Graham Barr

A criterion for comparing and selecting batsmen in limited overs cricket

The batting average statistic has been used almost exclusively to assess the worth of a batsman. It reveals a great deal about the potential performance of batsmen in cricket played at the first class level. However, in the one-day game, strict limits on the number of balls bowled have introduced a very important additional dimension to performance. In the one-day game, it is clearly not good enough for a batsman to achieve a high batting average with a low strike rate. Runs scored slowly, even without the loss of wickets, will generally result in defeat rather than victory in the one-day game. Assessing batting performance in the one-day game, therefore, requires the application of at least a two-dimensional measurement approach because of the time dimension imposed on limited overs cricket. In this paper, we use a new graphical representation with Strike rate on one axis and the Probability of getting out on the other, akin to the risk–return framework used in portfolio analysis, to obtain useful, direct and comparative insights into batting performance, particularly in the context of the one-day game. Within this two-dimensional framework we develop a selection criterion for batsmen, which combines the average and the strike rate. As an example of the application, we apply this criterion to the batting performances of the 2003 World Cup. We demonstrate the strong and consistent performances of the Australian and Indian batsmen as well as provide a ranking of batting prowess for the top 20 run scorers in the tournament.

Unregulated gambling in South African townships: a policy conundrum?

This study was designed to explore the nature of informal or illegal gambling in South African townships, to investigate what motivates people to participate in this form of gambling and what they perceive are the associated benefits and dis-benefits. A series of focus group workshops was conducted with two groups of gamblers, all of whom had experience of some form of township gambling: one group currently lived in townships and the other had previously resided in townships. Gambling for the township residents was a far more frequent activity than for non-township residents and consumed substantially more of their time. The majority of the township residents classified themselves as unemployed, while of those who were unemployed, most people indicated that gambling was a major source of their income; some even described it as their only source of income. The most significant difference between what township and non-township residents expressed as wanting and getting from gambling was that the former indicated quite clearly and unanimously that what they sought and gained from gambling was money. Township residents were far more likely to indicate that they used gambling to balance their budgets than ex-township residents who gambled primarily at casinos. A lottery type game called “Fahfee” is the most widely spread and pervasive form of gambling and was unanimously portrayed as a necessary and beneficial form of support for the poor and unemployed. Lottery and Casino gambling were, in contrast, widely perceived by the township participants as being ‘rigged’ and unfair. Township Dice and cards were perceived as being ‘fairer’ and as allowing punters to be more in control than casino gambling. The downside of township gambling was reported to be high levels of violence, crime and insecurity surrounding, in particular, the game of Dice. There was widespread inability to calculate expected payoffs or odds, and an apparent belief that these were not particularly helpful skills for gamblers. In Fahfee, the reliance on dreams to guide choice of numbers appears to eradicate any interest in the odds, or of playing strategically. The findings of this study are preliminary but have serious policy implications for education and for gambling regulation in South Africa.

Modelling the economics of gaming in South Africa.

This paper considers the application of two models for determining the optimal location and characteristics of a casino in a post-apartheid South Africa. The intention in developing the models was to allow provinces a facility for considering how to maximize the return to the stakeholders in the license award process, namely society at large, as represented by the provincial government, and the casino operator. The Allocation Model works on an estimate of total potential gambling spend and how that may be best distributed amongst a number of casinos. The Profitability model takes the estimated gaming spend from the allocation model and assesses the appropriate size and characteristics of the casino best suited to this level of gaming spend. It can then simulate levels of profitability for different proposed sizes and characteristics of proposed casinos. Together these models represent a powerful assessment mechanism for a country considering the introduction or radical changing of gaming legislation.

Addressing problem gambling: South Africa's National Responsible Gambling Programme.

In the English-speaking world and some parts of Europe, problem and pathological gambling are treated as a significant public health problem. At the same time, these jurisdictions recognise that for most of those who engage in it, gambling is a harmless leisure activity that may yield public benefits by contributing more in taxation than other leisure industries and/or contributing to out-of-town tourism. Strategies that combine minimising the harm caused with maximising the benefits of gambling are therefore crucial for good public policy. Such lessons may also be relevant to other legal and illegal industries, such as those involving the production and sales of alcohol, where analogous harms and benefits exist.

Price earnings ratios on the Johannesburg Stock Exchange - Are they a guide to value?

This paper tests whether there is an equilibrium relationship between prices and earnings on the Johannesburg Stock Exchange (JSE). Such a relationship would hold if the JSE Index and index earnings were cointegrated, A full explanation of the technique of cointegration is provided. It is shown that prices and earnings on the JSE are not cointegrated, which is aconsistent with similar results obtained for the New York Stock Exchange. The paper then offers a more general explanation of prices on the JSE to include, in addition to earnings, the influence of world markets and political and exchange rate risk, on the value of the JSE as represented by its Industrial and Financial Index. It is found that the variables of these models of the JSE are in fact cointegated. This means that there have been forces driving long term equilibrium values on the JSE. Movements away from such equilibrium values have represented market beating opportunities Current prices are thus not the best estimate of future prices, sug...

A Monte Carlo Analysis of Hypothetical Multi-Line Slot Machine Play

Behavioural research into slot machine gambling tends to focus on characteristics of the gambler or on qualitative aspects of the slot machine such as audiovisual displays and bonus features. In this paper we take a different approach by using Monte Carlo simulation to relate hypothetical slot machine gambling behaviour to the statistical characteristics of the slot machines themselves. The measures we use – expected monetary win, volatility of payouts, and the probability that any single play returns a winning result – have the advantage that they are mathematically precise and can be linked to psychological risk and return criteria that people may look to as they decide both whether to gamble or not and how to play.

The Discount to Net Asset Value, Unbundling and Shareholder Interests

The argument has recently been made by powerful political voices that the large South African corporate conglomerates (or groups) should be broken up into their constituents or “unbundled”, as the process has become known in South Africa. Critics of these groups in the financial markets have pointed to the existence of a discount of the quoted share price to the so-called Net Asset value of the Mining Finance houses, which are either the parent companies of the groups or constitute an Important element of them. Unbundling, it is contended, will “unlock” value for shareholders by eliminating this discount. This paper examines the notion of a discount to Net Asset value and shows why such claims about unlocking value are largely unfounded.

A comment on “Portfolio rebalancing in South Africa”

In this comment we add to the discussion on rebalancing portfolios by Sher and Barr (2011). In particular we highlight how a recent rebalancing proposal by Chan and Ramkumar (2011) is found to significantly improve rebalancing performance. An important feature of both studies is that they recognise the significant impact of rebalancing in stressed market conditions and consequently build this into their study designs. In this comment we adapt the tabled results of the first study and portray them in a graphical framework to be comparable with the results of the second study. A concerning feature of Sher and Barrs (2011) results is that the fixed-band strategies they propose still do not seem to adequately control the risks and costs of rebalancing arising in stressed market conditions. We consequently highlight how the Chan and Ramkumars (2011) rebalancing proposal is especially beneficial in stressed market conditions and is likely to improve on the results of the rebalancing proposal of Sher and Barr (2011). Chan and Ramkumars (2011) rebalancing proposal is based on a joint cost and tracking error minimisation optimisation. When we take heed of the fact that the South African environment is characterised by higher volatility than developed markets, and more so during stressed periods, this tracking error rebalancing proposal is likely to be practically appealing.

Spreadsheets and Simulation for Teaching a Range of Statistical Concepts

Fundamental statistical concepts remain elusive for many students in their introductory course on Statistics. The authors focus on the teaching of Statistics within a spreadsheet environment, wherein the students are required to master the basics of Microsoft Excel (Excel) to perform statistical calculations. This approach has the advantages of developing the students’ ability to work with data whilst also building an understanding of the algebraic relationships between elements embedded in the formulae which they use. The use of a classroom experiment aimed at exploring the distributions of a number of randomly generated pieces of information is demonstrated. Teaching sessions are built around a suite of Excel-based simulations based on this experiment that attempt to demonstrate the concept of random variation and show how statistical tools can be used to understand the different underlying distributions. The methodology is then extended to a further, more advanced, bivariate teaching example which investigates how this spreadsheet methodology can be used to demonstrate the effect of expected value and variability on the statistical measurement of covariance and correlation. The authors reflect on their experience with the spreadsheet-based simulation approach to teaching statistical concepts and how best to evaluate the approach and assess levels of student understanding.

Portfolio strategies for hedging against rand weakness

This paper considers how portfolios may be structured which provide protection against Rand exchange rate movement and, in particular, against Rand weakness. Two portfolio optimisation methods are used to estimate the portfolio weights of the Top 40 shares listed on the Johannesburg Stock Exchange (JSE) which provide the maximum protection against some pre-defined expectation of Rand weakness. The performance of these Rand-hedge portfolios is then compared to that of the Itrix FTSE 100 Exchange Traded fund (ETF) which mimics the London-based FTSE 100. While the portfolios based on the JSE Top 40 components provide slightly less Rand hedge protection than the Itrix FTSE 100 ETF, they are still able to provide a very effective exchange rate hedge. Moreover, they are also able to provide greater exposure to the South African market and this has resulted in a significant performance advantage over the Itrix FTSE 100 over the last five years.