I’ve got a four year old iPhone
It’s one of those mini phones
About four and a half inches tall

Anyway the battery seems to lose its storage capacity now
It drops down quickly after I recharge it

Do I need a new battery or a new charger?
And is it really worth bothering to get a new battery or charger?

Even the best batteries crap out after a while.

Probably not the charger as it does charge.

Look into cost of new battery vs new phone.

Thank you kindly Motown!
I’ll look into the cost of a new battery

You can check for the options below,
1. Check if the phone gets heated too much while charging and the same heat continues to stay even after you remove it from charge. In such cases, the battery could have started to bulge n it's quite dangerous to use as there can be chances it might

2. If (No.1) is not applicable, go to Settings -> App - to see if you have allowed any applications to run in background which might consume the charge. Disable the 'run in background' option in Settings to see if charge issue gets resolved. Sometimes certain automatic updates that keep running in phone can automatically enable 'run in background' for certain apps without our knowledge too in some versions.

3. It might sometimes lessen the charge if mingle or any other chatting app is opened n closed randomly in a repeated way or been used for a longer time, Cleaning up the cache and freeing up the memory can help too.

4.In rare cases, charge gets reduced if there is a backup happening in any of your apps.

I too faced similar issue but with a different mobile n (No.2) worked for me