be equal to b '.
After attending a lecture, you will also find out why in such a seemingly simple matter, as advertising, you need such complex things as machine learning and distributed computing.
Source: https://habr.com/ru/post/209482/
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