ranking

How To Calculate the Elo-Rating (including Examples)

In sports, most notably in chess, baseball and basketball, the Elo-rating system is used to rank players. The rating is also helpful in deducing win probabilities (see my blog post Elo-Rating and Win Probability for more details on that). Suppose two players or teams with the current ratings r(1) and r(2) compete in a match. What will be their updated rating r'(1) and r'(2) after said match? Let’s do this step by step, first in general terms and then in a numerical example.

The first step is to compute the transformed rating for each player or team:

R(1) = 10r(1)/400

R(2) = 10r(2)/400

This is just to simplify the further computations. In the second step we calculate the expected score for each player:

E(1) = R(1) / (R(1) + R(2))

E(2) = R(2) / (R(1) + R(2))

Now we wait for the match to finish and set the actual score in the third step:

S(1) = 1 if player 1 wins / 0.5 if draw / 0 if player 2 wins

S(2) = 0 if player 1 wins / 0.5 if draw / 1 if player 2 wins

Now we can put it all together and in a fourth step find out the updated Elo-rating for each player:

r'(1) = r(1) + K * (S(1) – E(1))

r'(2) = r(2) + K * (S(2) – E(2))

What about the K that suddenly popped up? This is called the K-factor and basically a measure of how strong a match will impact the players’ ratings. If you set K too low the ratings will hardly be impacted by the matches and very stable ratings (too stable) will occur. On the other hand, if you set it too high, the ratings will fluctuate wildly according to the current performance. Different organizations use different K-factors, there’s no universally accepted value. In chess the ICC uses a value of K = 32. Other approaches can be found here.

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Now let’s do an example. We’ll adopt the value K = 32. Two chess players rated r(1) = 2400 and r(2) = 2000 (so player 2 is the underdog) compete in a single match. What will be the resulting rating if player 1 wins as expected? Let’s see. Here are the transformed ratings:

R(1) = 102400/400 = 1.000.000

R(2) = 102000/400 = 100.000

Onto the expected score for each player:

E(1) = 1.000.000 / (1.000.000 + 100.000) = 0.91

E(2) = 100.000 / (1.000.000 + 100.000) = 0.09

This is the actual score if player 1 wins:

S(1) = 1

S(2) = 0

Now we find out the updated Elo-rating:

r'(1) = 2400 + 32 * (1 – 0.91) = 2403

r'(2) = 2000 + 32 * (0 – 0.09) = 1997

Wow, that’s boring, the rating hardly changed. But this makes sense. By player 1 winning, both players performed according to their ratings. So no need for any significant changes.

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What if player 2 won instead? Well, we don’t need to recalculate the transformed ratings and expected scores, these remain the same. However, this is now the actual score for the match:

S(1) = 0

S(2) = 1

Now onto the updated Elo-rating:

r'(1) = 2400 + 32 * (0 – 0.91) = 2371

r'(2) = 2000 + 32 * (1 – 0.09) = 2029

This time the rating changed much more strongly.

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Keywords: How To Use Them Properly On a Website or Blog

Because keywords help determine the ranking of your website, and therefore how visible your pages are to Internet traffic, it is important to use keywords properly in the creation of your blog or website.

In today’s world of Internet lingo, you may frequently hear the terms “keywords,” “search engine rankings,” and “keyword search results” bandied about. However, not everyone knows what keywords are, and how important they are to the success of a website.

Keywords are essentially words or phrases that summarize the topic of a site. When a Web surfer types a word or phrase into the blank field of a search engine such as MSN or Google, the search engine returns a list of related sites. Each site on this list is determined by the presence of the search terms, or keywords, in the site’s meta tags, image tags, and content.

Keywords and Meta Tags

Meta tags are like a site’s “dog tags.” They identify the site’s title, description, and keywords. Meta tags are invisible to Web surfers, but they are instrumental in a search engine’s recognition of the site’s content.

Title Tags

A title tag gives the title of the Web page. A title should only be around six words long, and the primary keyword – the word or phrase that the site is primarily identified with – should be in this title tag. The closer to the beginning of the title the primary keyword is, the stronger the association with that keyword will be.

Description Tags

A Web page’s description tag provides the search engines with a summary of the content contained on the page. Once again, the primary keywords for this page should be contained in the description, as close to the beginning as possible. Description tags only allow 200 characters of text.

Keyword Tags

The keyword tag lists all of the keywords that can be associated with the Web page. The primary keyword used in the title and description tags should be first, followed by other keywords in order of importance and relevance. Although keywords can be separated by commas, they don’t have to be; however, keywords should not be repeated more than three times, lest the Web page be rejected by the search engines as spam. Between 800 and 1,000 characters are allowed for keyword text.

Keywords and Image Tags

Image tags are the text that shows up in place of an image, if the image fails to load for any reason. However, image tags serve a more important function: they allow the search engines to “read” your images. Without image tags, search engines have no way of interpreting your images. Therefore, image tags can also help boost the visibility and relevancy of your site to search engines.

Keywords and Web Page Content

The tags that you use on a Web page are important identifiers for search engines. However, in order to maintain a respectable search engine ranking, your Web page must establish relevancy. In other words, the keywords in your tags must pertain to the actual content on the page. Therefore, the same keywords you list in your tags must be used within the text your page displays.

The most important part of the content is the opening paragraph. The primary keyword – the keyword that was used in the title and description, and listed first in the keyword text – should be used several times in the first paragraph, and then occasionally throughout the rest of the page. Other, less important keywords can be used occasionally throughout the content, as well. This will indicate to the search engines that your page really is relevant to the keywords listed in your tags.

Another way to judge keywords is via a concept called “keyword density.” Keyword density shows the frequency at which a keyword is used. The density is calculated by taking the total number of words and dividing it into the number of times keywords appear in the text. The resulting number is multiplied by 100 to create a percentage. Keyword density can be a tricky business, however. Too low a density will fail to be noticed by the search engines, whereas too high a density can cause a Web page to be rejected as spam. Typically, a keyword density of around 5% is sufficient.

The Importance of Keywords

Keywords are a vital part of the creation of Web pages because they directly affect how visible the page will be to search engine traffic. The presence of keywords needs to be a consideration in every aspect of designing a Web page: designing the tags as well as writing the content. Because of the impact keywords can have on the success of your site, it’s important to know how to use them properly.

Find out more on how to optimize your blog here: Increase Views per Visit by Linking Within your Blog.