The system starts tracking QS data from the day an AdWords account is linked to Optmyzr. This is why the date range before the account was added to Optmyzr shows grayed out in the tracker. Since Google doesn't store historical Quality Score data, the system can't pull it from AdWords like other statistics - Impressions, Click, Cost, etc. for any period.
The Quality Score is pulled each morning (PST time zone) for the previous day. This is because that is the time Google finalizes the Quality Score for the previous day. For example, the Quality Score on the 18th morning is the QS for the 17th and the weighted QS for 17th is calculated after the impression numbers are updated the next day. This is the reason they Quality Score shows one day late (by the PST time zone) in the Quality Score Tracker.
The tool calculates the Quality Score data (at an account, campaign, and ad group level) by multiplying the Quality Score of the keywords in the account by the impression volume of the previous day. Then, the calculated score is stored for yesterday's date, to make sure the impression count is complete as it takes a few hours for the data to update in AdWords. In other words, if today your QS is 7, we say this is the result of your performance yesterday.
We believe this is a reasonable approach, as the most important thing about QS is to see the trend and to know when it started changing.
In the Quality Score Tracker, all the statistics are displayed only for Google search. This could be a reason for the difference in the metrics.
The Quality Score Tracker shows items (campaigns, ad groups or keywords) that:
This is the data that is taken into account to calculate Quality Score. The items that don't show up in the tree view in the Quality Score Tracker are those that didn't meet all the conditions mentioned above.
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