To the extent we can measure these things, it looks like Sen. Ted Cruz's (R-Tex.) big gamble -- refusing to endorse Donald Trump at the Republican convention last week -- may have been a bad bet, at least with Republicans.

A new CNN/ORC poll finds that Cruz's public image among Republicans dropped some 50 percent from his image pre-convention. Before the convention, almost two-thirds of Republicans had a positive image of him. That's the kind of likability ratings that politicians who thirst for higher office dream of. (And we have reason to believe Cruz has his eye on 2020.)

After the convention, Cruz's likability tanked. Now, roughly one-third of Republicans have a positive image of him.

When politicians' numbers drop this dramatically, it's usually because of something they did. That something for Cruz, of course, was when he provided one of the most dramatic and defiant moments of the GOP convention by refusing to endorse Trump.

The audience's bookended emotions regarding the former Trump rival's speech actually mirror Cruz's image before and after the convention. As I wrote Wednesday: "[Cruz] was welcomed so warmly onto the stage in Cleveland by Republican delegates, he had to wait for the applause to die down before giving his speech. Some 2,000 words later — as it became clear he had no intention of endorsing Donald Trump — he was booed off it."

In the moment, Cruz didn't seem to care. Cruz was not speaking to those die-hard Trump fans booing him in the convention hall. He was speaking to a Republican Party watching on TV and still very much uncertain about whether to embrace Trump.

Cruz is a long-game kinda guy, and he appeared to be calculating that if and when Trump's campaign falls flat, his defiance of it will help vault him into a position as leader of a party that realized its mistake with Trump.

Whatever happens down the line, we have early results on the short-term impact. And they aren't good. According to the CNN/ORC poll, Cruz's image among all Americans also took a hit after his convention speech, falling almost 10 percentage points, from 36 percent to 27 percent.

This isn't the first time Cruz has grabbed headlines to the detriment of his public image. After he became the face of an October 2013 government shutdown, Cruz became twice as unpopular with Republicans who don't align with the tea party, according to the Pew Research Center. But his popularity soared with people who already liked Cruz. After the shutdown, some 74 percent of tea party-affiliated voters had a positive image of Cruz.

It's important to remember polls are a snapshot in time. How this plays out weeks, months, years from now has a lot to do with whether Trump wins or loses in November.

If Trump loses, Cruz might -- might -- have positioned himself well to take the mantle. If Trump wins, the world might well remember Cruz as the guy who torpedoed his career by defying Donald Trump.

Correction: This post originally misstated Cruz's poll numbers among all Americans after his speech at the Republican convention -- they went down, not up -- and, in our description, highlighted the wrong poll numbers from Pew Research Center.