Improved is a form of Improve. Compete requires Improve. Compete is a synonym of Contend. Contend is a synonym of Struggle. 
Runner is related to Horse. Horse is related to Field. Field is related to Degree. Quality is a type of Degree. 
Improved --FormOf--> Improve <--HasPrerequisite-- Compete <--Synonym--> Contend <--Synonym--> Struggle 
Runner <--RelatedTo--> Horse <--RelatedTo--> Field <--RelatedTo--> Degree <--IsA-- Quality 