University of Nottingham

It’s Just Not Cricket

An Investigation into the effects of Anchoring on Player Wages in the Indian Premier League

Oliver Haskins 4228781

Supervisor: Fabio Tufano

Word Count: 12,487

This Dissertation is presented in part fulfillment of the requirement for the completion of an MSc in the School of Economics, University of Nottingham. The work is the sole responsibility of the

candidate.The Indian Premier League, a Twenty-20 cricket tournament, is unique in the sporting world by assigning players to teams using an English auction. The auction system means that players can move quickly and easily between teams with a possible change in their wage level year on year. This allows for subconscious anchoring effects to influence the decisions of the franchises when bidding for players, and gives a real world environment where such an effect can be measured. This paper analyses the anchoring effect using a hedonic valuation estimate based on a player’s performance and their wage in the subsequent season. Supporting evidence of the anchoring effect is found using both cross-sectional models and novel panel estimation techniques.

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ContentsIntroduction...........................................................................................................................................1

Literature Review..................................................................................................................................3

Methodology.......................................................................................................................................14

The IPL.............................................................................................................................................14

Table 3.1 Finishing Positions of each team..............................................................................15

Rules................................................................................................................................................15

Auction............................................................................................................................................16

Data Collection................................................................................................................................16

Table 3.2 Performance Measures............................................................................................18

Hedonic Valuation Estimation.........................................................................................................19

Anchoring Model.............................................................................................................................21

Results.................................................................................................................................................22

Graph 4.1.........................................................................................................................................22

Graph 4.2........................................................................................................................................23

Graph 4.3.........................................................................................................................................24

Table 4.1......................................................................................................................................25

Table 4.2......................................................................................................................................25

Table 4.3......................................................................................................................................26

Table 4.4......................................................................................................................................26

Table 4.5......................................................................................................................................28

Concluding Remarks............................................................................................................................29

References:..........................................................................................................................................37

IntroductionReference-dependant prices and the anchoring and adjustment heuristic have long been studied and

analysed in behavioural economics literature, but have been mainly with a focus on an experimental

methodology. The first study identifying the heuristic is that of Tversky and Kahneman (1974) who

state that:

“Anchoring is the disproportionate influence on decision makers to make judgements that

are biased toward an initially presented value.”

Few have expanded into analysing the phenomenon using field data until more recently, with work

being conducted by Beggs and Graddy (2008), Johnson et al. (2009) and McAlvanah and Moul (2013)

– all of which will be discussed in more detail in the literature review. This paper aims to expand the

current area of research by looking at the effect of anchoring on player wages in the Indian Premier

League, a twenty-20 cricket tournament. The IPL is unique within the sporting world for the manner

in which it drafts players to franchises or teams through an English auction. This environment is ideal

for analysing any effects of anchoring on previous wage levels when assigning new player wages, as

buyers are given an almost free choice in assigning a value to a particular individual. Using data

compiled from numerous online sources, listed in the methodology, this paper estimates a hedonic

valuation estimate based on quality attributes of a player from the previous season. Using this

hedonic valuation and the previous salary of a given player, along with a series of external control

variables, the anchoring effect is able to be isolated and measured.

The current paper addresses the primary hypothesis;

i. Anchoring on a previous wage level causes wages to remain at a similar level, independent

of the past performance of the player.

As an additional test of the data, the following secondary hypothesis will also be analysed;

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ii. Due to the rule limiting the number of overseas players per team, the increased demand for

Indian players will cause a wage premium amongst those players.

Using field data will add to the depth of the current research by testing the established heuristic in a

realistic setting, not one composed in laboratory environments. This will help to establish whether

the heuristic is apparent and significant in real-world economic situations and how it influences the

buying and selling strategies of economic agents.

Consider for example, a player who performed exceptionally well in the build up to a particular IPL

season. As such teams will pay a premium for his services, given that he has not previously appeared

at the drafting process. The high price fetched in the debut season may hold his wage at a higher

level even if his performance falters during his IPL career. Conversely, an up and coming player may

fetch a low price at their initial auction due to inexperience or poor results leading up to the auction

date but may however, perform significantly above their expected level. Will their low initial wage

impact on their chance of their wage increasing despite subsequent strong performances?

This paper finds weak but significant support for the anchoring heuristic in a naturalistic

environment. The evidence apparent does not confirm whether anchoring carries the sole

responsibility in sticky player wages but it is noted that it makes some, however small, impact on the

determination of future wages. This paper will be structured as follows; a literature review of the

relevant studies will be discussed, highlighting the need for further research using field data; a

methodological approach taken by the paper will then be constructed and the intuition of the model

discussed; section 4 will analyse the results of the empirical strategy before being deliberated in the

concluding remarks where the scope for further research and interesting lines of enquiry are also

posited.

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Literature ReviewThe anchoring and adjustment heuristic has been studied in detail in a laboratory setting, first being

introduced by Tversky and Kahneman (1974) in their seminal paper on the subject. Their classic

experiment presented the subject with a randomly generated number or anchor, prior to asking the

participant to estimate a number from a set of general knowledge questions. Subjects

overwhelmingly displayed a bias toward the initial (often irrelevant) anchor value, in their final

estimate.

This initial finding gave rise to a plethora of research focusing on how anchor values influence

subjects decisions, from general knowledge questions (Epley & Gilovich, 2001; McElroy and Dowd,

2007; Mussweiler, 2003) and probability estimates (Chapman and Johnson, 1999) to legal judgments

(Englich, Mussweiler & Strack, 2006) to purchasing decisions (Ariely et al., 2003). Within each of

these environments the difference between a self-generated anchor or an externally-provided

anchor has been measured. Epley & Gilovich (2001) established that both forms of anchor, either

self-generated or externally-provided, impact on the decisions formed by subjects in subtly different

manners. The authors demonstrate that the adjustment process is activated when the self-

generated anchor is employed but that a ‘selective-accessibility’ mechanism is used upon external

anchor values. Selective accessibility is the process where an external anchor value is processed by

the subject and confirmed to be within reasonable degree of accuracy, prior to forming an estimate,

this is otherwise known as the confirmatory hypothesis. Subjects confirm the accuracy of the

external anchor value before forming their judgements, a process not possible under self-generated

anchors. One implication of this method is that if an anchor value is of complete irrelevance or

obviously heterogeneous from the perceived accurate range, then subjects will disregard the

information, a theory supported by the findings of Sugden et al. (2013). Their paper examined the

impacts of varying anchors on willingness-to-pay or willingness-to-accept valuations, through

studying the purchase decisions of their subjects. The prices of their anchor commodities may have

been generally well known. As such, an irrelevant price anchor may have been easy to identify and

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subsequently disregard leading to their supportive conclusions. The literature is divided in the belief

of which mechanism is the primary driving force behind the anchoring evidence. Epley and Gilovich

in their 2001 paper show evidence that both mechanisms are employed in different situations and

no single mechanism can explain the results found in the lab.

Most studies have remained laboratory-based to study how the various scenarios impact on the

heuristic, real world economic decisions or field experiments have been rather sparse in the

literature. Thorsteinson et al. (2008) began the cross-over from laboratory experiments to using

both laboratory generated data and field data to reinforce the robustness of the heuristic in a real

world environment. They measured the effects of irrelevant anchors on performance judgements,

such as job performance ratings and student evaluations of instructors using both laboratory

collected data and real-world data. They found that in both the lab and field experiments an

alternative anchoring manipulation affected the performance judgements of the subjects. Their

alternative method used no explicit comparative question to form an anchor, as in the case with

traditional methods. The authors posited that an indirect comparison would be drawn without the

need for a direct comparative question. Their findings support this hypothesis in both laboratory and

field settings. The field data was gathered using a questionnaire-based rating system, asking current

students to rate the performance of their course instructor under five separate treatments. There

was a significant anchoring effect under all treatments other than the control group, which was

subjected to no anchor. Their paper lends support to the theory that the anchoring and adjustment

heuristic is not only a phenomenon found in the laboratory but also has an impact on real-world

decisions. However, their methods may have mimicked a real-world performance rating scenario but

were still conducted and collected under laboratory conditions with the sample consisting of drafted

students who attended in exchange for course credit in the same manner as those students in the

laboratory settings. In this sense, laboratory data was collected mimicking a field setting but was not

in fact field data.

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Wolk and Spann (2008) collected field data from a popular online ‘Name-your-own-price” auction

site, and measured the effects of a reference price on the final bid valuation. For the seller, the only

control they had over the price they take is their advertised reference price, when controlling for all

other internal and external reference prices, such as similar items that have previously been sold, or

similar items from other websites to which all consumers have access. Despite this perceived lack of

control the authors did find evidence of anchoring towards the advertised value when it is

considered plausible, resulting in higher bids. However, when the advertised valuation was

implausible or exaggerated it was found to have a detrimental effect on the final bid price. This

supports the aforementioned paper by Sugden et al. (2013) and their work on the relevance of the

anchor value.

The need for field data from real world economic markets motivated Beggs and Graddy (2009) to

examine the heuristic in art auction markets in their paper, “Anchoring Effects, Evidence from Art

Auctions” published in the American Economic Review.

Beggs and Graddy, use data collected from auctions of Impressionist and Modern Art as well as

Contemporary Art to test whether previous sale price has an effect on the future sale price and on

experts’ presale valuations. The authors hypothesise that those paintings which sold in a “hot”

market, where they were sold for a high price, would resell for a higher price than those initially sold

in a “cold” market, where they obtained a low price.

The authors amalgamated data from two primary sources with over 12,000 observations in the

Impressionist Art dataset and just under 3,500 observations in the Contemporary dataset. Both

datasets span a period of roughly 10 years and the total dataset is used to predict art value. The

authors rejected larger datasets that contain many more repeat sales as the period of time between

sales was deemed too large to hold any anchoring effect. The assumption made here is that the

influence of a previous price anchor has an unidentified expiry after a certain date. The average

holding period in the dataset complied by Mei & Moses (2002), a viable alternative, is 28 years

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compared to 3 years in Beggs and Graddy’s dataset. Following this logic, Beggs and Graddy’s dataset

may contain many more examples of art work intended for quick trade as opposed to collection,

further enhancing the effect of any anchor present. If traders are involved in the quick sale of pieces

of artwork, then the transaction may turn from an emotionally attached artwork sale into an

opportunity for profit. Given the desire for profit, a seller is more likely to anchor their reservation

price or pre-sale estimate to that of the previous sale with no regard for the hedonic characteristics

of the actual artwork.

The distinct possibility that such art work was bought solely to trade may be the driving force behind

the strong anchoring effects seen in the market. Artwork bought for collection may hold a

sentimental value to the owner and any increase in resale price may be biased by such unobservable

characteristics.

In order to test for any anchoring effects, the authors needed to isolate the rational learning of

buyers and sellers form the irrational anchoring. They accomplished this through developing a

hedonic pricing estimate or prediction based on a set of discernible features of each painting and an

overall price index. They subsequently regressed actual sale price on their hedonic prediction, the

difference between previous price and their current predicted value, and on the difference between

the previous sale value and the previous predicted pricing estimate. The anchoring effect is captured

in the second expression and the final expression captures all other unobservable characteristics. It

is the change in demand and thus the change in overall price index which allows the authors to

isolate the anchoring, as all other unobservable characteristics are assumed to remain constant. This

model follows that developed by Genesove and Mayer (2001) and is formally represented:

PR = μπ + λ(P-1 – π) + ξ(P-1 – π -1)

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where,

πt = Xβ + δt

is their hedonic prediction of price. X signifies a painting’s hedonic characteristics whilst δt

represents the time-specific effects. By assuming that past prices influence current price in relative

rather than absolute terms, the authors work in log values. The effect of anchoring will be felt

relative to the previous price and to the price of surrounding items, thus each will not be considered

independently of one another or in absolute terms. It is the fact that the change is in relative terms

that gives rise to the anchoring effect; without relative comparison there would be no value from

which to anchor. An anchor value is thus interpreted to cause a percentage change in the resale

price, rather than a constant nominal change for all paintings, irrespective of value. For

completeness, anchoring is captured by the extent to which previous sale price affects actual sale

price.

Firstly, Beggs and Graddy use the complete dataset to form their hedonic predictions of the value of

the artwork. They estimate three separate predictions, Impressionist in London, Impressionist in

New York and Contemporary in New York using information on completed auctions (final selling

price). However, they argue that this specification biases their result by cropping the dataset below

the sellers’ reserve price, thus reducing any anchoring effect. By dropping observations without a

sale price, determined by the dependant variable, their ordinary least squares (OLS) estimation is

subject to sample selection or truncation bias.

To counter this, they ran a second specification using data on all items that were put up for auction

irrespective of whether or not they completed the sale and measured sale price of unsold items as

80% of the low estimate. As the item failed to sell, no sale price was available, hence the need for an

unsold proxy price. With 34.5% of their dataset being unsold auctions a substantial proportion of

their total dataset on final prices had to be estimated, possibly resulting in skewed results and

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heavily impacting on the validity of their results. They justify this decision by referring to Goetzmann

(1996) whom demonstrated that secret reserve prices are considered to average 80% of the low

estimate, thus taking 80% of the low estimate (secret reserve price) as the sale price for pieces that

failed to sell. Despite the reservations regarding the validity of the aforementioned assumption, the

authors chose to take this secondary step to eliminate any bias in the estimates of prices.

Secondly, in order to examine the effects of a reference point on presale low estimates, the authors

restricted the dataset to observations with a first sale and second listing (repeat sales/listings). This

reduced the dataset to 47 Contemporary paintings and 94 Impressionist, across both London and

New York samples. Drastically decreasing the sample size to such a small number of observations,

especially for the Contemporary data set, undeniably affected the validity of their results. Using a

dataset with fewer than 50 observations can result in the conclusions only being able to be

cautiously inferred due to the lack of explanatory power from such a small sample size. The small

sample size may not be representative of the larger population, inducing sample selection bias and

inconsistent estimators.

For the valuation predictions (πt) the authors regress the log of the sale price on the hedonic

characteristics of the paintings (date painted, size, signature, painting medium, artist etc.) and half-

year time dummies for each period, creating three separate predictions for New York Impressionist,

London Impressionist and Contemporary paintings respectively. Their hedonic characteristics are

shown to explain a large degree of the variation in the price; by removing these hedonic

characteristics the explanatory power of the artist and time dummy variables drops substantially. It

is also evident that the observable features of the paintings are all significant to the 10% level. The

overall results for the valuation predictions remain unchanged using either the complete (sold &

unsold paintings) or just the sold data samples.

Beggs and Graddy then ran an OLS regression on the model outlined above, using their estimated

valuation prediction. They used both actual sale price and the low value estimate as dependant

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variables in two separate regressions, using the complete and sold samples from their restricted

data set (repeat sales/listings), reporting similar findings across all categories.

The paper fails to show explicitly which variables are significant or insignificant and to what degree

these variables are significant. Instead they give standard errors in parentheses and leave the reader

to calculate the significance level of the mentioned variables. That being said, the anchoring effect

variable is significant across all specifications other than in the sold sample for Contemporary Art.

The authors attribute this lack of significance in the Contemporary art dataset to the truncating bias

from cropping the sample below the sellers’ reserve price, as previously mentioned. A bias in such a

manner could arise due to the sellers’ reserve price being adjusted less than that of the buyers, after

a painting has sold in a cold market, resulting in the lot not reaching the reserve price and thus

remaining unsold.

To further test the validity of their claims, Beggs and Graddy ran a series of robustness checks and

regressions with varying specifications and dropping a variety of variables from their model. They

concluded that these findings do not differ significantly from the main regression results under any

of their tested specifications and go on to stipulate that an exact specification of variables does not

influence the overall result. The authors proceed to check whether buyers anchor their valuations on

nominal or real prices. Intuitively, one would predict buyers to anchor on nominal values. To

demonstrate this, refer to Tversky and Kahneman’s definition of anchoring:

“Anchoring is the disproportionate influence on decision makers to make judgements that

are biased toward an initially presented value.”

If subjects were to take the initial value and consciously adjust for inflation, the process would no

longer be a subconscious assimilation toward an initially-presented value. Despite this, the authors

test for the source of the anchoring through deflating prices by the art index. They found no

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evidence of anchoring on real values, cautiously inferring subjects do behave as intuition would

suggest.

A probit model is developed alongside the main regressions to test whether sellers and auctioneers

are also subjected to anchoring effects from previous sales. The paper fails to display the results

formally but mentions in passing that no such anchoring is visible in the data. This suggests that,

whilst they certainly do not dismiss the possibility of anchoring affecting sellers, it does so in a

manner in line with buyers’ behaviour. Thus, any anchoring on the part of the sellers and

auctioneers is concealed by the actions of the buyers.

The specification of the model seems to have passed the robustness checks put in place by Beggs

and Graddy, and the hedonic pricing prediction is indeed commonplace in both the art auction

literature and the real-world anchoring literature. More on the hedonic pricing methods employed

in Beggs and Graddy’s paper will be explored within the context of sports player’s valuations.

The main criticisms with Beggs and Graddy’s methodology lie in the isolation of the influence of the

irrelevant anchor, the estimation of their perceived valuation, and the data that they choose to use.

Estimating the reserve price as 80% of the low valuation and taking this as a sale price, has a

significant bearing on the estimation of their valuation predictions, used to test for anchoring.

Despite the criticisms, the paper succeeds in contributing to the literature on anchoring in a field

setting. They find evidence supporting the heuristic in the real world and they go on to outline future

research being conducted on loss aversion and the role of traders in the auction houses.

The paper would benefit from a larger data set of repeat sales from more auction houses and could

aim to draw comparison across economies. Overall Beggs and Graddy accomplish their aim of

successfully contributing to the anchoring literature with field data but also leave many areas open

for further exploration.

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Further results supporting the anchoring heuristic are found in the housing market by Simonsohn

and Loewenstein (2006) who found that movers from more expensive cities spent more on housing

in cheaper cities. They also found they readjust their expenditures after a period of living in their

new city. A more recent example of anchoring in the housing market comes from Leung and Tsang

(2013) who follow the same empirical estimation as Beggs and Graddy. However, they also test for

loss aversion using the model proposed by Mei, Moses, Shapira and White (2010), by including a

dummy variable for gains and a sale-purchase ratio. They found that the anchoring effect diminished

over time and there was evidence supporting both loss aversion and anchoring in the Hong Kong

housing market.

Malpezzi’s paper ‘Hedonic Pricing Models: A Selective and Applied Review’ (2002) on the uses of,

and reviews of, hedonic pricing valuations in the housing market gives a well-rounded overview of

the uses of such quality driven pricing models in the art world. Their application to the art world can

also be transferred to that of the sporting auctions used in this paper as similar assumptions hold for

both environments.

Hedonic pricing valuations are used in a variety of sporting environments as well as in more

economy-focussed markets. Scully (1974) looked at the determinants of pay and performance across

major-league baseball players and estimated the relationship between the two. Scully found that the

skill set of the player was the determining factor behind their wage level and at the time of the data

collection, players were underpaid when compared to the marginal revenue they brought to their

club. Jones and Walsh in 1988 again looked at salary determination but for national hockey league

players instead. Once again, they found that the significant factor behind wages is the skill level of

the players, only finding slight levels of discrimination dependent upon player position.

Most relevant to this paper is a study conducted by Lenten, Geerling and Konya (2011) that analyses

a hedonic model of player valuations within the Indian Premier League. They also estimate separate

models using different data collected from various forms of the game; Twenty-20, One Day

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International and Test games. The results and significant variables are vastly different across

different forms of the game, which provides justification for using only IPL performance measures in

this paper. The functional form of their hedonic regression is log-linear, such that the dependant

variable is the log of the player value with all explanatory variables being linear. Their most

successful model (the model with the highest explanatory power) arises from the authors splitting

the data into Test and One Day International data sets. They find strong significance for domestic

(Indian) players, suggesting an Indian-premium, as well as a dummy variable they name the ‘X-

factor’. This X-factor dummy variable takes into account the marketability, support-pull or other

unobservable qualities a player may possess to generate extra value independent of their skill level.

How this X-factor variable is assigned is unclear but is most likely down to the authors’ intuition

based on cricketing knowledge. Parker, Burns and Natarajan (2008) draw similar conclusions to the

aforementioned authors, when running their own hedonic estimations of player values for the IPL.

They find similar significant results in terms of domestic premiums and the most important skill sets

to determine player wages. Where possible the significant variables apparent in both the Lenten

paper and the Parker paper will be used to determine the hedonic valuation estimates in this paper.

The auction environment lends itself to testing for anchoring bias as subjects are allowed to place

individual valuations on items without a set pricing structure. By allowing for such preferences to

dictate price it is then subjected to the subconscious effects of anchoring. This leads to the question;

is it the auction market that is subject to an anchoring bias, or is the heuristic present in all markets?

Betting markets have also been a popular source of anchoring analysis with a paper by Lui and

Johnson (2007) looking at the impact of anchoring on decision makers in the horserace betting

market. They find contradictory evidence in such a market and further reinforce the need for more

research to extend into other areas of economic decision making. McAlvanah and Moul (2013)

develop this line of enquiry by looking at the effects of anchoring among bookmakers in Australia.

They again look at horse racing but instead examine the impact of a horse pulling out of a race

immediately before the race commences and after betting has taken place. The authors find that the

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bookmakers fail to adjust fully from their anchored values and as a result are losing 20% of their

profit margin due to systematic under-adjustment.

It is clear from such contradictory results that the anchoring and adjustment heuristic is still in

debate when studying real world environments and further replication and adaptation is needed to

substantiate the theories.

Beggs and Graddy begin to answer whether anchoring can be sustained for long periods of time but

a more thorough exploration of time effects and estimation with a longer date series would be

beneficial. If the effects of the anchor values are long standing and robust in multiple economic

markets can sellers exploit such information and use it to their advantage? It is possible that some

corporations already do. Further analysis with field data collected from such corporations would be

needed to establish the validity of such a claim. In Beggs and Graddy’s paper the short time period

between sales suggest that many transactions are undertaken by traders rather than collectors of art

pieces. If this were the case, traders would display a much lower level of loss aversion, if any,

towards selling a piece of artwork and may be more influenced by the anchor value. If this is the case

in the auction market, is it also true of traders in other economic environments? Further study using

traders in betting markets, and subsequently financial markets, may bring new evidence on the

impact of anchor values in real world economic decisions.

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MethodologyThe Indian Premier League is one of the major sporting events on the calendar, especially amongst

cricket fans. The Twenty-20 series has excited the international cricket stage for the previous eight

seasons and is now a firm favourite with both Indian and international supporters. Not only does it

attract supporters but players relish the opportunity to play for one of the eight teams and soak up

the competitive atmosphere and earn one of the highest wages in cricketing history. The IPL is

unique within the sporting world, with the assignment of players’ wages and contracts determined

by an English auction pre-season. This gives teams the opportunity to bring in a set of new players

each season and maintain the fiercely competitive nature across all teams, a feat that cannot be

matched by any other sporting league. However, the auction format may not be the most efficient

method to assign players’ wages and could be subject to the same anchoring heuristic bias present

in other auction markets. Prior to discussing the impact of the anchoring heuristic, a study of the

rules, regulations and determinants of the Indian Premier League needs to be discussed.

The IPLThe inaugural season of the IPL took place in 2008 and consisted of eight teams, from cities around

the country of India, each secured on a franchise model. Please refer to table 3.1 for a complete list

of the competing teams in each season since the league’s initiation and their finishing positions. The

initial tournament was a huge success, no doubt helped by the competitiveness of all eight teams.

Since its inception the structure of the tournament has remained consistent, with each team playing

each other twice, in a home and away fixture, before the top four teams progress to the knockout

stages to compete for the title. Of the eleven teams which have ever taken part in the IPL five have

won the tournament at least once. In 2011 two new teams joined the league, forcing a slight change

in structure to the league system. Teams played a random selection of five other teams twice, again

in the home and away format, and four other teams once, playing a total of fourteen games prior to

the knockout stages. Upon completion of the fourth season, the Kochi franchise was terminated due

to financial irregularities, leaving nine teams to compete for the fifth title.

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The sixth season saw a change in the sponsorship from DLF (Delhi Land & Finance) to Pepsi Co,

resulting in a name change to The Pepsi Indian Premier League, and has remained this way since.

The 2015 season was the eight and most recent season.

Table 3.1 Finishing Positions of each team

Team 2008 2009 2010 2011 2012 2013 2014 2015Chennai Super Kings (CSK) 2nd 4th 1st 1st 2nd 2nd 3rd 2nd

Deccan Chargers (DC) 8th 1st 4th 7th 8th N/A N/A N/ADelhi Daredevils (DD) 4th 3rd 5th 10th 3rd 9th 8th 7th

Kochi Tuskers Kerala (KTK) N/A N/A N/A 8th N/A N/A N/A N/AKolkata Knight Riders (KKR) 6th 8th 6th 4th 1st 7th 1st 5th

Kings XI Punjab (KXIP) 3rd 5th 8th 5th 6th 6th 2nd 8th

Mumbai Indians (MI) 5th 7th 2nd 3rd 4th 1st 4th 1st

Pune Warriors India (PWI) N/A N/A N/A 9th 9th 8th N/A N/ARoyal Challengers Bangalore (RCB) 7th 2nd 3rd 2nd 5th 5th 7th 3rd

Rajasthan Royals (RR) 1st 6th 7th 6th 7th 3rd 5th 4th

Sunrisers Hyderabad (SH) N/A N/A N/A N/A N/A 4th 6th 6th

Source: www.iplt20.com/stats

RulesTeams in the inaugural season were given a single ‘Icon’ player who did not enter the auction and

represented the franchise from their home town. All other player signings were decided through the

English auction format. Since this, player transfers and team rosters have been updated and adapted

through three methods; the annual auction, inter-team trading, or signing domestic, uncapped or

replacement players. In 2008, each franchise was restricted to spend USD$5 million at the inaugural

auction. For the start of the 2012 season the auction rules were revised and the amount per team

was increased to $9 million. Teams were also allowed to retain a maximum of 4 players that were

charged at set prices, reducing the amount available to spend at auction if retention was

implemented. Given the drastic change in budgets and player retention rules, data will only be

collected from the 2012 5th season through to the latest, 8th season.

Teams were also subjected to rules regarding the composition of their squads. A maximum of ten

foreign players could be included in their roster, with a maximum of four included in the playing

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eleven at any one time. Of the remaining players, a minimum of fourteen had to be Indian-born and

six had to be younger than twenty two, giving young talent the opportunity to perform in the biggest

Twenty-20 tournament in the world.

AuctionAside from the signing of new talent, released players and new players can choose to be a part of

the auction format and allow the other teams to bid for them. Each franchise has a budget every

season to purchase players through the auction or choose to extend the contract of four of their

players from the previous season. The franchises then take part in an English auction to build their

squad roster around the core of retained players. This gives teams the opportunity to scout talent

from previous seasons and bid for them to become a member of their squad. The teams are bidding

for the players’ salary for that season, in that, the price any given player fetches at the auction is the

value of their salary, paid to them in either Indian Rupees or their domestic currency. The minimum

cap any player can earn is $20,000 with a maximum value increasing each year to a maximum of

$3,000,000 in the 8th season. In essence the auction system is a simple structure with the team

willing to pay the highest wage for a player earning that player’s signature. There are various other

detailed rules and regulations regarding the auction structure but for the purpose of this research

paper, these are not necessary to discuss.

Data CollectionRaw data has been collected from a variety of sources on the internet and compiled into one main

dataset with all drafted players across all seasons. ESPN’S Stat Guru has an extensive database of

player statistics that has been used on an individual player level to find control variables, to be

discussed in more detail later, such as age, nationality and experience (www.espncricinfo.com).

Individual batting and bowling statistics have been compiled from the Cricmetric database at a

season total for each capped player (www.cricmetric.com). From these individual statistics, formulae

have been developed to form important measures of performance, common within the cricket

18 | P a g e

world. These include a batsman’s strike-rate (runs scored per ball), a bowler’s economy (runs given

per ball) and their average runs per wicket among others. For a full list of statistics, variables,

formulae and description please refer to table 3.2.

As previously mentioned, all seasons prior to the 2012 season have been dropped due to the

significant alterations in tournament structure and financial regulations. Data from the 2012 season

through to the present leaves a total of 664 observations.

For a player’s wage to remain constant from season to season their contracted team must choose to

retain that player or fail to invoke their right-to-match opportunity. Given that players are retained

and changes to wages and contracts do not take place year on year, observations where a player has

not moved club or had no change to their wage structure are dropped, so as to analyse only the

observations where players where available for auction and a change in club caused a change in

their wage. Dropping observations with no wage change, or team change, year on year yields a total

of 153 observations. This leaves only the players who have entered the auction system and

undergone either a change in their wage or a change in their club; those observations that may be

subject to subconscious anchoring effects. Furthermore, the minimum salary of any signed player is

$20,000 whether this figure was attained at auction or not, if a team wants to obtain the services of

a particular player, the minimum they can pay them is $20,000, even if they think this is over-valuing

the particular player. As such, the real valuation of any player who earns the minimum wage is not

directly observed. Due to such difficulties in observing the value of players earning the minimum

$20,000, these observations are removed from the sample, leaving a total of 151 observations over

the aforementioned period.

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Table 3.2 Performance Measures

Variable Formulae Description

Batti

ng S

tatis

tics

Team Raw Data Team each player is contracted toSalary Raw Data The wage taken in a given season

Runs Scored (R) Raw Data Total season runs on an individual level

Balls Faced (B) Raw Data Total balls faced in the season on an individual level

Outs (W) Raw Data Total dismissals in the season on an individual level

Average (A) R/W The average runs per innings

Strike Rate (SR) (R/B)*100 Average runs scored per 100 balls faced

Wicket Rate (WR) W/B Number of wickets per ball

Rate Above Average (RAA)

((R – Season R)*B) + (Season A*B*(Season WR – WR))

Difference between individual and average strike rate plus the difference between the average wickets rate and the individual wicket rate multiplied by the season average score.

Win Weighting (WW) RAA/(10*Season A)The amount a player contributes to improve the chances of a team winning any one match

Bow

ling

Stati

stics

Overs (O) Raw Data Number of overs (6 balls) a bowler bowls

Runs (R) Raw Data Number of runs conceded by the bowler

Wickets (W) Raw Data Number of wickets takenBalls Bowled (B) O*6 Balls bowled by each bowlerEconomy (E) R/O Number of runs per overAverage (A) R/Q Number of runs per wicketWickets per Ball (WB) W/(O*6) Number of wickets per ball

Rate Above Average (RAA)

((Season R – R)*B) + (Season A*B*(WB – Season WB)

Difference between the average runs conceded and the individual runs conceded plus the difference between the wickets per ball and the average wickets per ball

Win Weighting (WW) RAA/(10*Season A)The amount a player contributes to improve the chances of a team winning any one match

Total Rate Above Average (TRAA) RAA + RAA The sum of the batting and bowling

rates above averageTotal Win Weighting (TWW) WW + WW The sum of the batting and bowling

win weightings

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Hedonic Valuation EstimationA hedonic pricing method is used to monetise the non-monetary quality characteristics of each

player (Malpezzi, 2002). The hedonic regression assumes that the determinants of quality are known

and can be measured; in this case, the measures of performance in table 3.2.

From the season performance measures a hedonic valuation estimate can be formed for each

player. This allows a monetary value to be placed upon every drafted player dependant on their

season performance, irrespective of their auction value. The hedonic valuation estimate is formed as

follows. Using the performance measures it is possible to give a player a ranking score known as the

rate above average. A precisely average player, based on this ranking system, will score a rate above

average of 0. Both the batting and bowling performance measures are provided for every player and

a total rate above average score is given, summing both the rate above average for batting and the

rate above average for bowling. This prevents all-rounders from suffering bias due to overweighting

of one or the other skills. For example, an all-rounder may not be the best batsman or bowler in a

team, but can still give an above average performance thus contributing to a team’s success rate.

Furthermore a specialist batsman may score very highly in the batting performance measures but

may suffer in the bowling performance, thus removing any skew from an exceptional batting

performance, or vice versa.

Based on the total rate above average (TRAA) measure, the highest performing player in the 2015

season was DJ Bravo with a score of 278.19. Using the TRAA, a win contribution weighting can be

formed allowing for a direct measure of how a player contributes to the overall chance of winning

any particular match within a season. See table 3.2 for the formulae used to calculate these

measures.

Using the win weighting and the total wage spend in a given season, the hedonic valuation

prediction can be calculated. The total spend on wages, divided by the total number of matches

yields the valuation of a single match win. The single match win value plus, the average salary

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multiplied by the win weighting, yields the hedonic valuation estimate. This means the highest

ranked player in 2015, DJ Bravo, was in fact worth a total of $1,507,374.29 – his wages were a mere

$200,000.

The hedonic valuation estimate places a monetary value on the non-monetary performance

indicators of each player, allowing for an entirely quality-based, comparable score. The hedonic

valuation can then be used to study the effects of previous wages on current wages, and thus the

subconscious anchoring effect. The hedonic pricing method allows many of the variables that are

attributed to quality to be given a monetary value, which would otherwise be unknown.

The model specification is similar to that employed by Genesove and Meyer (2001). The predicted

wage valuation is constructed using the form;

πt = Xβ + δt

where X is the set of performance measures of each player and δ represents a time-specific effect.

The observable performance measures have been chosen based on the attributes found to be

significant in Parker, Burns and Natarajan’s paper ‘Player Valuations in the Indian Premier League’

(2008). Their analysis finds strong support for significance of a variety of performance-related

measures and non-cricketing player characteristics, to be used as control variables.

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Anchoring ModelUsing the hedonic price estimate discussed above, the model is specified as follows:

W = μπ + λ(W-1 – π) + ξ(W-1 – π-1) + Xβj

where W denotes the wage of the player or the maximum bid for the player at auction and π

represents the hedonic price estimation. The amount that a past seasons wage affects the future

wage price, the influence of any anchoring present, is captured in the expression, W -1 – π. The

hedonic price estimation is included in this expression so as to isolate the effect of the anchoring

when placing bids for players’ wages. The final term captures the effects of any influence past price

has over the predicted wage estimate that are not directly captured in the performance measures,

such as leadership quality or the ability of a player to boost team morale. These unobservable

characteristics are captured in the previous wage amount as they are unobservable in the model but

are observed by buyers or team scouts at the player auction. This term captures these unobservable

characteristics using the assumption that no change in these characteristics was introduced between

the two auction periods.

Other unobservable market fluctuations, such as book-balancing, loss aversion or regret theory, may

all play a part in what appears to be an anchoring effect but are instead logical predetermined

choices made by any bidders. With a constant and homogenous budget across teams, their financial

records will be broadly similar, dependent on whether they choose to retain all, or any, of their

allocated retainable players. The more players they retain the more money comes out of their

budget for the remaining auction; this is consistent across all participating teams. As such, each team

can choose to allocate their remaining wage budget across the team as they wish but one would

expect more experienced Twenty-20 cricketers or internationally acclaimed cricketers to fetch a

higher price regardless of the team that signs them. Thus, the financial balancing of the teams may

be the driving forces behind maintaining a fairly constant wage across seasons, regardless of their

previous season’s performance. In an attempt to isolate the anchoring effect a set of control

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variables, X, will be incorporated in the model. These include, but are not limited to, age, experience

and nationality. Not only will this serve to further isolate any anchoring effects present in the data, it

will also allow for any analysis over a nationality premium, in other words, whether international

players are more expensive to sign than Indian domestic cricketers – The International Premium.

ResultsThe complete data set has been split into the four seasons for initial analysis and summary statistics,

from 2012 through to 2015. Graph 4.1 shows the distribution of the salary data over the four

seasons. From the graph it is clear that there is a negative skew to the data and thus a log

transformation will need to be applied to normalise the skew.

Graph 4.1

2015 2014 2013 20120

100000200000300000400000500000600000700000800000900000

1000000

Box Plot of Salary Across Seasons

Season

Wag

e Le

vel

Over the course of the seasons the distribution of the data remains constant, showing no signs of

drift with the increasing wage budgets for the team. In all but one of the seasons the maximum and

the minimum wage caps are met with the majority of the data toward the lower end of the salary

scale. After taking the log transformations across all four seasons, it is apparent that the data

conforms much closer to a normal distribution as shown in graphs 4.2 below.

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Graph 4.2

Despite the slight persistence in the negative skew to the data, arising from the minimum salary cap,

it is clear that the data at both the total level and individual season level conforms much closer to a

normal distribution.

An initial look at the scatter plot, Graph 4.3, suggests that there is a weak positive correlation

between the hedonic valuation estimate, based on the season’s performance measures, and the

players’ salary in the subsequent season. Some apparent outliers peak interest at both ends of the

scale, low wage with a high valuation and high wage with a low valuation. The former represents the

players that are of greatest value to a team, represented in the lower right quartile of the scatter

plot, and the latter represents the worst value players.

Three data points have been highlighted on the graph, data point 1 shows the player with the lowest

hedonic valuation estimate in all of the data, that of M Morkel in the 2013 season, where is

estimated value was -$869,159. The most expensive player in the dataset is shown by data point 2,

MS Dhoni in the 2012 season where he was paid $3,000,000 in a season, prior to the salary cap

being implemented. Finally, the most impressive statistic is that of MEK Hussey, who outperformed

his salary by $3,275,000 in the 2013 season.

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Graph 4.3

For the hedonic valuation estimates, the log of the player’s wage in the subsequent season is

regressed on the performance indicators of the prior season. This shows how the performance

indicators affect the future fee of each player. Results of the OLS regression are displayed in table

4.1. Various measures of performance are used in separate regressions, each shown in the

aforementioned tables, initially the raw data, followed by linear transformations creating more

detailed measures of performance. These measures are modelled in subsequent regressions to

measure their combined impact and to prevent multi-collinearity within the explanatory variables.

Multi-collinearity would almost certainly arise as variables like the strike rate of a batsman are

calculated using the runs they scored and the balls they faced. Finally, a players wage or salary is

regressed on the total rate above average score for the prior season and their win contribution

weighting.

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1

2

3

Table 4.1Regression 1 R2 = 0.2667Variables Coefficient Standard ErrorRuns Scored 0.00657* 0.003Balls Faced -0.00727 0.006Total Dismissals 0.07109 0.053Overs Bowled 0.04395* 0.026Runs Conceded -0.00522* 0.003Wickets Taken 0.01378 0.035

Regression 2 R2 = 0.1278Variables Coefficient Standard ErrorStrike Rate 0.00431 0.003Batting Average 0.00593 0.009Outs per Ball -0.37245 1.082Economy 0.01621 0.089Bowling Average -0.02321* 0.013Wickets per Ball -21.6993* 13.309

Regression 3 R2 = 0.0461Variables Coefficient Standard ErrorRate Above Average 0.00629 0.011Win Weighting -0.98589 2.784Note: *denotes variables significant at the 10% level

**denotes variables significant at the 5% level

The first regression performs the best out of the three modelled but is still a very poor fit for the

data and has very little explanatory power. This suggests that the model is underspecified and some

function of undefined variables are influencing future wage. Interestingly, when the log of the past

salary is included in the model, the performance is greatly improved. The results for this regression

are shown in table 4.2.

Table 4.2Regression 4 R2 = 0.5192Variables Coefficient Standard ErrorRuns Scored 0.00489* 0.002Balls Faced -0.00456 0.004Total Dismissals 0.01119 0.044Overs Bowled 0.01363 0.021Runs Conceded -0.00291 0.002Wickets Taken 0.04048 0.028Salary 0.57361** 0.082Note: *denotes variables significant at the 10% level

**denotes variables significant at the 5% level

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The results show that past wages have a large and significant effect on future wages. More directly,

a 10% increase in past salary would lead to a 5.7% increase in their new wage, providing superficial

support for the anchoring hypothesis, but may be explained by other mechanisms working within

the data. In order to isolate the anchoring effect, the following models are estimated.

Using the hedonic value estimate, the difference between past salary and the value estimate, and

the difference between the past salary and the past value estimate, an OLS regression is run allowing

for isolation of the anchoring effect, the results of which are presented in table 4.3.

Table 4.3Anchoring Regression 1 R2 = 0.61Variables Coefficients Standard ErrorsHedonic Value Estimate 1.0378** 0.0874Anchoring Effect -0.1051* 0.0504Residual from previous wage 0.9482** 0.0756Note: *denotes variables significant at the 5% level

**denotes variables significant at the 1% level

Including the control variables in the model (Indian and age), the results are shown in table 4.4.

Table 4.4Anchoring Regression 2 R2 = 0.58Variables Coefficients Standard ErrorsHedonic Value Estimate 1.0025** 0.1071Anchoring Effect -0.0706 0.0596Residual from previous wage 0.9046** 0.0924Indian -0.0512 0.0698Age 0.0031 0.0074 Note: *denotes variables significant at the 5% level

**denotes variables significant at the 1% level

Table 4.3 shows that all the variables are significant and a large proportion of the variability in the

data is explained by the model. Everything aside from the dummy variables are in logs; this equates

to the assumption that the change in wages is felt in relative and not absolute terms.

Directly interpreting the anchoring effect suggests that a 10% positive difference between the

previous salary and the hedonic prediction leads to the next salary being adjusted downward by

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approximately 1% - significant to 5% level. For completion, a positive difference between previous

salary and hedonic prediction means that a player has underperformed when measured against their

annual salary. Given a player has underperformed by a difference of 10%, results in his subsequent

wage being held closer to the previous wage (the anchor) by approximately 1%. The coefficient on

the hedonic value estimate is not significantly different from 1 in any of the model specifications.

Furthermore, the coefficient on the lagged residual is also significant suggesting that, as predicted,

the hedonic model does not pick up all of the fixed effects.

Including the control variables for Indian-born players and the ages of players yields a model with

reduced explanatory power. Both the control variables are insignificant even at the 10% level. The

coefficients on the explanatory variables, aside from the control variables, are not statistically

different from the previous specification, but the total explanatory power of the model falls. As such,

the prior specification found in table 4.3 is preferred and the insignificant control variables are

dropped. This suggests that neither age nor Indian-born players make an impact on determining the

level of a player’s future wages. As such, the Indian-premium hypothesis is rejected and it is

apparent that overseas players do not take a significantly different wage either.

This OLS model assumes that any losses are felt symmetrically to any gains. In the real world

however this may not be a suitable assumption to make. For example, teams may not want to lose

an underperforming player to a rival for a much lower salary and so will bid up his wage value.

Conversely, a player may have a relatively poor season prior to auction but his past poor form may

cause very few bids from other teams, causing an asymmetric impact to gains and losses. That is to

say, a poor performance, or loss, decreases value more than the equivalent strong performance, or

gain, will increase value. In order to allow for asymmetric effects in the model it is not simply enough

to add the residual from the previous wage. Instead, one must proxy the loss term as in Genesove

and Mayer (2001), this however, yields inconsistent and biased estimators and cannot be used to

draw reliable conclusions.

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Treating the data as panel data may improve the ability of the current model given that the data is

split into seasonal variables. This also allows control for player specific-effects and any cross-player

interactions that are not directly observable. The results yielded utilising the panel estimation

method are in line with those of the OLS regression and again explain approximately 70% of the

variation within the model. The panel estimation coefficients are shown in table 4.5 below.

Table 4.5Anchoring Regression 3 – Panel Estimation R2 = 0.69Variables Coefficients Standard ErrorsHedonic Value Estimate 0.9897** 0.0992Anchoring Effect -0.1065* 0.0526Residual from previous wage 0.8995** 0.0837Note: *denotes variables significant at the 5% level

**denotes variables significant at the 1% level

As before, adding the control variables for age and Indian-born players lowers the performance of

the model and both are insignificant.

Macro panel estimation uses certain time-series techniques that will provide an interesting take on

the data collected. On initial perusal, the current data set seems suitable due to the seasonal nature

and short time series aspects of player’s careers. Due to the 5% increase of franchise budgets year

on year, player wages may be non-stationary over a longer time span. Furthermore, the advantages

of allowing for parameter heterogeneity and cross section dependence, thus treating each player

separately, may return interesting results with a more suitable data set. The results of the panel

estimation are broadly in line with that of the OLS estimation and so provide further weak support

for the anchoring hypothesis. As before, the control variables are all insignificant and follow the

same interpretation as above. As such, the secondary hypothesis of a nationality premium is

rejected at all significance levels.

From the above results it is apparent that past salary has a significant impact on future salary but

only a small proportion of this can be attributed to the anchoring heuristic. It is instead the role of

other market factors that are tying past wages with future wages, such as teams maintaining their

30 | P a g e

financial homeostasis or a player not willing to take a lower salary and so pulling out of the

tournament. Although the hedonic valuation estimate does show some positive impact it is not

driving the changes to a player’s wage by the degree reported in previous papers on the anchoring

heuristic (Beggs and Graddy, 2009). This could be down to the fact that, even after one bad season, a

player’s reputation will not be hampered and teams will be willing to maintain a higher wage for that

given player. This follows the logic that form is only temporary and any drastic changes in a player’s

form will converge to a mean level of ability over time, thus causing the wage to remain fairly

constant over that time period as well.

Concluding RemarksThe hedonic valuation estimate used to determine players’ wages as a direct consequence of their

performance lacks any explanatory power when modelling it using OLS. The lack of significance in

the explanatory variables may explain the poor predictive power, along with the omission of other

measures of a players’ performance that were either unobtainable or unmeasurable. These include,

but are not limited to, measures such as leadership quality, sportsmanship or the ability to raise a

team’s morale. Basing the anchoring model on such an under-specified estimate of player value may

lead to misspecification and bias in the results. Despite the lack of significance in the hedonic

valuation the anchoring model performed much better and gave significant results for both the

effect of the anchor and the unobservable residuals omitted from the model. Due to the

methodology for calculating the hedonic valuation, some observations returned negative values and

others grossly above the wage cap. In order to apply log transformations to the valuations, the

negative observations (those players significantly underperforming) were dropped from the model.

The negative observations would also have been interesting to analyse and test whether, after a

particularly bad season, their wage would fall. In order to analyse these players, absolute values

would have to be used in the data, resulting in the assumption that any effect of anchoring would be

felt in absolute rather than relative terms. Despite this, including such unrealistic valuations in the

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model may have induced bias toward the extremes or outliers within the data. The hedonic

valuations were not subject to the same stringent rules applied to the wages of the players in real

life and as such were uncapped at either end of the scale. Including similar conditions for the

valuations would have eliminated the problem with player’s values being negative and would have

kept top performing players with realistic valuations, potentially improving the predictive power of

the model.

The valuation estimates also assume linearity of the explanatory variables which may not necessarily

have been a suitable assumption to make. Some measures of performance, such as strike rate, may

impact on the independent variable (wage) in an exponential manner given that higher strike rate is

extremely desirable but often very difficult to achieve. Non-linear explanatory variables were

transformed into linear variables through log transformations or quadratic transformations but in all

cases the variables lacked significance and the explanatory power of the model was still poor.

The poor explanatory power of the hedonic valuation estimate lead to some concerns with the data

that was available or chosen to be collected. The performance measures used were specific to past

seasons within the Indian Premier League. Instead players wages may not be purely determined on

their performance solely in the IPL and instead, from their entire career performance. This follows

the logic that a player’s wage will not be determined on their performance in the previous season

but on an amalgamation of their performances across their career, form is temporary but ability will

converge to an average. A player’s career reputation will carry more weight when coming to value

them in the IPL than just their performance in that specific tournament, even if this reputational

concern is both unobservable and subconscious.

The hedonic valuation employed here was based on a previous specification employed by Parker,

Burns and Natarajan (2008), where they attempted to isolate the observable quality measures

significant in driving cricketer values. Their model explained a large degree of the variability within

their dataset and yet the same model explained very little variation with the dataset employed here.

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Again, this is most likely due to the exclusion of career performance measures and focussing more

on player performance in the IPL. The justification for this is due to the very different manner in

which each form of the game is played. In test cricket, a batsman’s patience is crucial and the ability

to stay in is regarded much higher than maintaining a high strike rate. The opposite is said of the

twenty-20 leagues and the IPL.

A surprising result arising from the data was that none of the control variables such as nationality or

age were significant. In terms of the ages of a player, this may be down to the stringent rules

enforced by the governing body of the IPL that sets a minimum number of young players earning a

minimum salary level per team. The restriction of overseas players to each team may result in a

premium being paid for young Indian talent that is forcing the data to converge and reducing

significance. The premium would arise through relative scarcity of Indian players due to the

restrictions on overseas players being included in a team, and a minimum number of players per

team. Furthermore, this promotes young talent and ensures they are paid a fair wage, in line with

that of more experienced players, resulting in variable insignificance. Once again if total career

experience rather than IPL experience were used, this may return a significant result. An Indian

premium was tested in the model but again returned an insignificant result, from which we can

cautiously infer that neither Indian nor overseas players are paid a premium. Again this may be

down to the stringent rules of the IPL being enforced upon teams with a maximum number of

overseas players and a minimum and maximum salary cap. Regressing the log of the salary on just

the control variables yields a positive and significant result for age and experience but not for any

nationality premium. This results can be taken as a positive for the IPL as a whole as it shows that no

set of players are paid a higher wage simply to conform to the rules of the competition.

Finally the data may be subjected to a truncation bias through dropping observations at the

minimum end of the scale and removing players who returned a negative valuation. At the higher

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end of the wage scale further truncation bias may arise from the salary cap placed on teams prior to

the auction commencing.

The anchoring model used, although performing better than the hedonic valuation model, was still

under-specified and lagged explanatory power. This may be down to the inclusion of the

misspecified valuation estimate or due to omitted control variables. The effect of anchoring,

although small, was significant to the 5% level suggesting some attribution of the sticky wages to the

heuristic. Despite this seemingly positive support for the anchoring heuristic, the model may be

returning results driven by other market forces, such as franchises maintaining their financial

homeostasis, either by their own business models or through the enforced rules.

The large coefficient of the lagged residuals is down to a large number of unobserved explanatory

variables in the model, all of which are being picked up by the residual from the previous wage. Due

to the poor predictive power of the model, previous wage is more revealing about the unobserved

characteristics, and as such are captured in the larger lagged residual term. The unobservable

variables within the data will include variables like the marketing power of a particular player or the

extra support and ‘buzz’ a player will bring to a team. These are all potentially taken into account by

franchises when buyer a player but are unmeasurable using current techniques. It is unknown prior

to auction how much a particular player will improve support or revenue but it is known that it will

affect them to some degree.

Models of prospect theory may help to determine the nature of and the attribution to what is

seemingly anchoring of wages in the IPL. Loss aversion is the theory that losses are felt more than

relatively sized gains (Tversky and Kahneman, 1992). In terms of players this would be applied

through clubs feeling the departure of a current player more than the inclusion of a similar standard

of player. As such, teams may choose to raise the wage of the player internally and prevent them

from joining the auction. In fact, due to the nature of the auction all players available to buy have

been released by clubs or their contracts have expired. Despite this, the selling club has the option of

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first refusal on a player in its previous squad. As a result, any anchoring that is perceived in the

model could in fact be driven by loss aversion and clubs choosing to maintain their current squad

roster. If loss aversion were present in the model the effects of performance on wages would be

asymmetric, larger effects in terms of losses than gains. The model employed above assumes

symmetric effects and so the theory of loss aversion cannot be tested directly. As previously

mentioned, allowing for asymmetric effects could yield biased and inconsistent estimators.

Secondly, reference dependant wages may be driven by regret theory, the notion that subjects

include the concept of regret when forming their decisions (Loomes & Sugden, 1982). To apply this

to the current model, franchises would regret losing an underperforming player to a rival, hoping

that he might improve in the coming season. In order to adjust for such regret, franchises would

extend a player’s contract or improve their wage so they can keep them in their team roster.

Furthermore, at auction a team may choose to employ their first refusal rule to prevent a team from

taking a player they auctioned for a cheaper price. This would result in neither the players wage nor

team changing, and based on current data specifications, these players would have dropped from

the model. Without knowing the exact details of all of the auctions these actions would be

impossible to decipher and infeasible to model.

As a secondary model for analysis, macro panel estimation techniques were employed but in order

for these methods to be consistent and unbiased certain criteria for the data had to be fulfilled. The

criteria for such estimation have been previously mentioned in the results section, and so this

section is focussed on the suitability of the data and the consistency of the results. Firstly, the model

uses time-series aspects, suitable due to the seasonal nature of the data and as such some of the

variables may be nonstationary, most of all the salaries of the players. Year upon year, franchises are

allowed to increase their spending budget on players’ wages at a rate of around 5% a year. This

persistent increase in wage allowance may translate into a persistent increase in player wages,

resulting in a nonstationary variable. However, for this to really translate into the data, a span of

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around 15 – 20 years is a more appropriate measure of time, not the 4 year span that has been

available with this data set. Again, for every year included in the model, each player would need to

have their performance measures, salary and all control variables recorded. Over a 20 year period,

this would be an incredible feat for any sportsman, especially playing within one tournament for that

many years, or even having a career lasting that long. As such, the data available across the eight

years since the inaugural season of the IPL, is insufficient to be able to model the time series aspect

of the macro panel estimation.

Furthermore, given the nature of players’ careers, it is unlikely that they would be playing in

consecutive seasons, resulting in highly unbalanced panels. Although not a necessity, unbalanced

data, specifically non-random missing observations, can lead to loss of efficiency and a biased

sample, along with the assumption of exogeneity failing.

A strong bonus for using panel estimation techniques is that it allows for parameter heterogeneity,

the persistence to vary across players. The greater flexibility in relaxing the variability across the

panels means that each player can be modelled individually rather than averaging across all

parameters. Along with the parameter heterogeneity panel estimation also allows for cross section

dependence. The impact of a common shock will affect all players but not all in the same manner or

magnitude. Consider a change in the minimum salary level; this would raise players’ salaries

significantly at the lower end of the scale, and would potentially impact on players with a higher

salary if a team’s budget is not adjusted accordingly. As such, a common shock like a change in the

rules, would impact differently on players depending on their wage levels.

Despite the obvious advantages of using macro panel estimation techniques, the current data set is

not suitable to draw new conclusions from and instead is used as more of a robustness check on the

previous OLS regression employed. A player’s career cannot last long enough to make such time-

series techniques seriously useful, and with such small panels over a short time period the

regressions act very closely with that of the OLS techniques. However, the panel analysis may be

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interesting to observe with real-world data that fits the conditions for macro panel estimation.

Anchoring in house prices may return interesting results using such techniques, as the longer time

periods and greater availability of the hedonic characteristics would lend themselves to macro panel

estimations. Novel estimation techniques like macro panel estimation have yet to be applied to

models explaining anchoring and a more reserved for growth economics and data with a greater

suitability to time series. Applying these techniques to the art auction data from Beggs and Graddy

or house price data may return novel results that cross-sectional techniques cannot measure.

Anchoring effects may also be apparent in the price stickiness of artificially-inflated stock markets

and house prices. Despite the collapse of the house prices in the UK post financial crisis, the prices of

London homes have remained at particularly high levels. Could this be attributed to the effects of

anchoring on behalf of the sellers, keeping the values of their homes at previous high levels, even

though these were predominantly inflated beforehand? Again the effects of the anchor value are

likely to be asymmetric and so loss aversion would need to be built into the model to allow for such

asymmetries. Separating anchoring effects from other market movements, such as loss aversion,

should still be the predominant direction of the literature using field data as such no model or paper

has managed to isolate both and maintain consistent and unbiased estimators. Anchoring in a

laboratory is a much less complex heuristic to analyse as the anchor values can be artificially

introduced in a hypothetical context. In the real world, finding situations where anchor values are

truly irrelevant and not just hidden within a greater mechanism driving prices, is a much more

difficult task and would only be observable in certain market mechanisms.

Overall, this research provides weak support for the anchoring hypothesis and both methods return

similar conclusions, showing significant but small effects. Isolation of the anchoring heuristic is

always a challenge when using real world data as other market forces may be driving the apparent

reference dependent wages. The methodology employed, following that of Beggs and Graddy

(2009), attempts to isolate the heuristic through differencing the previous wage and the hedonic

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valuation estimate. To improve the current research, the hedonic valuation estimate would need to

be revised so as to improve the performance in explaining the variation in the model. Added

variables with added significance and possibly using total career performance measures as oppose to

IPL specific performance could serve to improve the predictive power.

The fact that salary levels are not directly correlated with player performance or the chance of

winning is in fact a bonus for the game. The competitive nature and excitement of every game are

founded in the unpredictability of the IPL. If players’ wages were a perfect model for performance,

all excitement for the game would be lost.

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References:

Ariely, D., Loewenstein, G., Prelec, D., 2003. “Coherent Arbitrariness”: stable demand curves without stable preferences. The Quarterly Journal of Economics 118, 73–105.

Beggs, A., & Graddy, K. (2009). Anchoring effects: Evidence from art auctions. The American Economic Review, 1027-1039.

Chapman, G. B., & Johnson, E. J. (1999). Anchoring, activation, and the construction of values. Organizational behaviour and human decision processes,79(2), 115-153.

Englich, B., Mussweiler, T., & Strack, F. (2006). Playing dice with criminal sentences: The influence of irrelevant anchors on experts’ judicial decision making. Personality and Social Psychology Bulletin, 32(2), 188-200.

Epley, N., & Gilovich, T. (2001). Putting adjustment back in the anchoring and adjustment heuristic: Differential processing of self-generated and experimenter-provided anchors. Psychological Science, 12(5), 391-396.

Genesove, D., & Mayer, C. (2001). Loss aversion and seller behaviour: Evidence from the housing market (No. w8143). National bureau of economic research.

"IPL Season Stats." IPLT20. Indian Premier League, n.d. Web. 22 May 2015. <http://www.iplt20.com/stats>.

Johnson, J. E., & Liu, S. (2013). Searching for anchoring effects in a naturalistic environment: evidence from the Hong Kong horserace betting market. The Journal of Gambling Business and Economics, 1(1), 69-84.

Jones, J. C., & Walsh, W. D. (1988). Salary determination in the National Hockey League: The effects of skills, franchise characteristics, and discrimination. Industrial & Labor Relations Review, 41(4), 592-604.

Lenten, L. J., Geerling, W., & Kónya, L. (2012). A hedonic model of player wage determination from the Indian Premier League auction: Further evidence.Sport Management Review, 15(1), 60-71.

Leung, T. C., & Tsang, K. P. (2013). Anchoring and loss aversion in the housing market: implications on price dynamics. China Economic Review, 24, 42-54.

Loomes, G., & Sugden, R. (1982). Regret theory: An alternative theory of rational choice under uncertainty. The economic journal, 805-824.

Malpezzi, S. (2003). Hedonic pricing models: a selective and applied review. Section in Housing Economics and Public Policy: Essays in Honor of Duncan Maclennan.

McAlvanah, P., & Moul, C. C. (2013). The house doesn’t always win: Evidence of anchoring among Australian bookies. Journal of Economic Behavior & Organization, 90, 87-99.

McElroy, T., & Dowd, K. (2007). Susceptibility to anchoring effects: How openness-to-experience influences responses to anchoring cues. Judgment and Decision Making, 2(1), 48-53.

Mei, Jianping, and Michael Moses. 2002. Art as an Investment and the Underperformance of Masterpieces. American Economic Review, 92(5): 1656–68.

39 | P a g e

Mei, J., Moses, M. A., Shapira, Z. B., & White, L. J. (2010). Loss Aversion? What Loss Aversion? Some Suprising Evidence from the Art Market. InWorking Paper.

Mittal, S. "Indian Premier League Series Data." Cricmetric. N.p., n.d. Web. 22 May 2015. <http://www.cricmetric.com/series.py?series=ipl2014>

Mussweiler, T. (2001). The durability of anchoring effects. European Journal of Social Psychology, 31(4), 431-442.

Parker, D., Burns, P., & Natarajan, H. (2008). Player valuations in the Indian premier league. Frontier Economics, 1-17.

Scully, G. W. (1974). Pay and performance in major league baseball. The American Economic Review, 915-930.

Simonsohn, U., & Loewenstein, G. (2006). Mistake# 37: The Effect of Previously Encountered Prices on Current Housing Demand*. The Economic Journal, 116(508), 175-199.

"Statistics." ESPN Cricinfo Statistics. N.p., n.d. Web. 22 May 2015. <http://www.espncricinfo.com/ci/content/stats/index.html>

Sugden, R., Zheng, J., Zizzo, D.J. (2013). Not all anchors are created equal. Journal of Economic Psychology, 39, 21–31

Thorsteinson, T. J., Breier, J., Atwell, A., Hamilton, C., & Privette, M. (2008). Anchoring effects on performance judgments. Organizational Behavior and Human Decision Processes, 107(1), 29-40.

Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. science, 185(4157), 1124-1131.

Tversky, A., & Kahneman, D. (1991). Loss aversion in riskless choice: A reference-dependent model. The quarterly journal of economics, 1039-1061.

Wolk, A., & Spann, M. (2008). The effects of reference prices on bidding behavior in interactive pricing mechanisms. Journal of Interactive Marketing,22(4), 2-18.

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