There are many factors which determine whether Google shows a product for PLA and/or Shopping, and its associated position on the results page.
a. The quality score of the product (what Google assess is the strength of the product page v/s the keyword search used). This is not disclosed by Google, but includes assessment of the product page for relevance in respect of the keyword search. This includes meta data as well as on page content.
b. Relevance of the product name/description to the search phrase, with the title of the product carrying more weight.
c. Inclusion of reference data (or not) where this is a ranking factor. In this respect matching of Google’s indexation of Brand, MPN and EAN (if included as part of the product detail) is very important
d. What has been set as the maximum CPC bid price in Adwords v/s whatever your competition is doing. As far as PLAs are concerned, you may be being outbid in the auction for a specific product. Google may also not rank your product very well for the one phrase you typed in. Remember that a product has only one title, searching for variants on the product title or on isolated parts of the title string can produce very different results.
e. Additional data used by Google to weight the product for inclusion in results (review stars, impression and click history, click through rate). Popular long standing products with good response (click) history will perform better for relevance and ranking.
f. Your budget. Where you have no daily budget left or in periods when the advertising schedule is paused you will see no entries in Shopping/PLA.
Even if Google showed its hand on quality score by product (which it won’t), the weightings of their algorithm (which it never will), and what the auction bids are for each merchant (again it won’t), we could not predict where you would sit for any keyword search variation across hundreds of products compared to anyone else for all of the above reasons.
In any case what you see and what we see are entirely governed by what Google decides to show in our individual browser. That’s not the same either.
In short, good accurate data quality will assist product positions. Inclusion of the right reference data will ensure Google understands what they are. Bids are important, but as with everything Google, response rates make a big difference. Unpopular products (where for example prices are uncompetitive) will be relegated in the rankings whatever the bid.
And of course a poor quality landing page will have a very negative effect on everything.
Generally speaking click through rates of 2% are the norm. Anything higher indicates a popular /well performing product.
This is not intended to be a definitive answer for all merchants on all products, but I hope this helps you understand some of the complexity of how all of this works together.