Good question ! I would say go for the focus of creating a well defined navigation as there seems to be a lot of user data about users greatly preferring to use a clear cut navigation as opposed to a search feature to find what they want.
Taking this article Navigation is more important than search
Recently, we did some extensive task testing with a technical
audience. 70 percent started the task by clicking on a link, 30
percent used search.
Similarly Jared spool's article Are There Users Who Always Search?
In our study, we observed 30 users performing 121 different shopping
tasks. Each user visited between 3 and 6 web sites, shopping for items
they told us they were interested in purchasing; no two users were
interested in exactly the same products.
If the search-dominance theory is true, we should've seen a subset of
our users always relying on the search engine to find product
information, while others relied on the links.
When we looked at the data from our study, we found that there wasn't
a single user out of 30 who always used the search engine first when
looking for product information. None of the users in our study were
search dominant. However, we did uncover some link-dominant users.
About 20% of our participants chose links exclusively.
Then, when we looked at the individual sites, we saw that for 21% of
the sites, every single user who visited only used search. It seems
that these sites were search dominant, not the users. Thirty-two
percent of the sites were link dominant (users only used the links on
the site) and 47% were not dominant to search or links.
We find it fascinating that on 53% of the sites we tested, each
visitor stuck with a single location strategy — the same strategy
employed by all the other visitors to that site. This implies that
there is something inherent in the site's design that causes users to
choose the search engine or the links, not a hard-and-fast preference
of the user.
As we talk with the users, we often hear them tell us that they do
have a preference for search — that they are search dominant. All the
time, we hear, "I always go to search immediately." But none of our
users actually did always go to search immediately — yet another piece
of evidence to suggest that what users say they do and what they
actually do are very different.
Taking inputs from this article Navigation Vs Search on The Web Usability Blog
When we do visitor behaviour analysis we often see that the search
feature is rarely used by more than 5% of a site’s total number of
visitors. On our blogs the number of searchers is even lower: around
1,5%. On the website of a Flemish province we’re working for it’s just
Things we know about search During user tests we see the following happen time and time again:
Most people only use the search feature after they’ve tried the navigation or the content links. Search is seen as the last resort.
If people are looking for something very specific, like a product they know the name of, they’re be more inclined to search.
Programmers and engineers use the search feature more often than ‘normal people’.
Lastly this article Search Vs. Browse On Websites has some interesting data found by using heatmaps to determine the user focus
We've studied many websites and watched as some users use a search
first strategy while others go right for the top navigation. We
examined the data from nine recent usability studies with 25 tasks
involving over 1500 users. The websites were a mix of large ecommerce
retail websites, mobile phone carriers, rental car companies and
On average about 14% of users started with search. There was a fair
amount of variability in the data with a low search percentage by task
of 2% and high of 75%.
We noticed the more densely packed retail websites had higher search
(>50%) but more data is needed to confirm that relationship. Given
the sample of websites and tasks we can be 90% confident between 11%
and 21% of users will start with search.
Another study found about a 5% search rate. In 2005, Katz and
Byrne, in a more rigorous examination, found that participants
searched less than 10% of the time, but searched almost 40% of the
time when faced with "narrow, low-scent menus." As expected they
found nuances to why users search based on the labeling, information
architecture and the prominence of the search boxes
I would really draw your attention to the above line that if your search box is prominent and very noticeable, you might have a larger number of users who opt in for search.
The image above has a very prominent large text box which draws attention and is in a prime location and not surprisingly about 50% of participants in this evaluation used the prominent pick-up location text-box as a search box
Lastly coming to the question, do I need a search box at all ? I am not sure what your site is about but I would recommend keeping it based upon the experience I had while conducting some user tests for a Ecommerce site I recently built.
Though users were able to find what they were looking for really quickly using the defined navigation, not keeping a search bar was a bone of contention for some users as they had very predefined search requests in mind. When we did keep a search feature in the site, we found that the users were happy to have an additional navigation feature though the search results were not really that exceptional (we just enabled the basic search featured offered by the CMS)