Why do police effect most arrests without a warrant?

Because most offenses occur within their presence or under conditions under which there is 'fresh pursuit. Also, due to the fact that the identify of the actual offender and their physical appearance, and addresses of the wanted offenders is known. Warrants are necessary for offenses in which the identity of the offender is not immediately known or clear, and require investigation and the development of probable cause to make an arrest, or for misdemeanors which do not occur in the officers presence. Traffic offenses are, of course, self-explanatory.