Why Averages Suck and Percentiles are Great?
Anyone that ever monitored or analyzed an application uses or has used averages. They are simple to understand and calculate. We tend to ignore just how wrong the picture is that averages paint of the world. To emphasis the point let me give you a real world example outside of the performance space that I read recently in a newspaper.
The article was explaining that the average salary in a certain region in Europe was 1900 Euro’s (to be clear this would be quite good in that region!). However when looking closer they found out that the majority, namely 9 out of 10 people, only earned around 1000 Euros and one would earn 10.000 (I over simplified this of course, but you get the idea). If you do the math you will see that the average of this is indeed 1900, but we can all agree that this does not represent the “average” salary as we would use the word in day to day live. So now let’s apply this thinking to application performance.
The Average Response Time:
The average response time is by far the most commonly used metric in application performance management. We assume that this represents a “normal” transaction, however this would only be true if the response time is always the same (all transaction run at equal speed) or the response time distribution is roughly bell curved.
A Bell curve represents the “normal” distribution of response times in which the average and the median are the same. I rarely ever occurs in real applications
In a Bell Curve the average (mean) and median are the same. In other words observed performance would represent the majority (half or more than half) of the transactions.
In reality most applications have few very heavy outliers; a statistician would say that the curve has a long tail. A long tail does not imply many slow transactions, but few that are magnitudes slower than the norm.
This is a typical Response Time Distribution with few but heavy outliers – it has a long tail. The average here is dragged to the right by the long tail.
We recognize that the average no longer represents the bulk of the transactions but can be a lot higher than the median.
You can now argue that this is not a problem as long as the average doesn’t look better than the median. I would disagree, but let’s look at another real-world scenario experienced by many of our customers:
This is another typical Response Time Distribution. Here we have quite a few very fast transactions that drag the average to the left of the actual median
In this case a considerable percentage of transactions are very, very fast (10-20 percent), while the bulk of transactions are several times slower. The median would still tell us the true story, but the average all of a sudden looks a lot faster than most of our transactions actually are. This is very typical in search engines or when caches are involved, some transactions are very fast, but the bulk are normal. Another reason for this scenario are failed transactions, more specifically transactions that failed fast. Many real world applications have a failure rate of 1-10 percent (due to user errors or validation errors). These failed transactions are often magnitudes faster than the real ones and consequently distorted an average.
Of course performance analysts are not stupid and regularly try to compensate with higher frequency charts (compensating by looking at smaller aggregates visually) and by taking in minimum and maximum observed response times. However we can often only do this if we know the application very well, those unfamiliar with the application might easily misinterpret the charts. Because of the depth and type of knowledge required for this, it’s difficult to communicate your analysis to other people – think how many arguments between IT teams have been caused by this. And that’s before we even being to think about communicating with business stakeholders!
A better metric by far are percentiles, because they allow us to understand the distribution. But before we look at percentiles, let’s take a look a key feature in every production monitoring solution: Automatic Baselining and Alerting.
Automatic Baselining and Alerting
In real world environments, performance gets attention when it is poor and has a negative impact on the business and users. But how can we identify performance issues quickly to prevent negative effects? We cannot alert on every slow transaction, since there are always some. In addition, most Operations teams have to maintain a large number of applications are not familiar with all of them, so manually setting thresholds can be inaccurate, quite painful and time consuming.
The industry has come up with a solution called Automatic Baselining. Baselining calculates out the “normal” performance and only alerts us when an application slows down or produces more errors than usual. Most approaches rely on averages and standard deviations.
Without going into statistical details, this approach again assumes that the response times are distributed over a bell curve:
The Standard Deviation represents 33% of all transactions with the mean as the middle. 2xStandard Deviation represents 66% and thus the majority, everything outside could be considered an outlier. However most real world scenarios are not bell curved…
Typically, transactions that are outside 2 times standard deviation are treated as slow and captured for analysis. An alert is raised if the average moves significantly. In a bell curve this would account for the slowest 16.5 percent (and you can of course adjust that), however if the response time distribution does not represent a bell curve it becomes inaccurate. We either end up with a lot of false positives (transactions that are a lot slower than the average but when looking at the curve lie within the norm) or we miss a lot of problems (false negatives). In addition if the curve is not a bell curve than the average can differ a lot from the median, applying a standard deviation to such an average can lead to quite a different result than you would expect! To work around this problem these algorithms have many tunable variables and a lot of “hacks” for specific use cases.
Anyone that ever monitored or analyzed an application uses or has used averages. They are simple to understand and calculate. We tend to ignore just how wrong the picture is that averages paint of the world. To emphasis the point let me give you a real world example outside of the performance space that I read recently in a newspaper.
The article was explaining that the average salary in a certain region in Europe was 1900 Euro’s (to be clear this would be quite good in that region!). However when looking closer they found out that the majority, namely 9 out of 10 people, only earned around 1000 Euros and one would earn 10.000 (I over simplified this of course, but you get the idea). If you do the math you will see that the average of this is indeed 1900, but we can all agree that this does not represent the “average” salary as we would use the word in day to day live. So now let’s apply this thinking to application performance.
The Average Response Time:
The average response time is by far the most commonly used metric in application performance management. We assume that this represents a “normal” transaction, however this would only be true if the response time is always the same (all transaction run at equal speed) or the response time distribution is roughly bell curved.
A Bell curve represents the “normal” distribution of response times in which the average and the median are the same. I rarely ever occurs in real applications
In a Bell Curve the average (mean) and median are the same. In other words observed performance would represent the majority (half or more than half) of the transactions.
In reality most applications have few very heavy outliers; a statistician would say that the curve has a long tail. A long tail does not imply many slow transactions, but few that are magnitudes slower than the norm.
This is a typical Response Time Distribution with few but heavy outliers – it has a long tail. The average here is dragged to the right by the long tail.
We recognize that the average no longer represents the bulk of the transactions but can be a lot higher than the median.
You can now argue that this is not a problem as long as the average doesn’t look better than the median. I would disagree, but let’s look at another real-world scenario experienced by many of our customers:
This is another typical Response Time Distribution. Here we have quite a few very fast transactions that drag the average to the left of the actual median
In this case a considerable percentage of transactions are very, very fast (10-20 percent), while the bulk of transactions are several times slower. The median would still tell us the true story, but the average all of a sudden looks a lot faster than most of our transactions actually are. This is very typical in search engines or when caches are involved, some transactions are very fast, but the bulk are normal. Another reason for this scenario are failed transactions, more specifically transactions that failed fast. Many real world applications have a failure rate of 1-10 percent (due to user errors or validation errors). These failed transactions are often magnitudes faster than the real ones and consequently distorted an average.
Of course performance analysts are not stupid and regularly try to compensate with higher frequency charts (compensating by looking at smaller aggregates visually) and by taking in minimum and maximum observed response times. However we can often only do this if we know the application very well, those unfamiliar with the application might easily misinterpret the charts. Because of the depth and type of knowledge required for this, it’s difficult to communicate your analysis to other people – think how many arguments between IT teams have been caused by this. And that’s before we even being to think about communicating with business stakeholders!
A better metric by far are percentiles, because they allow us to understand the distribution. But before we look at percentiles, let’s take a look a key feature in every production monitoring solution: Automatic Baselining and Alerting.
Automatic Baselining and Alerting
In real world environments, performance gets attention when it is poor and has a negative impact on the business and users. But how can we identify performance issues quickly to prevent negative effects? We cannot alert on every slow transaction, since there are always some. In addition, most Operations teams have to maintain a large number of applications are not familiar with all of them, so manually setting thresholds can be inaccurate, quite painful and time consuming.
The industry has come up with a solution called Automatic Baselining. Baselining calculates out the “normal” performance and only alerts us when an application slows down or produces more errors than usual. Most approaches rely on averages and standard deviations.
Without going into statistical details, this approach again assumes that the response times are distributed over a bell curve:
The Standard Deviation represents 33% of all transactions with the mean as the middle. 2xStandard Deviation represents 66% and thus the majority, everything outside could be considered an outlier. However most real world scenarios are not bell curved…
Typically, transactions that are outside 2 times standard deviation are treated as slow and captured for analysis. An alert is raised if the average moves significantly. In a bell curve this would account for the slowest 16.5 percent (and you can of course adjust that), however if the response time distribution does not represent a bell curve it becomes inaccurate. We either end up with a lot of false positives (transactions that are a lot slower than the average but when looking at the curve lie within the norm) or we miss a lot of problems (false negatives). In addition if the curve is not a bell curve than the average can differ a lot from the median, applying a standard deviation to such an average can lead to quite a different result than you would expect! To work around this problem these algorithms have many tunable variables and a lot of “hacks” for specific use cases.
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