Click here to close now.


Containers Expo Blog Authors: Lori MacVittie, Peter Silva, Ian Goldsmith, Elizabeth White, Pat Romanski

Related Topics: Java IoT, Microservices Expo, Adobe Flex, IoT User Interface, Apache

Java IoT: Article

Why Averages Are Inadequate, and Percentiles Are Great

Averages are ineffective because they are too simplistic and one-dimensional

Anyone who 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. It 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We recognize that the average no longer represents the bulk of the transactions but can be a lot higher than the median.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 begin 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 and 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 two 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, then 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.

Why I Love Percentiles
A percentile tells me which part of the curve I am looking at and how many transactions are represented by that metric. To visualize this look at the following chart:

This chart shows the 50th and 90th percentile along with the average of the same transaction. It shows that the average is influenced far mor heavily by the 90th, thus by outliers and not by the bulk of the transactions

The green line represents the average. As you can see it is very volatile. The other two lines represent the 50th and 90th percentile. As we can see the 50th percentile (or median) is rather stable but has a couple of jumps. These jumps represent real performance degradation for the majority (50%) of the transactions. The 90th percentile (this is the start of the "tail") is a lot more volatile, which means that the outliers slowness depends on data or user behavior. What's important here is that the average is heavily influenced (dragged) by the 90th percentile, the tail, rather than the bulk of the transactions.

If the 50th percentile (median) of a response time is 500ms that means that 50% of my transactions are either as fast or faster than 500ms. If the 90th percentile of the same transaction is at 1000ms it means that 90% are as fast or faster and only 10% are slower. The average in this case could either be lower than 500ms (on a heavy front curve), a lot higher (long tail) or somewhere in between. A percentile gives me a much better sense of my real world performance, because it shows me a slice of my response time curve.

For exactly that reason percentiles are perfect for automatic baselining. If the 50th percentile moves from 500ms to 600ms I know that 50% of my transactions suffered a 20% performance degradation. You need to react to that.

In many cases we see that the 75th or 90th percentile does not change at all in such a scenario. This means the slow transactions didn't get any slower, only the normal ones did. Depending on how long your tail is the average might not have moved at all in such a scenario.!

In other cases we see the 98th percentile degrading from 1s to 1.5 seconds while the 95th is stable at 900ms. This means that your application as a whole is stable, but a few outliers got worse, nothing to worry about immediately. Percentile-based alerts do not suffer from false positives, are a lot less volatile and don't miss any important performance degradations! Consequently a baselining approach that uses percentiles does not require a lot of tuning variables to work effectively.

The screenshot below shows the Median (50th Percentile) for a particular transaction jumping from about 50ms to about 500ms and triggering an alert as it is significantly above the calculated baseline (green line). The chart labeled "Slow Response Time" on the other hand shows the 90th percentile for the same transaction. These "outliers" also show an increase in response time but not significant enough to trigger an alert.

Here we see an automatic baselining dashboard with a violation at the 50th percentile. The violation is quite clear, at the same time the 90th percentile (right upper chart) does not violate. Because the outliers are so much slower than the bulk of the transaction an average would have been influenced by them and would not have have reacted quite as dramatically as the 50th percentile. We might have missed this clear violation!

How Can We Use Percentiles for Tuning?
Percentiles are also great for tuning, and giving your optimizations a particular goal. Let's say that something within my application is too slow in general and I need to make it faster. In this case I want to focus on bringing down the 90th percentile. This would ensure sure that the overall response time of the application goes down. In other cases I have unacceptably long outliers I want to focus on bringing down response time for transactions beyond the 98th or 99th percentile (only outliers). We see a lot of applications that have perfectly acceptable performance for the 90th percentile, with the 98th percentile being magnitudes worse.

In throughput oriented applications on the other hand I would want to make the majority of my transactions very fast, while accepting that an optimization makes a few outliers slower. I might therefore make sure that the 75th percentile goes down while trying to keep the 90th percentile stable or not getting a lot worse.

I could not make the same kind of observations with averages, minimum and maximum, but with percentiles they are very easy indeed.

Averages are ineffective because they are too simplistic and one-dimensional. Percentiles are a really great and easy way of understanding the real performance characteristics of your application. They also provide a great basis for automatic baselining, behavioral learning and optimizing your application with a proper focus. In short, percentiles are great!

More Stories By Michael Kopp

Michael Kopp has over 12 years of experience as an architect and developer in the Enterprise Java space. Before coming to CompuwareAPM dynaTrace he was the Chief Architect at GoldenSource, a major player in the EDM space. In 2009 he joined dynaTrace as a technology strategist in the center of excellence. He specializes application performance management in large scale production environments with special focus on virtualized and cloud environments. His current focus is how to effectively leverage BigData Solutions and how these technologies impact and change the application landscape.

Comments (1) View Comments

Share your thoughts on this story.

Add your comment
You must be signed in to add a comment. Sign-in | Register

In accordance with our Comment Policy, we encourage comments that are on topic, relevant and to-the-point. We will remove comments that include profanity, personal attacks, racial slurs, threats of violence, or other inappropriate material that violates our Terms and Conditions, and will block users who make repeated violations. We ask all readers to expect diversity of opinion and to treat one another with dignity and respect.

Most Recent Comments
rtalexander 11/21/12 12:58:00 AM EST

Hey, could you post a reference or two that covers the theory and/or practicalities of the approach you describe?


@ThingsExpo Stories
The broad selection of hardware, the rapid evolution of operating systems and the time-to-market for mobile apps has been so rapid that new challenges for developers and engineers arise every day. Security, testing, hosting, and other metrics have to be considered through the process. In his session at Big Data Expo, Walter Maguire, Chief Field Technologist, HP Big Data Group, at Hewlett-Packard, will discuss the challenges faced by developers and a composite Big Data applications builder, focusing on how to help solve the problems that developers are continuously battling.
As enterprises capture more and more data of all types – structured, semi-structured, and unstructured – data discovery requirements for business intelligence (BI), Big Data, and predictive analytics initiatives grow more complex. A company’s ability to become data-driven and compete on analytics depends on the speed with which it can provision their analytics applications with all relevant information. The task of finding data has traditionally resided with IT, but now organizations increasingly turn towards data source discovery tools to find the right data, in context, for business users, d...
“The Internet of Things transforms the way organizations leverage machine data and gain insights from it,” noted Splunk’s CTO Snehal Antani, as Splunk announced accelerated momentum in Industrial Data and the IoT. The trend is driven by Splunk’s continued investment in its products and partner ecosystem as well as the creativity of customers and the flexibility to deploy Splunk IoT solutions as software, cloud services or in a hybrid environment. Customers are using Splunk® solutions to collect and correlate data from control systems, sensors, mobile devices and IT systems for a variety of Ind...
Apps and devices shouldn't stop working when there's limited or no network connectivity. Learn how to bring data stored in a cloud database to the edge of the network (and back again) whenever an Internet connection is available. In his session at 17th Cloud Expo, Bradley Holt, Developer Advocate at IBM Cloud Data Services, will demonstrate techniques for replicating cloud databases with devices in order to build offline-first mobile or Internet of Things (IoT) apps that can provide a better, faster user experience, both offline and online. The focus of this talk will be on IBM Cloudant, Apa...
Clearly the way forward is to move to cloud be it bare metal, VMs or containers. One aspect of the current public clouds that is slowing this cloud migration is cloud lock-in. Every cloud vendor is trying to make it very difficult to move out once a customer has chosen their cloud. In his session at 17th Cloud Expo, Naveen Nimmu, CEO of Clouber, Inc., will advocate that making the inter-cloud migration as simple as changing airlines would help the entire industry to quickly adopt the cloud without worrying about any lock-in fears. In fact by having standard APIs for IaaS would help PaaS expl...
Organizations already struggle with the simple collection of data resulting from the proliferation of IoT, lacking the right infrastructure to manage it. They can't only rely on the cloud to collect and utilize this data because many applications still require dedicated infrastructure for security, redundancy, performance, etc. In his session at 17th Cloud Expo, Emil Sayegh, CEO of Codero Hosting, will discuss how in order to resolve the inherent issues, companies need to combine dedicated and cloud solutions through hybrid hosting – a sustainable solution for the data required to manage I...
SYS-CON Events announced today that ProfitBricks, the provider of painless cloud infrastructure, will exhibit at SYS-CON's 17th International Cloud Expo®, which will take place on November 3–5, 2015, at the Santa Clara Convention Center in Santa Clara, CA. ProfitBricks is the IaaS provider that offers a painless cloud experience for all IT users, with no learning curve. ProfitBricks boasts flexible cloud servers and networking, an integrated Data Center Designer tool for visual control over the cloud and the best price/performance value available. ProfitBricks was named one of the coolest Clo...
SYS-CON Events announced today that IBM Cloud Data Services has been named “Bronze Sponsor” of SYS-CON's 17th Cloud Expo, which will take place on November 3–5, 2015, at the Santa Clara Convention Center in Santa Clara, CA. IBM Cloud Data Services offers a portfolio of integrated, best-of-breed cloud data services for developers focused on mobile computing and analytics use cases.
Learn how IoT, cloud, social networks and last but not least, humans, can be integrated into a seamless integration of cooperative organisms both cybernetic and biological. This has been enabled by recent advances in IoT device capabilities, messaging frameworks, presence and collaboration services, where devices can share information and make independent and human assisted decisions based upon social status from other entities. In his session at @ThingsExpo, Michael Heydt, founder of Seamless Thingies, will discuss and demonstrate how devices and humans can be integrated from a simple clust...
As more and more data is generated from a variety of connected devices, the need to get insights from this data and predict future behavior and trends is increasingly essential for businesses. Real-time stream processing is needed in a variety of different industries such as Manufacturing, Oil and Gas, Automobile, Finance, Online Retail, Smart Grids, and Healthcare. Azure Stream Analytics is a fully managed distributed stream computation service that provides low latency, scalable processing of streaming data in the cloud with an enterprise grade SLA. It features built-in integration with Azur...
You have your devices and your data, but what about the rest of your Internet of Things story? Two popular classes of technologies that nicely handle the Big Data analytics for Internet of Things are Apache Hadoop and NoSQL. Hadoop is designed for parallelizing analytical work across many servers and is ideal for the massive data volumes you create with IoT devices. NoSQL databases such as Apache HBase are ideal for storing and retrieving IoT data as “time series data.”
SYS-CON Events announced today that HPM Networks will exhibit at the 17th International Cloud Expo®, which will take place on November 3–5, 2015, at the Santa Clara Convention Center in Santa Clara, CA. For 20 years, HPM Networks has been integrating technology solutions that solve complex business challenges. HPM Networks has designed solutions for both SMB and enterprise customers throughout the San Francisco Bay Area.
Mobile messaging has been a popular communication channel for more than 20 years. Finnish engineer Matti Makkonen invented the idea for SMS (Short Message Service) in 1984, making his vision a reality on December 3, 1992 by sending the first message ("Happy Christmas") from a PC to a cell phone. Since then, the technology has evolved immensely, from both a technology standpoint, and in our everyday uses for it. Originally used for person-to-person (P2P) communication, i.e., Sally sends a text message to Betty – mobile messaging now offers tremendous value to businesses for customer and empl...
SYS-CON Events announced today that MobiDev, a software development company, will exhibit at the 17th International Cloud Expo®, which will take place November 3-5, 2015, at the Santa Clara Convention Center in Santa Clara, CA. MobiDev is a software development company with representative offices in Atlanta (US), Sheffield (UK) and Würzburg (Germany); and development centers in Ukraine. Since 2009 it has grown from a small group of passionate engineers and business managers to a full-scale mobile software company with over 150 developers, designers, quality assurance engineers, project manage...
SYS-CON Events announced today that Cloud Raxak has been named “Media & Session Sponsor” of SYS-CON's 17th Cloud Expo, which will take place on November 3–5, 2015, at the Santa Clara Convention Center in Santa Clara, CA. Raxak Protect automates security compliance across private and public clouds. Using the SaaS tool or managed service, developers can deploy cloud apps quickly, cost-effectively, and without error.
Who are you? How do you introduce yourself? Do you use a name, or do you greet a friend by the last four digits of his social security number? Assuming you don’t, why are we content to associate our identity with 10 random digits assigned by our phone company? Identity is an issue that affects everyone, but as individuals we don’t spend a lot of time thinking about it. In his session at @ThingsExpo, Ben Klang, Founder & President of Mojo Lingo, will discuss the impact of technology on identity. Should we federate, or not? How should identity be secured? Who owns the identity? How is identity ...
SYS-CON Events announced today that Solgeniakhela will exhibit at SYS-CON's 17th International Cloud Expo®, which will take place on November 3–5, 2015, at the Santa Clara Convention Center in Santa Clara, CA. Solgeniakhela is the global market leader in Cloud Collaboration and Cloud Infrastructure software solutions. Designed to “Bridge the Gap” between Personal and Professional Social, Mobile and Cloud user experiences, our solutions help large and medium-sized organizations dramatically improve productivity, reduce collaboration costs, and increase the overall enterprise value by bringing ...
Sensors and effectors of IoT are solving problems in new ways, but small businesses have been slow to join the quantified world. They’ll need information from IoT using applications as varied as the businesses themselves. In his session at @ThingsExpo, Roger Meike, Distinguished Engineer, Director of Technology Innovation at Intuit, will show how IoT manufacturers can use open standards, public APIs and custom apps to enable the Quantified Small Business. He will use a Raspberry Pi to connect sensors to web services, and cloud integration to connect accounting and data, providing a Bluetooth...
SYS-CON Events announced today that Micron Technology, Inc., a global leader in advanced semiconductor systems, will exhibit at the 17th International Cloud Expo®, which will take place on November 3–5, 2015, at the Santa Clara Convention Center in Santa Clara, CA. Micron’s broad portfolio of high-performance memory technologies – including DRAM, NAND and NOR Flash – is the basis for solid state drives, modules, multichip packages and other system solutions. Backed by more than 35 years of technology leadership, Micron's memory solutions enable the world's most innovative computing, consumer,...
Nowadays, a large number of sensors and devices are connected to the network. Leading-edge IoT technologies integrate various types of sensor data to create a new value for several business decision scenarios. The transparent cloud is a model of a new IoT emergence service platform. Many service providers store and access various types of sensor data in order to create and find out new business values by integrating such data.