[Docs] Small edits to Ranking Evaluation API docs (#51116)

Small updates to grammar, syntax, and unclear wordings.

docs/reference/search/rank-eval.asciidoc

@@ -23,7 +23,7 @@ _precision_ or _discounted cumulative gain_.
 
 Search quality evaluation starts with looking at the users of your search 
 application, and the things that they are searching for. Users have a specific 
-_information need_, for example they are looking for gift in a web shop or want 
+_information need_; for example, they are looking for gift in a web shop or want 
 to book a flight for their next holiday. They usually enter some search terms 
 into a search box or some other web form. All of this information, together with 
 meta information about the user (for example the browser, location, earlier 
@@ -31,21 +31,21 @@ preferences and so on) then gets translated into a query to the underlying
 search system.
 
 The challenge for search engineers is to tweak this translation process from 
-user entries to a concrete query in such a way, that the search results contain 
-the most relevant information with respect to the users information need. This 
+user entries to a concrete query, in such a way that the search results contain 
+the most relevant information with respect to the user's information need. This 
 can only be done if the search result quality is evaluated constantly across a 
 representative test suite of typical user queries, so that improvements in the 
-rankings for one particular query doesn't negatively effect the ranking for 
+rankings for one particular query don't negatively affect the ranking for 
 other types of queries.
 
-In order to get started with search quality evaluation, three basic things are 
-needed:
+In order to get started with search quality evaluation, you need three basic
+things:
 
 . A collection of documents you want to evaluate your query performance against, 
   usually one or more indices.
 . A collection of typical search requests that users enter into your system.
-. A set of document ratings that judge the documents relevance with respect to a 
-  search request.
+. A set of document ratings that represent the documents' relevance with respect
+  to a search request.
   
 It is important to note that one set of document ratings is needed per test 
 query, and that the relevance judgements are based on the information need of 
@@ -53,7 +53,7 @@ the user that entered the query.
 
 The ranking evaluation API provides a convenient way to use this information in 
 a ranking evaluation request to calculate different search evaluation metrics. 
-This gives a first estimation of your overall search quality and give you a 
+This gives you a first estimation of your overall search quality, as well as a 
 measurement to optimize against when fine-tuning various aspect of the query 
 generation in your application.
 
@@ -133,26 +133,26 @@ GET /my_index/_rank_eval
 -----------------------------
 // NOTCONSOLE
 
-<1> the search requests id, used to group result details later 
+<1> the search request's id, used to group result details later 
 <2> the query that is being evaluated
-<3> a list of document ratings, each entry containing the documents `_index` and 
-`_id` together with the rating of the documents relevance with regards to this 
+<3> a list of document ratings, each entry containing the document's `_index` and 
+`_id` together with the rating of the document's relevance with regard to this 
 search request
 
 A document `rating` can be any integer value that expresses the relevance of the 
-document on a user defined scale. For some of the metrics, just giving a binary 
+document on a user-defined scale. For some of the metrics, just giving a binary 
 rating (for example `0` for irrelevant and `1` for relevant) will be sufficient, 
-other metrics can use a more fine grained scale.
+while other metrics can use a more fine-grained scale.
 
 
-===== Template based ranking evaluation
+===== Template-based ranking evaluation
 
 As an alternative to having to provide a single query per test request, it is 
 possible to specify query templates in the evaluation request and later refer to 
-them. Queries with similar structure that only differ in their parameters don't 
-have to be repeated all the time in the `requests` section this way. In typical 
-search systems where user inputs usually get filled into a small set of query 
-templates, this helps making the evaluation request more succinct.
+them. This way, queries with a similar structure that differ only in their 
+parameters don't have to be repeated all the time in the `requests` section. 
+In typical search systems, where user inputs usually get filled into a small 
+set of query templates, this helps make the evaluation request more succinct.
 
 [source,js]
 --------------------------------
@@ -194,27 +194,27 @@ GET /my_index/_rank_eval
 
 ===== Available evaluation metrics
 
-The `metric` section determines which of the available evaluation metrics is 
-going to be used. The following metrics are supported:
+The `metric` section determines which of the available evaluation metrics 
+will be used. The following metrics are supported:
 
 [float]
 [[k-precision]]
 ===== Precision at K (P@k)
 
 This metric measures the number of relevant results in the top k search results. 
-Its a form of the well known 
+It's a form of the well-known 
 https://en.wikipedia.org/wiki/Information_retrieval#Precision[Precision] metric 
 that only looks at the top k documents. It is the fraction of relevant documents 
-in those first k search. A precision at 10 (P@10) value of 0.6 then means six 
-out of the 10 top hits are relevant with respect to the users information need.
+in those first k results. A precision at 10 (P@10) value of 0.6 then means six 
+out of the 10 top hits are relevant with respect to the user's information need.
 
 P@k works well as a simple evaluation metric that has the benefit of being easy 
-to understand and explain. Documents in the collection need to be rated either 
-as relevant or irrelevant with respect to the current query. P@k does not take 
-into account where in the top k results the relevant documents occur, so a 
-ranking of ten results that contains one relevant result in position 10 is 
-equally good as a ranking of ten results that contains one relevant result in 
-position 1.
+to understand and explain. Documents in the collection need to be rated as either 
+relevant or irrelevant with respect to the current query. P@k does not take 
+into account the position of the relevant documents within the top k results, 
+so a ranking of ten results that contains one relevant result in position 10 is 
+equally as good as a ranking of ten results that contains one relevant result  
+in position 1.
 
 [source,console]
 --------------------------------
@@ -255,7 +255,7 @@ If set to 'true', unlabeled documents are ignored and neither count as relevant
 ===== Mean reciprocal rank
 
 For every query in the test suite, this metric calculates the reciprocal of the 
-rank of the first relevant document. For example finding the first relevant 
+rank of the first relevant document. For example, finding the first relevant 
 result in position 3 means the reciprocal rank is 1/3. The reciprocal rank for 
 each query is averaged across all queries in the test suite to give the 
 https://en.wikipedia.org/wiki/Mean_reciprocal_rank[mean reciprocal rank].
@@ -297,7 +297,7 @@ in the query. Defaults to 10.
 
 In contrast to the two metrics above, 
 https://en.wikipedia.org/wiki/Discounted_cumulative_gain[discounted cumulative gain] 
-takes both, the rank and the rating of the search results, into account.
+takes both the rank and the rating of the search results into account.
 
 The assumption is that highly relevant documents are more useful for the user 
 when appearing at the top of the result list. Therefore, the DCG formula reduces 
@@ -346,16 +346,16 @@ http://olivier.chapelle.cc/pub/err.pdf[Expected reciprocal rank for graded relev
 It is based on the assumption of a cascade model of search, in which a user 
 scans through ranked search results in order and stops at the first document 
 that satisfies the information need. For this reason, it is a good metric for 
-question answering and navigation queries, but less so for survey oriented 
+question answering and navigation queries, but less so for survey-oriented 
 information needs where the user is interested in finding many relevant 
 documents in the top k results.
 
 The metric models the expectation of the reciprocal of the position at which a 
-user stops reading through the result list. This means that relevant document in 
-top ranking positions will contribute much to the overall score. However, the 
-same document will contribute much less to the score if it appears in a lower 
-rank, even more so if there are some relevant (but maybe less relevant) 
-documents preceding it. In this way, the ERR metric discounts documents which 
+user stops reading through the result list. This means that a relevant document
+in a top ranking position will have a large contribution to the overall score. 
+However, the same document will contribute much less to the score if it appears 
+in a lower rank; even more so if there are some relevant (but maybe less relevant) 
+documents preceding it. In this way, the ERR metric discounts documents that 
 are shown after very relevant documents. This introduces a notion of dependency 
 in the ordering of relevant documents that e.g. Precision or DCG don't account 
 for.
@@ -385,7 +385,7 @@ The `expected_reciprocal_rank` metric takes the following parameters:
 [cols="<,<",options="header",]
 |=======================================================================
 |Parameter |Description
-| `maximum_relevance` | Mandatory parameter. The highest relevance grade used in the user supplied
+| `maximum_relevance` | Mandatory parameter. The highest relevance grade used in the user-supplied
 relevance judgments.
 |`k` | sets the maximum number of documents retrieved per query. This value will act in place of the usual `size` parameter
 in the query. Defaults to 10.
@@ -444,6 +444,6 @@ potential errors of individual queries. The response has the following format:
 <3> the `metric_score` in the `details` section shows the contribution of this query to the global quality metric score
 <4> the `unrated_docs` section contains an `_index` and `_id` entry for each document in the search result for this
 query that didn't have a ratings value. This can be used to ask the user to supply ratings for these documents
-<5> the `hits` section shows a grouping of the search results with their supplied rating
+<5> the `hits` section shows a grouping of the search results with their supplied ratings
 <6> the `metric_details` give additional information about the calculated quality metric (e.g. how many of the retrieved
-documents where relevant). The content varies for each metric but allows for better interpretation of the results
+documents were relevant). The content varies for each metric but allows for better interpretation of the results