The statistic will also change in other areas besides WHP. I wondered what "Status Of The Equipped Weapon Changed" meant one time, so I wrote down the exact numbers for the equipped weapon and waited for the next circle.
Sure enough, on the bad side, Holy went down one point on one occasion, on another it was the WHP. I also had, of all things, a point go down on the Metal Breaker chart, which kind of makes sense, since it's the hardest Breaker in the game to get to 99 (unless you throw bombs at the Pirate's Chariots), or buy/find lots of Opals.
Also, if you have $10,000 or more, if you run over one of these circles and get the "Funds Increased A Little" event, it won't be a little. You'll find your funds have increased by a full $10,000. I read this on GameFAQS and was dubious about it, but it actually works. ;^)