I had a bit same case in my project. When I investigated how **Azure Search** works underhood I found that string types all times converted to `Contains` query in **Azure Search**. You can see that if taking a look into **Search.log** for your environment. 

The same issue with the `StartsWith()` function and etc. [check this link][1]: 

In your case I see some scenarios to resolving this issue: 

1. Make a computed field/change type of field `year` on any numeric type. That can be `int`. (Equals for numeric types works well) 
2. Switch to **Solr** (it will take 1-day max but will save a lot of time with Search work). Anyway, the azure search will be deprecated in the next version of Sitecore. Check [this link][2].
3. Use straight requests to Azure Search instead of Sitecore LINQ provider. There exists an Equals function that can be used. (take a lot of time for rewriting and hard to support solution like this)
4. Take a look at the `Wildcard()` LINQ function that allows using Search Engine syntaxis for field requests. Probably it will help too. 

My experience with **Azure Search** was a nightmare till we didn't switch to **Solr Engine** in all environments and removed Azure-related things from a project (before we had Azure Search for production and Solr for development). Because they're a lot of limitations.  


  [1]: https://doc.sitecore.com/developers/90/platform-administration-and-architecture/en/sitecore-azure-search-overview.html
  [2]: https://dev.sitecore.net/Downloads/Sitecore%20Experience%20Platform/100/Sitecore%20Experience%20Platform%20100/Release%20Notes