Measure your battery dimensions and look on the chart at the link below to find a matching group number.
Your mention as a "large motorcycle battery" sort of leads me to think of a group 22 battery.

Here is a link that might be useful: Some battery sizes chart

You mention Briggs.
Briggs OHV engines require the valves to be properly adjusted for the compression release to function.
Many a battery & starter motor has been replaced on these engines NEEDLESSLY.
Your battery may be on its last legs, but you can get it load tested for free at many battery retailers/auto parts stores.
I'd suggest you do that if the valve adjustment doesn't work.

Thanks folks! The battery link will be real handy, and not only for this situation.

As to the valves... It was 26 degrees the night before and the battery is 7 years old. About 30 minutes on the charger and the machine fired up just fine. I will check my maintenance log to verify that I checked the valve adjustment on schedule.

Back to the battery size - my bad. I dipped my tape measure down the side of the battery to measure the depth of the battery box. It must have hung up on something as I had recorded 7" which is less than the height to the top of a U1 size battery. I searched the Scag manual and found that the battery is "not stocked by Scag" according to a parts diagram.

I called the dealer and was told they use "a 12 volt Exide battery" to replace OEM battery in Scag mowers. Not entirely helpful. I then started to make the rounds of the auto parts stores to see if they could match the battery. At the first store the clerk said it was a U1. I indicated that my (incorrect) measurement showed a U1 to be too tall. Upon close examination of the OEM battery they found U1 and some other numbers vibra penciled on the top of the battery case. A re-measurement showed that a U1 would in fact fit. However...

There are several U1 species. The store had a U1 rated for 12 HP, a U1H rated for 19 HP and a U1JD (John Deere) rated for 35 HP. I went to the the Scag dealer next to find out which U1 battery was correct. They stated it should be 325 CCA. the one they had in stock was 300 CCA.

Bottom line... I will run the current battery until I get all the goody out of it. Then I my replace it with a U1 "riding mower battery" although they only have a 30 day warranty. Or I may spring for an AGM battery which is a little more resistant to vibration and generally carries a better warranty. Although 7 years from a U1 is not too bad.

Thanks again,

Ken