Applying The Theory of Sets In Match Types

When I was a math teacher, I spent a lot of time doing what I thought was, well, ‘teaching.’ In my first few months on the job, I focused on the logic behind the mathematics, not the formulas or other shortcuts. Students constantly complained about this, and they were failing tests, so, after higher-level discussions, I started going over the easy way to do things: the formulas.

I was rather surprised when students started doing really well on tests – but when I verbally assessed their understanding of the logic, I was still greatly disappointed.

Furthermore, they completely fell flat on more complicated problems that require more than just plug and chug. Students were just cramming and memorizing and didn’t truly learn that much.

In paid search, there are a lot of parallels. I run across many account managers who believe in exact match and don’t believe in broad match. It’s a rule to them, in fact – an axiom in their minds. When prodding further by simply asking ‘why,’ I feel like a math teacher all over again. Ask ‘why’ and you get shallow half-answers that remind me of the plug-and-chug crew,

I’m not much of a paid search historian, but imagine it’s about 1997, and you’re part of the team developing the first pay-per-click platform. There’s no such thing as match type, so how do you create the concept? What question was “match types” trying to answer?

match types

You can do better than these.

Well, to me (and assuming “keyword” was already a concept), it’s “how do we determine which sets of queries keywords are matched to?”

If you’re focusing on match types in paid search, you’re focusing on the ‘formulas’ – which means that a lot of the logic is being lost. To understand how to best use the ‘formulas’ of match types, you must understand the theory of sets.

First, we’ll define the match types based on sets. Then we’ll explore query-to-keyword mappings by match type – what works, what doesn’t, what we should strive to achieve.

Then, we’ll show how layers of complexity like negative keywords can create chaos within match types.

By the time we hit the conclusion, my hope is that you’ll have decided for yourself that simply managing accounts by match type leaves a lot to be desired – and a lot of ROI on the table.

Defining Match Types Based On Sets

Depending on the platform, the sets of queries matched to a particular keyword match type varies. Here’s the current AdWords definition of each match type. (Note that I’ve replaced the word ‘searches’ with the phrase ‘set of queries.’):

  • Broad match allows your ad to show for the set of queries on similar phrases and relevant variations.
  • Broad match modifier allows your ad to show for the set of queries that include your broad match keyword or close variations of your broad match keyword.
  • Phrase match allows your ad to show only for the set of queries that include the exact phrase, or close variations of that exact phrase, and possibly other words as well.
  • Exact match allows your ad to show only for the set of queries that use that exact phrase, or close variations of that exact phrase, and no other words.

By now we should have consensus that match types are not required to exist. They vary in quantity and definition across platforms and capture slightly different sets depending on current match type definitions. They are simply answers (they could be correct or incorrect answers, by the way) to the question of how to capture queries.

In PPC, we’re required to use match types; we don’t have any other choice. However, now that we understand that our actual question is ‘how do we deal with sets,’ our perspective on what makes a good SEM may change.


When dealing with sets, you must also deal with mappings – in our case, query-to-keyword mappings. When studying mappings, you will find Google employs one-to-many mappings and many-to-one mappings, but it almost never uses one-to-one mappings.

The first image is a ‘one-to-one’ mapping, the second ‘many-to-one,’ and the last ‘one-to-many.’ The input (X), in this case, is the query, which is matched to the keyword, the output (Y).

query mappings

Query/set mappings


Looking at these images, which do you think would be the most optimal way to run a PPC account?

Hopefully we all agree it’s better to be in control of mappings, and the one-to-one mapping is best in instances where there is enough actionable data to make use of it. Despite this, I don’t think I’ve ever seen a true one-to-one mapping, unless we force the one-to-one mapping with crafty account structure.

The other mappings are essentially the advertiser giving the platform liberty to control the mappings, and, when given the chance, the platform will do mass experimentation to maximize the SERPs eCPM.

To really nail PPC, optimization efforts must be made on consistent, hopefully non-overlapping sets. If the sets are constantly changing, then you are optimizing against a moving target.

Some may think that exact match creates one-to-one mappings, which is why so many people “believe in exact match, but not broad match.” However, at best, exact match creates a one-to-many relationship. This means that, yes, the exact match keyword can only be matched to one query, but the query can be matched to many other different keywords. It could, for example, be matched to the broad-match version of your exact match keyword if it exists.

Going back to our match type definitions, the query ‘wedding invitations’ could be matched to not only the exact match [wedding invitations] but also the phrase match, broad match, or modified broad match version. By viewing the search query report, you should see one query being matched to multiple different keywords at different times.

Essentially, the factor that determines where the query is matched is ad rank (QS x bid). And, you’ll find that most of the time for similar keywords the QS is similar, so the match usually finds its way to the highest-bidded term.

With ‘near match,’ exact match can also become a many-to-one mapping, where multiple queries are matched to one keyword. This means that advertisers are not in control of much of anything, particularly if they follow the common best practice of ‘using all match types.’

I don’t want to simply make a blanket statement and say that one-to-one mappings are what all advertisers should strive for with every query. That’s impossible, and it’s also not optimal! I do, however, think it’s important to understand the mappings within an account and, based on what the advertiser has determine is optimal, create the desired mappings.

In general, however, one-to-one mappings are best (one query goes to one keyword every time), and many-to-one (many queries go to one keyword every time) are second-best. Worst is one-to-many mappings (one query goes to many different keywords) from an advertiser’s perspective because there is very little control, and data is very fluidly going one from keyword to the next.

From Google’s perspective, the opposite ordering is true, and they prefer one-to-many mappings. That is why Google sends so much traffic to your broad-match keywords! For Google, more chaos equals more money. Most of the time, advertisers have nothing but one-to-many mappings across their account.

Sets Influence Other Sets

Think of a negative keyword as a knife. It must be used with care, otherwise you’ll cut out some good stuff. But be too conservative with your knife, and you’ll be left with a lot of wasted spend.

What a negative is doing is removing queries from your reach. So, it’s taking one set, whether it is the set of queries matched to your campaign or the set matched to your ad group, and eliminating a sub-set.

This isn’t the most complex logic until you start thinking of how, in actuality, the removed sub-set actually impacts many sets at once. In the case of campaign negatives, it impacts the entire set of queries sent to any one of your keywords at any time.

Where this can get really scary is when people start to create account structure based off of match type considerations, and not sets. For example, it’s common to set up one campaign in exact match (no negatives), one in phrase (only exact negatives), and another in broad (phrase and exact negatives). Each campaign would have the same positive keywords.

Consider the set of queries an advertiser who sells iPads and iPad 2s would find relevant. The advertiser may conclude he/she only needs two keywords: iPad and iPad 2. Let’s agree with this assumption for the purpose of simplicity.

So, you’d have the following:

Campaign A – the set of queries ‘ipad’ and ‘ipad 2’:


[iPad 2]

Campaign B – the set of queries containing, but not equal to ‘ipad’ and ‘ipad 2’


“iPad 2”


-[iPad 2]

Campaign C – the set of queries to whatever Google deems relevant but not containing or equal to ‘ipad’ or ‘ipad 2’


iPad 2


-[iPad 2]


-“iPad 2”

If a user then queries ‘buy ipad 2,’ where does the query get sent to? The answer is….somewhere in campaign B but I don’t know where. I think ‘ipad 2’ is more likely than ‘ipad’, but it depends on the ad rank!

This is starting to sound like quantum physics, and I don’t think it’s good to run accounts like quantum physics (set theory is hard enough).

Instead, consider the following:

Campaign A – The set of queries that contains ‘ipad’(or minor variation) but not ‘2’ AND (in a different ad group) the set of queries that contains the token ‘ipad’ (or minor variation) but in only conjunction with ‘2’.

Ad Group 1



Ad group 2

+ipad +2

Campaign B – The set of queries Google deems relevant but not those containing the phrase ‘ipad’.

Ad Group 1


Ad Group 2

iPad 2

Campaign negative

-“ipad” (feel free to add in -“ipad 2” if you’re a neat freak!)

In this structure, which is quite a bit simpler in my opinion, I’d know that any query containing ‘2’ and ‘ipad’ goes to the ad group for the ipad 2 in Campaign A.

That’s important because I have different ad copy for that ad group, and probably a different bid. Not to mention I have different margins for each product, and a different quantity in stock. So, I know when someone queries ‘buy ipad 2’ it goes to my ‘+ipad +2’ ad group.


I don’t think this is the type of an article that needs a conclusion. My hope is that you’ll say ‘hmmm,’ and ‘I’m not quite sure about that’ a whole bunch! The idea is simply for everyone to get their thinking caps on and start thinking about queries and query sets, and not keywords.

Making great accounts is about more than great copy, great landing pages, and great products; it’s also about great query mappings and valid data based on consistent sets. Many paid search accounts are like whack-a-mole, where fixing a problem one place just results in it popping up elsewhere. If you can create a solution to the whack-a-mole problem, then you’ve got a great PPC account.

All right, “class,” this week’s homework assignment is to tell me what is wrong with my proposed campaign structure!

Opinions expressed in the article are those of the guest author and not necessarily Search Engine Land.

Related Topics: Channel: SEM | Paid Search Column


About The Author: is Senior Manager of Client Services at PPC Associates.

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  • Terry Whalen

    But wait – I thought it was Alpha/Beta or bust!! No?

  • Mike Nelson

    Hey Terry

    This logic is the same that we use when talking about Alpha/Beta. Typically in our publications we are speaking to the higher volume Alpha queries. In this article I am trying to discuss the logic behind the ‘beta’ side of things. Though, my example doesn’t not have an ‘alpha’ portion so to speak, but it can be easily added in.

    As the highest level goal we are trying to control ad serving as best as possible. With ‘alpha’ queries, we are focusing on ad serving for a single element set (1 keyword ad groups) whereas here we’re talking about semantic clustering for a group of tail queries.

    Perhaps at one point we’ll be less obtuse and publish a blog that completes the entire concept :)

  • Pat Grady

    I need to be sat down in my chair and have the teacher explain it more, cuz my only question is how did this get past editorial. Perhaps I’m a dogmatic, cramming memorizer. How can I prove or disprove that? If I were, I suspect it’d blind me to the truth… yup, I definitely need a talking to.

  • Cassie Allinger

    I love how you took such a simple topic (one of my favorites) and truly made it sound like quantum physics! Great explanation and I love the whack-a-mole analogy.

  • Mike Nelson

    This is sort of a depressing comment!

    The point I’m trying to make is that if someone were to understand the logic behind PPC they could, with confidence, more optimally answer any question that arises about the account. There are so many questions that require knowledge of sets.

    What happens if I pause all keywords with no conversions?
    What is a keyword level bid and is it really optimal?
    What happens when I change a bid on a non exact match keyword?
    What value does a unique keyword being to the portfolio?
    Is historical data valid today, how do we leverage it effectively?
    Am I reaching the ceiling of my account?

    None of these can be accurately answered without knowledge of sets. I was aiming for “teaching a man to fish” in this blog post. Or, at least, asking we all think of keywords as a group of queries with aggregated data.

    I feel if someone can understand set theory as it relates to PPC they will get more value out of that understanding than reading 10 blog posts that pass editorial :) This logic is a bit different, and I’m still trying to understand it completely myself, but I definitely think it’s on the right track.

  • Mike Nelson

    Thanks Cassie – stuff this really makes PPC fun! Even better, there are often some nice conclusions that come about as a result, and really improve the numbers.

  • Cassie Allinger

    It sure does! :)

  • Ravi Sodha

    Great article! Thinking cap is firmly on…

    Lots to think about and understand, I look forward to any follow ups on this concept

  • Mike Nelson

    Hey Rob

    Exactly – so, “2″ as a negative in broad or phrase negative is the same thing. Single token negatives have the same effect whether broad or phrase. I wrote an article on negatives here ( which you might like :)

    Thanks for the comment!

  • Mike Nelson

    Thanks Ravi…hopefully I get a chance to keep contributing ;)

  • Rob Tyrrell

    Hey Mike – Interesting ideas, I hadn’t really thought about match types in these terms before.

    My problem with your suggested structure is that ‘Campaign A’ is still going to receive queries with a very wide range of intent. “iPad”, “white iPad” and “iPad cover” end up potentially receiving the same bid and landing page, which definitely isn’t optimal.

    Campaign B is basically set up for keyword discovery, which is fine, but I always expect those campaigns to have the lowest ROI. For instance, if you noticed that the query “new apple tablet” was converting well in Campaign B you’d probably want to build out a new campaign based on like queries.

    At the end of the day the goal is to have highly segmented campaigns based on query intent and the ‘traditional’ structure still seems like the best way to ensure that happens. Thanks for making me wrap my mind around set theory though!

  • Mike Nelson

    Hey Rob

    Thanks for the comment.

    I definitely hear where you’re coming from. In this sample, I kept the KW set very underdeveloped for illustrative purposes. The actual campaign would certainly have more KWs, and we would funnel things based on intent.

    As a fully formed campaign, we would certainly be much more granular with our approach. The high level point is the to illustrate the theory of how match types are really just ways to captured defined sets.

  • Sarah Peduzzi

    Woah, this article made me think. And you’re right, there really is no…conclusive conclusion. What it did do was make me think about campaign structure in a new way. Having the option to view the keyword that triggered the SQ helps with examining what the “sets” like you explained.


  • CollinTate

    I’m the type of guy that likes to know the WHY behind the WHAT, but have been guilty of cramming and memorizing. To be honest, when I first read this, I was a bit lost. But, after a few re-reads and letting the concepts sink in, I get it. As a result I’ve started studying set theory. First rate article Mike!

  • Mike Nelson

    Thanks Sarah, it was fun to think about while writing too!

  • Mike Nelson

    I think this type of mindset (“why” behind the “what”) is key to next level account management.

    Set theory doesn’t have to be hard…we’ve actually been learning it since venn diagrams. Google has images of these running all around the adwords UI now, so it’s really useful to understand the basics of set theory.A Schaum outline should give you all you need to know about set theory.

    Thanks for reading :)


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