Short answer: the evidence is mixed, and the common claim that online haggling reliably gets you a better price is not well supported.
What tends to help is the price information you gather online, not the message you send. Compare the dealer's listed price with what similar cars sold for (sites like Kelley Blue Book, Edmunds and the dealer's own list of recent sales are good places to start), and ask for an out-the-door price in writing, which includes taxes, documentation fees and add-ons. Being able to name a specific competing offer is what moves a dealer most.
What tends to hurt is the form: many dealers respond to an online price request with a generic 'come on in' message, a lowball figure meant to get you through the door, or a quote that drops fees when you arrive. A written out-the-door quote from two or three dealers, each sent by email, is a cleaner test than one haggled number.
The math that matters is the total you pay, not the sticker. A $500 cut on a $35,000 car is about 1.4%, and fees or financing terms can easily swing more than that. Ask for the total, the loan term and the rate separately so one can't hide the others.
I don't have a current study that measures how much online negotiation saves on average, so I can't give you a typical percentage. If you tell me the make, model and region, I can search recent price data and dealer reviews for you.
To Tally's point that there's no current study on average savings, there is a well-known one that's older but directly on this question. Scott Morton, Zettelmeyer and Silva-Risso published "How the Internet Lowers Prices: Evidence from Matched Survey and Auto Transaction Data" in the Journal of Marketing Research in 2006. The authors matched survey responses from car buyers with their actual transaction prices, and they found that buyers who used internet price information paid less than comparable buyers who didn't, with the savings concentrated among people who used the internet to learn dealers' costs or other buyers' prices. What it measured is real purchase prices in the US car market in the early-to-mid 2000s, so it can't tell you how dealers or online forms work today. It also suggests a modest effect rather than a guaranteed discount, which fits Tally's advice to focus on the information you gather rather than the message you send. I'd check the paper's own tables for the size of the effect before relying on any single percentage, since I'm working from memory on that figure. The practical takeaway from the study is the same one Tally gave: use the data to get an out-the-door price in writing from more than one dealer.
