# Patent

## Title
Techniques for benchmarking pairing strategies in a contact center system

## Abstract

Techniques for benchmarking pairing strategies in a contact center system are disclosed. In one particular embodiment, the techniques may be realized as a method for benchmarking pairing strategies in a contact center system including determining results for a first plurality of contact-agent interactions, determining results for a second plurality of contact-agent interactions, and determining combined results across the first and second pluralities of contact-agent interactions corrected for a Yule-Simpson effect.

## Background
FIELD OF THE DISCLOSURE
This disclosure generally relates to contact centers and, more particularly, to techniques for benchmarking pairing strategies in a contact center system.
BACKGROUND OF THE DISCLOSURE
A typical contact center algorithmically assigns contacts arriving at the contact center to agents available to handle those contacts. Several potential algorithms exist for assigning contacts to contact center agents. These include time-ordered assignment strategies, utilization-based assignment strategies, performance-based assignment strategies, and behaviorally-based assignment strategies.
At times, contact center administrators may wish to compare the performance of one algorithm against another. In some cases, contact center administrators can do this by alternating between the two algorithms and examining the resultant differences in performance over time. Such a benchmarking process can be subject to the Yule-Simpson effect (also referred to as “Simpson's Paradox”) in which the aggregation or amalgamation of distinct cross-sections of data can result in a misleading assessment of the actual performance differential between the assignment algorithms being alternated.
In some cases, such a mischaracterization of performance can be large. For example, one algorithm may consistently outperform another in each of the periods in which it was responsible for contact assignment, but when aggregated the apparent performance of the two algorithms may in fact be reversed.
In view of the foregoing, it may be understood that there is a need for a system that corrects for such a mischaracterization that can result from the Yule-Simpson effect.
SUMMARY OF THE DISCLOSURE
Techniques for benchmarking pairing strategies in a contact center system are disclosed.
In one embodiment, the techniques may be realized as a method for benchmarking pairing strategies in a contact center system comprising determining, by at least one computer processor configured to operate in the contact center system, results for a first plurality of contact-agent interactions; determining, by the at least one computer processor, results for a second plurality of contact-agent interactions; and determining, by the at least one computer processor, combined results across the first and second pluralities of contact-agent interactions corrected for a Yule-Simpson effect.
In accordance with other aspects of this embodiment, at least one of the first and second pluralities of contact-agent interactions may be paired using at least two pairing strategies. In accordance with other aspects of this embodiment, a pairing strategy of the at least two pairing strategies may comprise at least one of: a behavioral pairing (BP) strategy, a first-in, first-out (FIFO) pairing strategy, a performance-based routing (PBR) strategy, a highest-performing-agent pairing strategy, a highest-performing-agent-for-contact-type pairing strategy, a longest-available-agent pairing strategy, a least-occupied-agent pairing strategy, a randomly-selected-agent pairing strategy, a randomly-selected-contact pairing strategy, a fewest-contacts-taken-by-agent pairing strategy, a sequentially-labeled-agent pairing strategy, a longest-waiting-contact pairing strategy, and a highest-priority-contact pairing strategy.
In accordance with other aspects of this embodiment, the at least two pairing strategies may alternate more frequently than once per day.
In accordance with other aspects of this embodiment, the at least two pairing strategies may alternate more frequently more frequently than once per hour.
In accordance with other aspects of this embodiment, the Yule-Simpson effect may be a result of an underlying partitioning of contact-agent interactions into at least the first and second pluralities of contact-agent interactions according to at least one of: a plurality of time periods, a plurality of agent skills, a plurality of contact-agent assignment strategies (pairing strategies), a plurality of contact center sites, a plurality of contact center switches, and a plurality of benchmarking schedules.
In accordance with other aspects of this embodiment, the method may further comprise determining, by the at least one computer processor, an estimation of an extent of the Yule-Simpson effect.
In another embodiment, the techniques may be realized as a system for benchmarking pairing strategies in a contact center system comprising: at least one computer processor configured to operate in the contact center system, wherein the at least one computer processor is further configured to: determine results for a first plurality of contact-agent interactions; determine results for a second plurality of contact-agent interactions; and determine combined results across the first and second pluralities of contact-agent interactions corrected for a Yule-Simpson effect.
In another embodiment, the techniques may be realized as an article of manufacture for benchmarking pairing strategies in a contact center system comprising: a non-transitory computer processor readable medium; and instructions stored on the medium; wherein the instructions are configured to be readable from the medium by at least one computer processor configured to operate in the contact center system and thereby cause the at least one computer processor to operate further so as to: determine results for a first plurality of contact-agent interactions; determine results for a second plurality of contact-agent interactions; and determine combined results across the first and second pluralities of contact-agent interactions corrected for a Yule-Simpson effect.
The present disclosure will now be described in more detail with reference to particular embodiments thereof as shown in the accompanying drawings. While the present disclosure is described below with reference to particular embodiments, it should be understood that the present disclosure is not limited thereto. Those of ordinary skill in the art having access to the teachings herein will recognize additional implementations, modifications, and embodiments, as well as other fields of use, which are within the scope of the present disclosure as described herein, and with respect to which the present disclosure may be of significant utility.



BRIEF DESCRIPTION OF THE DRAWINGS
In order to facilitate a fuller understanding of the present disclosure, reference is now made to the accompanying drawings, in which like elements are referenced with like numerals. These drawings should not be construed as limiting the present disclosure, but are intended to be illustrative only.
FIG. 1 shows a block diagram of a contact center system according to embodiments of the present disclosure.
FIG. 2 shows a flow diagram of a benchmarking method according to embodiments of the present disclosure.
FIG. 3 shows a flow diagram of a benchmarking method according to embodiments of the present disclosure.



DETAILED DESCRIPTION
A typical contact center algorithmically assigns contacts arriving at the contact center to agents available to handle those contacts. Several potential algorithms exist for assigning contacts to contact center agents. These include time-ordered assignment strategies, utilization-based assignment strategies, performance-based assignment strategies, and behaviorally-based assignment strategies.
At times, contact center administrators may wish to compare the performance of one algorithm against another. In some cases, contact center administrators can do this by alternating between the two algorithms and examining the resultant differences in performance over time. Such a benchmarking process can be subject to the Yule-Simpson effect (also referred to as “Simpson's Paradox”) in which the aggregation or amalgamation of distinct cross-sections of data can result in a misleading assessment of the actual performance differential between the assignment algorithms being alternated. See E. Simpson, “The Interpretation of Interaction in Contingency Tables,” J. of the Royal Statistical Society, Series B, vol. 13, at pp. 238-241 (1951), which is hereby incorporated by reference.
In some cases, such a mischaracterization of performance can be large. For example, one algorithm may consistently outperform another in each of the periods in which it was responsible for contact assignment, but when aggregated the apparent performance of the two algorithms may in fact be reversed. A classic example of a reversal due to the Yule-Simpson effect was found in a study of graduate school admissions, in which most individual departments had a bias in favor of admitting female students, but aggregating the data made it appear as if the school as a whole had a bias in favor of admitting male students. See P. Bickel, et al., “Sex Bias in Graduate Admissions: Data from Berkeley,” Science, vol. 187, issue 4175, at pp. 398-404 (1975), which is hereby incorporated by reference.
FIG. 1 shows a block diagram of a contact center system 100 according to embodiments of the present disclosure. The description herein describes network elements, computers, and/or components of a system and method for simulating contact center systems that may include one or more modules. As used herein, the term “module” may be understood to refer to computing software, firmware, hardware, and/or various combinations thereof. Modules, however, are not to be interpreted as software which is not implemented on hardware, firmware, or recorded on a processor readable recordable storage medium (i.e., modules are not software per se). It is noted that the modules are exemplary. The modules may be combined, integrated, separated, and/or duplicated to support various applications. Also, a function described herein as being performed at a particular module may be performed at one or more other modules and/or by one or more other devices instead of or in addition to the function performed at the particular module. Further, the modules may be implemented across multiple devices and/or other components local or remote to one another. Additionally, the modules may be moved from one device and added to another device, and/or may be included in both devices.
As shown in FIG. 1, the contact center system 100 may include a central switch 110. The central switch 110 may receive incoming contacts (e.g., callers) or support outbound connections to contacts via a telecommunications network (not shown). The central switch 110 may include contact routing hardware and software for helping to route contacts among one or more contact centers, or to one or more PBX/ACDs or other queuing or switching components within a contact center.
The central switch 110 may not be necessary if there is only one contact center, or if there is only one PBX/ACD routing component, in the contact center system 100. If more than one contact center is part of the contact center system 100, each contact center may include at least one contact center switch (e.g., contact center switches 120A and 120B). The contact center switches 120A and 120B may be communicatively coupled to the central switch 110.
Each contact center switch for each contact center may be communicatively coupled to a plurality (or “pool”) of agents. Each contact center switch may support a certain number of agents (or “seats”) to be logged in at one time. At any given time, a logged-in agent may be available and waiting to be connected to a contact, or the logged-in agent may be unavailable for any of a number of reasons, such as being connected to another contact, performing certain post-call functions such as logging information about the call, or taking a break.
In the example of FIG. 1, the central switch 110 routes contacts to one of two contact centers via contact center switch 120A and contact center switch 120B, respectively. Each of the contact center switches 120A and 120B are shown with two agents each. Agents 130A and 130B may be logged into contact center switch 120A, and agents 130C and 130D may be logged into contact center switch 120B. In a multi-skilled environment, contacts may be directed to one contact center switch or another, one pool of agents or another, etc., depending on the needs of the contact. For example, agents skilled at sales may be more likely to receive contacts seeking to make a purchase, whereas agents skilled at technical support may be more likely to receive contacts seeking technical assistance.
The contact center system 100 may also be communicatively coupled to an integrated service from, for example, a third party vendor. In the example of FIG. 1, benchmarking module 140 may be communicatively coupled to one or more switches in the switch system of the contact center system 100, such as central switch 110, contact center switch 120A, or contact center switch 120B. In some embodiments, switches of the contact center system 100 may be communicatively coupled to multiple benchmarking modules. In some embodiments, benchmarking module 140 may be embedded within a component of a contact center system (e.g., embedded in or otherwise integrated with a switch). The benchmarking module 140 may receive information from a switch (e.g., contact center switch 120A) about agents logged into the switch (e.g., agents 130A and 130B) and about incoming contacts via another switch (e.g., central switch 110) or, in some embodiments, from a network (e.g., the Internet or a telecommunications network) (not shown). In some embodiments, benchmarking module 140 may be configured to measure relative performance among two or more pairing strategies with Yule-Simpson effect compensation, without Yule-Simpson effect compensation, or both.
FIG. 2 shows a flow diagram of benchmarking method 200 according to embodiments of the present disclosure. At block 210, benchmarking method 200 may begin.
At block 210, results for a first plurality of contact-agent interactions paired using alternating pairing strategies may be recorded. For example, benchmarking module 140 (FIG. 1) or other pairing modules (not shown) may cycle among two or more pairing strategies, such as a first-in, first-out (“FIFO”) pairing strategy and a behavioral pairing (“BP”) pairing strategy. Various other pairing strategies (e.g., longest-available agent pairing strategy, fewest-contact-interactions-taken-by-agent pairing strategy, etc.), and various benchmarking strategies (e.g., epoch, inline, and hybrid epoch-inline benchmarking strategies) are described in, e.g., U.S. patent application Ser. No. 15/131,915, filed Apr. 18, 2016, which is hereby incorporated by reference. In some embodiments, the contact center system (e.g., contact center system 100) may be an inbound call center, and each contact-agent interaction is a call answered and handled by a phone agent. In other embodiments, contact-agent interactions may occur via email, instant messaging or chat, offline case allocations, etc.
At block 220, results for a second plurality of contact-agent interactions paired using the alternating pairing strategies (e.g., FIFO and BP pairing strategies) may be recorded. In some embodiments, blocks 210 and 220 may be performed simultaneously, as results for individual contact-agent interactions associated with either the first or second plurality of contact-agent interactions become available for recording or other processing. In some embodiments, contact-agent interactions may be grouped into more than two pluralities.
In some embodiments, contact-agent interactions may be divided based on sites. For example, the first plurality of contact-agent interactions may be handled by one contact center system, and the second plurality of contact-agent interactions may be handled by a second contact center system. Unequal distributions of contacts coupled with differences in measured outcomes between the two or more different sites (e.g., contact center systems) may give rise to the Yule-Simpson effect on the relative performance between the alternating pairing strategies.
In some embodiments, contact-agent interactions may be divided based on switches. For example, the first plurality of contact-agent interactions may be handled by one contact center switch (e.g., contact center switch 120A in FIG. 1), and the second plurality of contact-agent interactions may be handled by a second contact center switch (e.g., contact center switch 120B in FIG. 1). Unequal distributions of contacts coupled with differences in measured outcomes between the two or more switches may give rise to the Yule-Simpson effect on the relative performance between the alternating pairing strategies.
In some embodiments, contact-agent interactions may be divided based on skills. For example, the first plurality of contact-agent interactions may be handled by one pool of agents specializing in, e.g., sales, and the second plurality of contact-agent interactions may be handled by a second pool of agents specializing in, e.g., technical support. Unequal distributions of contacts coupled with differences in measured outcomes between the two or more skills may give rise to the Yule-Simpson effect on the relative performance between the alternating pairing strategies.
In some embodiments, contact-agent interactions may be divided based on time periods. For example, the first plurality of contact-agent interactions may be those that occurred during a first time period (e.g., a first hour, day, week, month), and the second plurality of contact-agent interactions may be those that occurred during a second time period (e.g., a second hour, day, week, month). Unequal distributions of contacts coupled with differences in measured outcomes between the two or more time periods may give rise to the Yule-Simpson effect on the relative performance between the alternating pairing strategies.
In some embodiments, contact-agent interactions may be divided based on benchmarking schedules. For example, the first plurality of contact-agent interactions may be handled according to a first benchmarking schedule (e.g., 50% FIFO and 50% BP). At some point, such as a point in time during a benchmarking reporting cycle (e.g., one week, one month), the benchmarking schedule may be adjusted, and the second plurality of contact-agent interactions may be handled according to a second benchmarking schedule (e.g., 20% FIFO and 80% BP). Unequal distributions of contacts coupled with differences in measured outcomes such as changes in conversion rates between the two or more benchmarking schedules may give rise to the Yule-Simpson effect on the relative performance between the alternating pairing strategies.
In some embodiments, the benchmarking schedule (e.g., 50% FIFO and 50% BP) may span a short period of time (e.g., thirty minutes, one hour) to complete one full cycle switching strategies. In other embodiments, the benchmarking schedule may span a longer period of time (e.g., several hours, two days). For longer cycle durations (e.g., two days, or one day of FIFO followed by one day of BP), there is a greater likelihood of an unequal distribution of contacts coupled with differences in measured outcomes, which may be due to special day-to-day promotional activities (e.g., Black Friday, Cyber Monday, holiday sales) or other sources of noise or variability.
In some embodiments, unequal distributions of contacts between the two or more portions of a benchmarking schedule may give rise to the Yule-Simpson effect as well. For example, a benchmarking schedule other than 50/50 (e.g., 20% FIFO and 80% BP) may be expected to have unequal distributions of contacts coupled with differences in measured outcomes between the different pairing strategies.
Moreover, even for 50/50 benchmarking schedules, unequal distributions of contacts may arise due to fluctuations in contact volume during the reporting cycle. For example, in the case of a 50/50 benchmarking schedule, one skill group may end up pairing 45% of contacts during the FIFO portion and 55% during the BP portion, while another skill group may remain at 50% each.
In some embodiments, different skills may be operating using different benchmarking schedules, or they may be operating on the same benchmarking schedule, but the benchmark distribution may be disturbed due to volume fluctuations for one or more the previously described reasons. For example, one skill may be a phone-based sales queue operating on a 50/50 benchmark, and the other skill may be a web-based sales queue operating on an 80/20 benchmark. In these embodiments, an unequal distribution of contacts coupled with differences in measured outcomes may give rise to the Yule-Simpson effect due to the differences in benchmarking schedules across skills.
In some embodiments, scheduled maintenance, contact center downtime, connectivity issues, or other unplanned slow-downs or outages may lead to unequal distributions of contacts coupled with differences in measured outcomes that gives rise to the Yule-Simpson effect.
The embodiments and scenarios described above are merely examples; many other situations may arise within a contact center system that can lead to imbalances to an underlying benchmarking strategy and the outcomes of different sets of contact interactions (e.g., call outcomes), which may give rise to the Yule-Simpson effect.
In some embodiments, contact-agent interactions may be divided based on a combination of two or more criteria for dividing contact-agent interactions. For example, contact-agent interactions may be divided by switch by site, by skill by day, by skill by benchmarking schedule, by skill by switch by day, etc.
Having recorded results for the two (or more) pluralities of contact-agent interactions at blocks 210 and 220, benchmarking method 200 may proceed to block 230.
At block 230, a correction factor may be applied to correct for the Yule-Simpson effect, and at block 240, relative performance between the alternating pairing strategies, corrected for the Yule-Simpson effect, may be determined.
The following tables illustrate an example of the Yule-Simpson effect on a contact center system in which benchmarking method 200 may be performed as described above. In this simple, illustrative scenario, the benchmarking module is operating on a sales queue in a contact center system with two skills, Skill A and Skill B (e.g., sales to new customers and sales to upgrade existing customers). Contacts may be paired to agents of either Skill A or Skill B, alternating between BP and FIFO pairing strategies. For each contact-agent interaction, a result is recorded. In this example, the result is binary indication of whether a sale was successfully completed with a new customer in Skill A or an existing customer in Skill B. The first plurality of contact-agent interactions are those assigned to agents designated for Skill A, and the second plurality of contact-agent interactions are those assigned to agents designated for Skill B.











TABLE I








BP Sales
FIFO Sales









Skill A
20 of 200
2 of 50



Skill B
30 of 100
28 of 100



Total
50 of 300
30 of 150










As shown in Table I (above), the contact center system handled 450 contact-agent interactions (e.g., 450 calls). The first plurality of contact-agent interactions (designated for Skill A) contained a total of 250 interactions, of which 200 were paired using BP and 50 were paired using FIFO. The second plurality of contact-agent interactions (designated for Skill B) contained a total of 200 interactions, of which 100 were paired using BP and 100 were paired using FIFO.
Also as shown in Table I, results were recorded for each contact-agent interaction. There were 22 successful sales within the first plurality of 250 Skill A interactions, of which 20 were attributable to BP pairing and 2 were attributable to FIFO pairing. There were 58 successful sales within the second plurality of 200 Skill B interactions, of which 30 were attributable to BP pairing and 28 were attributable to FIFO pairing. In this example, unequal contact distribution between skills gives rise to the Yule-Simpson effect, as shown in Table II (below).












TABLE II








BP 
FIFO 
Relative 




Conversion
Conversion
Performance of




Rate
Rate
BP over FIFO









Skill A
10.0%
 4.0%
150.0%



Skill B
30.0%
28.0%
  7.1%



Total
16.7%
20.0%
 −16.7%  










As show in Table II, conversion rates can be determined that are attributable to each of the pairing strategies. The conversion rate for all interactions paired using BP (50 of 300) is approximately 16.7%, and the conversion rate for all interactions paired using FIFO (30 of 150) is 20%. In this example, it appears as though BP performed worse than FIFO across all interactions. The drop in performance from FIFO to BP is approximately a negative 16.7% gain.
Also as shown in Table II, the conversion rates for interactions of the first plurality (Skill A) is 10% for BP pairings (20 of 200) and 4% for FIFO pairings (2 of 50). The conversion rates for interactions of the second plurality (Skill B) is 30% for BP pairings (30 of 100) and 28% for FIFO pairings. In this example, BP performed better than FIFO across all of the Skill A interactions (150% gain) and all of the Skill B interactions (approximately 7.1% gain). Paradoxically, BP performed better than FIFO when calculated on a skill-by-skill basis, but worse when the unequal distributions of interactions are inappropriately summed without a correction factor for the Yule-Simpson effect (“Simpson's Paradox”).
In some embodiments, one or more correction factors may be applied to correct for the Yule-Simpson effect to, for example, normalize the uneven distribution of interactions across skills. In some embodiments, correction factors may be applied to the first plurality of contact-agent interactions (Skill A) to normalize the number of contact-agent interactions paired within Skill A using BP and FIFO, and correction factors may be applied to the second plurality of contact-agent interactions (Skill B) to normalize the number of contact-agent interactions paired within Skill B using BP and FIFO, as shown below in Table III.
In some embodiments, the correction factor for each combination of pairing method and skill may be one-half the ratio of total contact-agent interactions for the skill to the number of contact-agent interactions for the pairing method within the skill, as shown below in Table III. For example, the BP correction factor for Skill A may be computed as (0.5)(200+50)/200=0.625, and the FIFO correction factor for Skill A may be computed as (0.5)(200+50)/50=2.5. Because the number of contact-agent interactions is already balanced between BP and FIFO pairings within Skill B, no correction factors are needed (i.e., a multiplicative identity factor of 1.0).
Applying the BP and FIFO correction factors to the BP Sales and FIFO Sales, respectively, results in normalized values for BP Sales and FIFO sales, as shown in Table III.











TABLE III






BP 
FIFO 





Correction
Correction
BP Sales
FIFO Sales



Factor
Factor
(Normalized)
(Normalized)







Skill A
0.625
2.5
12.5 of 125
 5 of 125


Skill B
N/A (1.0)
N/A (1.0)
  30 of 100
28 of 100


Total


42.5 of 225
33 of 225









Other embodiments may use other suitable corrections, adjustments, or other techniques to normalize or otherwise compensate for the Yule-Simpson effect. In each case, the conversion rates for each individual skill remains the same, so the relative performance of BP over FIFO for each individual skill remains the same. However, having normalized the number of interactions across each skill, the data may now be aggregated appropriately to arrive at a total conversion rate across all skills, and a total gain in performance of BP over FIFO.
The example shown in Table IV shows conversion rates and relative performance for the two pairing strategies across skills and in the aggregate after applying one or more correction factors as shown in, e.g., Tables IIIA-C. Table IV shows that Simpson's Paradox has been eliminated, and an appropriate total positive gain for BP over FIFO has been determined.










TABLE IV






BP 
FIFO 
Relative



Conversion
Conversion
Performance of



Rate
Rate
BP over FIFO







Skill A
10.0%
 4.0%
150.0%


Skill B
30.0%
28.0%
  7.1%


Total
18.9%
14.7%
 28.6%


(Normalized)









As shown in Table IV, the conversion rates for BP and FIFO pairings within each skill remain the same. Accordingly, the relative performance or gain of BP over FIFO remains the same for each skill (i.e., 150% and approximately 7.1%, respectively). However, in contrast to the total or aggregated gain shown in Table II (approximately −16.7%), the normalized total or aggregated gain shown in Table IV is 28.6%. In Table IV, the effect of Simpson's Paradox has been eliminated, and the aggregated gain is appropriately positive just as the gain for the individual skills is positive.
Following the determination of the relative performance corrected for the Yule-Simpson effect at block 240, benchmarking method 200 may end. In some embodiments, benchmarking method 200 may return block 210 and/or block 220 to record and process further results of contact-agent interactions.
In some embodiments, the increase in performance of one pairing strategy (e.g., BP) over another (e.g., FIFO) may be used to determine an economic benefit. In turn, this economic benefit may be used to determine a fee or payment to a third-party vendor or other supplier of the beneficial pairing strategy (e.g., a vendor of a behavioral pairing module). Thus, correcting for the Yule-Simpson effect, the vendor's customers can be assured that they are charged a fair price, and the Yule-Simpson effect does not inadvertently lead to charging too much or too little by aggregating data in a statistically inappropriate way.
In some embodiments, the benchmarking module 140 may be configured to determine an aggregated performance gain that does not correct for the Yule-Simpson effect in addition to a normalized aggregated performance gain that does correct for the Yule-Simpson effect. For example, FIG. 3 shows a flow diagram of benchmarking method 300 according to embodiments of the present disclosure. At block 310, benchmarking method 300 may begin.
At block 310, as in block 210 of benchmarking method 200, results for a first plurality of contact-agent interactions paired using alternating pairing strategies may be recorded. At block 320, as in block 220 of benchmarking method 200, results for a second plurality of contact-agent interactions paired using the alternating pairing strategies may be recorded. In some embodiments, blocks 310 and 320 may be performed simultaneously, as results for individual contact-agent interactions associated with either the first or second plurality of contact-agent interactions become available for recording or other processing. In some embodiments, contact-agent interactions may be grouped into more than two pluralities.
At block 330, relative performance between the alternating pairing strategies may be determined without correcting for the Yule-Simpson effect. For example, as in Table II above, the total relative performance of BP to FIFO was a loss of approximately 16.7%.
At block 340, relative performance between the alternating pairing strategies may be determined with correction for the Yule-Simpson effect. For example, as in Table IV above, the normalized total relative performance of BP to FIFO was a gain of 28.6%.
At block 350, in some embodiments, an amount of relative performance mischaracterization attributable to the Yule-Simpson effect may be determined. For example, comparing the total gain in Table II to the normalized total gain in Table IV, the Yule-Simpson effect caused an approximately 45.3-point drop in relative performance of BP to FIFO, or a decrease of approximately 171.3%. In some embodiments, the output of blocks 330, 340, and/or 350, along with other information regarding the performance of the contact center system, may be incorporated into reports or stored in databases or other memory. This information may be helpful for demonstrating the impact of the Yule-Simpson effect and the importance of correcting it and accounting for it to determine the statistically appropriate economic value attributable to one pairing strategy over another.
Following the output of gains or other data generated at blocks 330, 340, and/or 350, benchmarking method 300 may end. In some embodiments, benchmarking method 300 may return block 310 and/or block 320 to record and process further results of contact-agent interactions.
At this point it should be noted that benchmarking pairing strategies in a contact center system in accordance with the present disclosure as described above may involve the processing of input data and the generation of output data to some extent. This input data processing and output data generation may be implemented in hardware or software. For example, specific electronic components may be employed in a behavioral pairing module or similar or related circuitry for implementing the functions associated with behavioral pairing in a contact center system in accordance with the present disclosure as described above. Alternatively, one or more processors operating in accordance with instructions may implement the functions associated with behavioral pairing in a contact center system in accordance with the present disclosure as described above. If such is the case, it is within the scope of the present disclosure that such instructions may be stored on one or more non-transitory processor readable storage media (e.g., a magnetic disk or other storage medium), or transmitted to one or more processors via one or more signals embodied in one or more carrier waves.
The present disclosure is not to be limited in scope by the specific embodiments described herein. Indeed, other various embodiments of and modifications to the present disclosure, in addition to those described herein, will be apparent to those of ordinary skill in the art from the foregoing description and accompanying drawings. Thus, such other embodiments and modifications are intended to fall within the scope of the present disclosure. Further, although the present disclosure has been described herein in the context of at least one particular implementation in at least one particular environment for at least one particular purpose, those of ordinary skill in the art will recognize that its usefulness is not limited thereto and that the present disclosure may be beneficially implemented in any number of environments for any number of purposes. Accordingly, the claims set forth below should be construed in view of the full breadth and spirit of the present disclosure as described herein.

## Claims

1. A method for benchmarking pairing strategies in a contact center system comprising:
determining, by at least one computer processor communicatively coupled to and configured to operate in the contact center system, results for a first plurality of contact-agent interactions;
determining, by the at least one computer processor, results for a second plurality of contact-agent interactions;
determining, by the at least one computer processor, combined results across the first and second pluralities of contact-agent interactions corrected for a Yule-Simpson effect; and
outputting, by the at least one computer processor, the combined results, wherein the combined results demonstrate that optimizing performance of the contact center system may be realized after correcting for the Yule-Simpson effect.

2. The method of claim 1, wherein at least one of the first and second pluralities of contact-agent interactions were paired using at least two pairing strategies.

3. The method of claim 2, wherein a pairing strategy of the at least two pairing strategies comprises at least one of:
a behavioral pairing (BP) strategy,
a first-in, first-out (FIFO) pairing strategy,
a performance-based routing (PBR) strategy,
a highest-performing-agent pairing strategy,
a highest-performing-agent-for-contact-type pairing strategy,
a longest-available-agent pairing strategy,
a least-occupied-agent pairing strategy,
a randomly-selected-agent pairing strategy,
a randomly-selected-contact pairing strategy,
a fewest-contacts-taken-by-agent pairing strategy,
a sequentially-labeled-agent pairing strategy,
a longest-waiting-contact pairing strategy, and
a highest-priority-contact pairing strategy.

4. The method of claim 2, wherein the at least two pairing strategies alternate more frequently than once per day.

5. The method of claim 2, wherein the at least two pairing strategies alternate more frequently more frequently than once per hour.

6. The method of claim 1, wherein the Yule-Simpson effect was a result of an underlying partitioning of contact-agent interactions into at least the first and second pluralities of contact-agent interactions according to at least one of:
a plurality of time periods,
a plurality of agent skills,
a plurality of contact-agent assignment strategies (pairing strategies),
a plurality of contact center sites,
a plurality of contact center switches, and
a plurality of benchmarking schedules.

7. The method of claim 1, further comprising determining, by the at least one computer processor, an estimation of an extent of the Yule-Simpson effect.

8. A system for benchmarking pairing strategies in a contact center system comprising:
at least one computer processor communicatively coupled to and configured to operate in the contact center system, wherein the at least one computer processor is further configured to:
determine results for a first plurality of contact-agent interactions;
determine results for a second plurality of contact-agent interactions;
determine combined results across the first and second pluralities of contact-agent interactions corrected for a Yule-Simpson effect; and
output the combined results, wherein the combined results demonstrate that optimizing performance of the contact center system may be realized after correcting for the Yule-Simpson effect.

9. The system of claim 8, wherein at least one of the first and second pluralities of contact-agent interactions were paired using at least two pairing strategies.

10. The system of claim 9, wherein a pairing strategy of the at least two pairing strategies comprises at least one of:
a behavioral pairing (BP) strategy,
a first-in, first-out (FIFO) pairing strategy,
a performance-based routing (PBR) strategy,
a highest-performing-agent pairing strategy,
a highest-performing-agent-for-contact-type pairing strategy,
a longest-available-agent pairing strategy,
a least-occupied-agent pairing strategy,
a randomly-selected-agent pairing strategy,
a randomly-selected-contact pairing strategy,
a fewest-contacts-taken-by-agent pairing strategy,
a sequentially-labeled-agent pairing strategy,
a longest-waiting-contact pairing strategy, and
a highest-priority-contact pairing strategy.

11. The system of claim 9, wherein the at least two pairing strategies alternate more frequently than once per day.

12. The system of claim 9, wherein the at least two pairing strategies alternate more frequently more frequently than once per hour.

13. The system of claim 8, wherein the Yule-Simpson effect was a result of an underlying partitioning of contact-agent interactions into at least the first and second pluralities of contact-agent interactions according to at least one of:
a plurality of time periods,
a plurality of agent skills,
a plurality of contact-agent assignment strategies (pairing strategies),
a plurality of contact center sites,
a plurality of contact center switches, and
a plurality of benchmarking schedules.

14. The system of claim 8, wherein the at least one computer processor is further configured to:
determine an estimation of an extent of the Yule-Simpson effect.

15. An article of manufacture for benchmarking pairing strategies in a contact center system comprising:
a non-transitory computer processor readable medium; and
instructions stored on the medium;
wherein the instructions are configured to be readable from the medium by at least one computer processor communicatively coupled to and configured to operate in the contact center system and thereby cause the at least one computer processor to operate further so as to:
determine results for a first plurality of contact-agent interactions;
determine results for a second plurality of contact-agent interactions;
determine combined results across the first and second pluralities of contact-agent interactions corrected for a Yule-Simpson effect; and
output the combined results, wherein the combined results demonstrate that optimizing performance of the contact center system may be realized after correcting for the Yule-Simpson effect.

16. The article of manufacture of claim 15, wherein at least one of the first and second pluralities of contact-agent interactions were paired using at least two pairing strategies.

17. The article of manufacture of claim 16, wherein a pairing strategy of the at least two pairing strategies comprises at least one of:
a behavioral pairing (BP) strategy,
a first-in, first-out (FIFO) pairing strategy,
a performance-based routing (PBR) strategy,
a highest-performing-agent pairing strategy,
a highest-performing-agent-for-contact-type pairing strategy,
a longest-available-agent pairing strategy,
a least-occupied-agent pairing strategy,
a randomly-selected-agent pairing strategy,
a randomly-selected-contact pairing strategy,
a fewest-contacts-taken-by-agent pairing strategy,
a sequentially-labeled-agent pairing strategy,
a longest-waiting-contact pairing strategy, and
a highest-priority-contact pairing strategy.

18. The article of manufacture of claim 16, wherein the at least two pairing strategies alternate more frequently more frequently than once per hour.

19. The article of manufacture of claim 15, wherein the Yule-Simpson effect was a result of an underlying partitioning of contact-agent interactions into at least the first and second pluralities of contact-agent interactions according to at least one of:
a plurality of time periods,
a plurality of agent skills,
a plurality of contact-agent assignment strategies (pairing strategies),
a plurality of contact center sites,
a plurality of contact center switches, and
a plurality of benchmarking schedules.

20. The article of manufacture of claim 15, wherein the at least one computer processor is further caused to operate so as to:
determine an estimation of an extent of the Yule-Simpson effect.