ASR is the ratio of Successfully Connected Calls to Call Attempts

Usually, shown as a percentage (%), the formula is:   Successful (answered) Calls / Calls attempts * 100.  

Where call attempts ("seizures") relate to all calls, regardless of success or failure and,  where Successful (answered) calls are answered by a human or recording machine (such as voicemail).

The acceptable level (%) of ASR depends on the type of voice traffic you are passing, and your goals in terms of revenue and traffic statistics.  It is generally understood that carriers with very low ASRs (~20%) have a high volume of calls that fail, and therefore calls that consume infrastructure resources, with no (or very little) revenue.   As such, higher ASRs generally equate to higher revenue/margins.  If you are experiencing low ASR statistics, you will generally see a low ACD (Average Call Duration) - often caused by a high volume of calls from Outbound Call Centers (See below).   Your Sippy Softswitch does not typically affect ASR.  

To understand how you can create and modify routing based on quality (ASR) - please see: Quality Based Routing

Regular National Carriers (Incumbent Carriers)

Incumbent residential carriers generally have long ACD (Average Call Duration), and high ASR rations (typically around 70%) due to the natural, conversational traffic that occurs on the network and because they have sufficient network resources to place all the calls made.   At peak times (such as New Year and other holidays) where customers are attempting to call with higher frequency - the network ASR may temporarily decrease due to lack of network resources - and busy phone lines.   National Carriers will also limit interconnections with international wholesale SIP clients that have ASR levels that are too low (usually between ~ 50%-60%) 

International SIP carriers

Wholesale international SIP carriers generally aim for an ASR of roughly 50%, If they are interconnecting with a national carrier, they may seek to have 50%-60%+ to ensure best rates and access.   Wholesale carriers need to move high volumes of calls across multiple vendors (routes) at the lowest cost possible. The result is more requests (call attempts) to the vendor network (route) than the vendor is able to process.  In the previous case, calls will often fail to the next available vendor (Route) or are dropped - thus resulting in lower number of connected calls to call attempts (a lower ASR).   

Wholesale operators with good (high) ASR rates may "blend" some Outbound Call Center traffic with their standard wholesale traffic; this lowers the average ASR, so they will impose strict limits on the volume (CPS) and concurrent capacity (CC) of calls that they accept.

Outbound Call Centers Solution Providers (carriers)

Call centers are measured in "seats" (number of active agents).  The goal of a call center is to have an active call for every agent all the time (i.e. no agent should be sitting idle).  If agents dial the numbers individually, it takes time to place the call and connect with a real human - time that can be automated.  For optimal efficiency, most large Outbound Call Centers use "Auto-Dialers" to place calls.   The auto-dialer will continually place calls - non-stop.  When a call is answered, the dialer plays a message and attempts to connect the "live" call with an available agent. Ensuring that there is an answered call for every agent means that the auto-dialer has to make more phone calls than there are agents as it can take 20-30 calls to get an answered call at the same time as the agent is free. 

Outbound Call Centers only care about, and pay for, connected calls and will pass all requests to multiple vendors (many of which usually terminate to the same carrier).  Many of the calls are "trash" (wrong or incorrect numbers, poorly formatted phone numbers, etc.), sent at high calls per second (CPS).  The result is a low ratio of successfully connected calls to call attempts (ASR Usually <20%).