Maybe I missed something in your question but I don't really understand Harold's answer... Here is a code that does strictly what you asked for, it counts the total cumulative value of 4 numbers entered in a form and shows it on a Spreadsheet.
I called the 4 questions "race number 1", "race number 2" ... and the result comes on row 2 so you can setup headers.
I striped out any non numeric character so you can type responses more freely, only numbers will be retained.
form here and SS here (raw results in sheet1 and count in Sheet2)
script goes in spreadsheet and is triggered by an onFormSubmit trigger.
function onFormSubmit(e) {
var sh = SpreadsheetApp.getActiveSpreadsheet().getSheetByName('Sheet2');
var responses = []
responses[0] = Number(e.namedValues['race number 1'].toString().replace(/\D/g,''));
responses[1] = Number(e.namedValues['race number 2'].toString().replace(/\D/g,''));
responses[2] = Number(e.namedValues['race number 3'].toString().replace(/\D/g,''));
responses[3] = Number(e.namedValues['race number 4'].toString().replace(/\D/g,''));
var totals = sh.getRange(2,1,1,responses.length).getValues();
for(var n in responses){
totals[0][n]+=responses[n];
}
sh.getRange(2,1,1,responses.length).setValues(totals);
}
edit : I changed the code to allow you to change easily the number of responses... range will update automatically.
EDIT 2 : a version that accepts empty responses using an "if" condition on result:
function onFormSubmit(e) {
var sh = SpreadsheetApp.getActiveSpreadsheet().getSheetByName('Sheet2');
var responses = []
responses[0] = Number((e.namedValues['race number 1']==null ? 0 :e.namedValues['race number 1']).toString().replace(/\D/g,''));
responses[1] = Number((e.namedValues['race number 2']==null ? 0 :e.namedValues['race number 2']).toString().replace(/\D/g,''));
responses[2] = Number((e.namedValues['race number 3']==null ? 0 :e.namedValues['race number 3']).toString().replace(/\D/g,''));
responses[3] = Number((e.namedValues['race number 4']==null ? 0 :e.namedValues['race number 4']).toString().replace(/\D/g,''));
var totals = sh.getRange(2,1,1,responses.length).getValues();
for(var n in responses){
totals[0][n]+=responses[n];
}
sh.getRange(2,1,1,responses.length).setValues(totals);
}