The George W Bush presidential library is opening this week. Not surprisingly, fans of the former president are out in full force trying to help with the rehabilitation's of Bush's image.

Bush, of course, ended his presidency with an approval rating around 30%. This previous low, combined with the library opening, has helped give an impression of elevation to a new ABC/Washington Post poll that put his retrospective job approval rating at 47%.

The fact that President Obama's approval rating in the current HuffPollster aggregate is a similar 48% only helps with the intrigue. The Washington Free Beacon wrote an article titled "Dubya's Approval Matches Obama's". Add on the fact that Obama's approval rating and Bush's retrospective approval on the economy approval rating are about the same, and you got the makings of a great press narrative.

Let me be the one who tries to nip this story in the bud. I have no clue what type of person George W Bush is, or how history will view him in the future. What I do know is that the 47% retrospective approval rating should be put in context.

First, retrospective approval ratings should almost never be compared to current job approval ratings. Humans have a tendency to remember their elected officials more fondly than they did when they left office. Back in 2010, Gallup asked Americans what their retrospective approval rating was for Presidents John F Kennedy through George W Bush. In every instance except for one, the retrospective approval was higher than the final approval was when they left office.

Most Republicans, for instance, love to make fun of Jimmy Carter. Carter was the only president of the 20th century to lose re-election after replacing a president of a different party. He left office with a 34% job approval rating. His retrospective job approval rating in the 2010 Gallup poll jumped by 18pt.

Second, Bush's retrospective approval is the second worst among presidents in the last 50 years ago. To save you doing the math, Carter's 52% approval rating is higher than Bush's 47%. Only the Watergate-tainted Richard Nixon recorded a lower retrospective approval than Bush.

Most presidents have retrospective approval ratings above 60%. All but Nixon and Bush have +10 or better retrospective net approval ratings. Thus, not only did Bush tie for the second worst final approval rating while in office, but he is also has the second worst retrospective job approval rating.

Third, the Gallup data should make clear that George W Bush hasn't seen much recovery over the past three years in his retrospective approval rating. The 47% in the latest Washington Post poll is the same as the 47% that Gallup found in 2010. The 50% disapproval now is nearly identical to the 51% three years ago. Yes, people view him more rosily now than they did during his presidency, but that effect has been baked in for a while now. He's not getting more loved as time goes by.

Finally, the retrospective approval rating probably gives a false sense of how Americans view Bush now. Remember that a retrospective approval is exactly that – retrospective. The better way to view how Bush stands with the American public is his current favorable ratings. In the past two years, there have been five polls conducted that have asked about Bush's favorable rating with the American public.

Bush currently holds an average -5pt net favorable rating with the American public. President Obama's favorable rating is almost exactly the reverse of that, at +7pt in the HuffPollster aggregate. Indeed, even the losing Republican nominee Mitt Romney ended the 2012 campaign with a higher net favorable than Bush, at -3pt.

It's no wonder that President Bush continues to hurt the Republican party. Mitt Romney tried his hardest to tie what many saw as a lackluster economy in 2012 to President Obama. The problem was that most Americans still blamed Bush over Obama. In the network exit polls, 53% said the economic problems were more Bush's than Obama's fault. Only 38% of Americans disagreed.

So, George W Bush may be more fondly thought of now than he was when he left office, yet this is to be expected – and discounted. Almost all presidents see a boost after they leave office. Bush is still quite unpopular compared with other former presidents, and his current favorable rating is far worse than President Obama's. No library opening is changing that. Republicans would be wise to stay away from embracing George W Bush for the time being.

• This article has been amended to reflect updated polling data as of 25 April 2013.