Need we nofollow all links from sidebar

[alexod]

Hello

One month ago one our Spasish print media partners (we pay for offline adv on this magazine) include our banner in their website sidebar with th link (dofollow) to spanish main page (domain.com/spanish/). The problem was that for a short time we got >30k backlinks (from www + w/o www + IP).
Magazine's domain is Ok - have DA >50, but they have 3 versions of their website online (www + w/o www + IP) indexed by G.

Two weeks ago i asked their webmaster to switch all links to Nofollow.

1. Please let me know is right decision or it will be better to keep this links Dofollow ?

2. All these links were dofollow 2 weeks, now we turned off this links to nofollow, can this hurt our website ranking (lost of such huge amount of links for short time ) ?

any advice will be appreciated !

[martinibuster]

The course of action that adheres to recommendations by Google is to turn the advertising into nofollow.

[NickMNS]

I agree with Martinibuster above, but it may hurt your ranking.

[toidi]

(we pay for offline adv on this magazine) 

Does this mean you pay for print ads? Are you paying for the links in question?

[martinibuster]

Are "free" ads still advertising
Some periodicals throw in Internet advertising for free. But it's still advertising and it's still paid for (even if it's thrown in for "free"). You can't get the "free" ad unless you purchase the print ad, right?

Anecdotal evidence
As for whether putting no-follows on the ads after the fact will cause a penalization, I only have anecdotal evidence from clients who've done that and not suffered for it.

I am aware there is a ten or twelve year old discussion here by a longtime WebmasterWorld member who suffered a rankings drop from Run of Site (ROS) links in the navigation. Not quite the same but similar.

Does Google still rely on statistical analysis of links?
Just my opinion but I don't think Google relies on statistical analysis of inbound/outbound link features as it once did, not since Penguin. As I understand it, statistical analysis had a spam catching success rate of about 80-81% and a false positive rate of between 1-3%. It's possible that it's still in use in some way, but it seems to me that Penguin has superseded statistical analysis.

Ways in which Google devalues links
Then there's the consideration that Google (highly likely) devalues links that are in proximity to words like "sponsors" (just as it devalues links for other reasons, like those in the footer).

Another consideration is the possibility that those links may have been devalued (if they were image links) because they were formatted in an IAB standard height and width.

Yet one more consideration is that those links were additionally devalued because of their status of being ROS, which are dampened so that they do not produce the effect of 30,000 links but just the effect of one link (in addition to any further diminution of link power).

One more consideration is that legitimate links are normally added and dropped from ROS placements, like blogs. So a temporary addition and subtraction of a ROS link might or might not invite scrutiny. Probably less likely if all other Penguin related ducks are ok.

But that's just my opinion and not a statement of fact and is open for debate.

So please do not hesitate to ask questions or explain in detail why you may have doubts about any of the above statements. :)