This may be an obvious exercise to some, but I overcomplicated it initially and after trawling through Google, wanted to document my solution for javascript/Salesforce beginners:
{!REQUIRESCRIPT("/soap/ajax/37.0/connection.js")}
var mpArray = [];
try{
var updateMP = new sforce.SObject("Media_Placement__c");
updateMP.Id = "{!Media_Placement__c.Id}";
var incorrectCount = "{!Media_Placement__c.Incorrect_Name_Count__c}"
alert(updateMP.Id);
//Intializing a number data object
var newNumber = Number(0);
//alert(incorrectCount);
//Ensuring 1 is initialized as a number when added to the incorrectCount SObject field
incorrectCount = newNumber + 1;
//alert(incorrectCount);
//Adding the existing value in the field; if field is null SF passes in 0 digit value
updateMP.Incorrect_Name_Count__c = {!Media_Placement__c.Incorrect_Name_Count__c} + incorrectCount;
mpArray.push(updateMP)
result = sforce.connection.update(mpArray);
//don't forget error handling-- for another thread
}
This by itself is likely overcomplicated, but I wanted to ensure that I wasn't concatenating strings but actually performing a mathematical operation since Javascript is infamously loosely typed.
Hope this helps!