Ad request, impression, eCPM, and match rate are critical metrics in Google AdMob that play important roles in measuring ad performance and success. Below is an explanation of how these metrics are related to each other and how they work together in a typical AdMob ad campaign.

Ad Request:
An ad request is the first step in the process of serving an ad in an app. When a mobile app requests an ad from AdMob, it sends a request that includes parameters like ad format, ad size, and targeting information. Ad requests are important because they determine the number of opportunities an app has to display an ad.

Impression:
An impression refers to the number of times an ad is displayed to users within an app. In other words, it is the measurement of the visibility of an ad. When an ad is displayed to a user, it counts as one impression. Impressions are important because they provide valuable information about ad performance, such as click-through rates, engagement, and conversion rates.

Match Rate:
Match Rate is the percentage of ad requests that AdMob is able to match with an ad. In other words, it is the ratio of the number of times an ad is successfully displayed to the number of ad requests. Match rate is important because it measures the effectiveness of an ad campaign and the ad inventory quality. It also affects the revenue generated through ads as matching an ad unit with a high paying ad significantly boosts the app revenue.

eCPM:
eCPM (Effective Cost per Mile) is a key metric used to measure ad revenue. It is defined as the revenue generated for every thousand impressions. eCPM is important because it determines the revenue generated per impression and it plays a critical role in app monetization. It is a widely used metric by advertisers and app developers to measure the financial performance of an ad campaign or an app.

The relationship between Ad Request, Impression, Match rate, and eCPM:
The relationship between Ad request, impression, match rate, and eCPM is interrelated. When an ad is requested, AdMob's ad mediation engine examines the ad request properties for targeting and ad format information, and then offers this ad to multiple third-party ad networks to compete for the ad space to fill the ad request. AdMob's machine learning will choose a specific ad based on the highest bid for the best eCPM.

If all the ad requests are successfully matched with an ad, the match rate would be 100%, and the number of impressions would be equal to the number of ad requests. A high match rate means that AdMob is successful in serving ads, which is important for making impressions.

If an ad is displayed to a user, it will count as one impression. The number of impressions impacts the eCPM generated, as each impression contributes to the app's overall revenue. A high eCPM means that each impression is generating more revenue, which is an important metric for app monetization.

The match rate also affects the eCPM, and vice versa. A high match rate implies that the app has a high fill rate and, therefore, should generate more revenue. The eCPM is affected by the ad quality and the demand for ad space. If the ad quality is low, the eCPM will also be low. On the other hand, when demand for a particular ad space is high, the ad inventory can generate a high eCPM.

In summary, ad request, impression, match rate, and eCPM are important metrics in AdMob campaigns. Ad requests determine the number of opportunities to display ads. Impressions indicate how many times an ad was actually displayed, which is directly related to the revenue generated by the ad. Match rate is the percentage of ad requests that were matched with an ad and is critical to track because it measures the effectiveness of the ad inventory. eCPM measures ad revenue and is important for app monetization. Through tracking these metrics, AdMob developers can optimize their ad campaigns and maximize revenue.