Wednesday, 24 December 2014

Some proper economics research for a change: LBW decisions and bias by umpires.

One of the most important questions in economics has to do with whether pressure from home crowds affects decision making of sports officials. A new column at investigates this problem using new data from cricket matches. The authors find that neutral umpires decrease the bias against away teams, making neutral officials very important for a fair contest.

'Leg before wicket' decisions in cricket provide a fascinating case study in which to study the issue of bias in decision making by umpires.
Umpiring decisions in cricket provide a fascinating case study in which to study the issue. In the first place, decisions such as whether the batsman is out ‘leg before wicket’ (LBW) require significant judgement from the umpire in a very short period of time (less than 10 seconds). At least until recently, umpires have had complete discretion over these decisions, which can have crucial impacts on the outcome of matches (Chedzoy 1997). Unusually amongst professional sports, international cricket continues to use officials of the same nationality as the home team. Throughout most of the history of test cricket, both umpires were from the same country as the home team. In 1994, the regulations were changed and one of the umpires was required to be from a neutral country. From 2002, both umpires were required to be neutral. In One Day International (ODI) cricket, there is still one home and one neutral umpire in most matches. Unsurprisingly, cricket fans and sometimes players have long held suspicions that decisions by home umpires tend to favour the home team. The notorious altercation between the former England cricket captain Mike Gatting and Pakistani umpire Shakoor Rana in 1987 led to an international diplomatic incident, the ramifications of which were felt for many years.

Despite this, academic study of officials’ decision making in cricket has been limited to a handful of articles. An investigation by Sumner and Mobley in the New Scientist in 1981 was the first to focus on leg before wicket decisions against home and away teams, followed by Crowe and Middeldorp (1996) and Ringrose (2006). Although these articles broadly concluded that away teams suffer more leg before wicket decisions against them than do home teams, none was able to establish statistically meaningful links between neutrality of umpire and decisions against home and away teams.
Recent research by Ian Gregory-Smith, David Paton and Abhinav Sacheti takes a new look at the issue.
It was this issue that we sought to address in our recent article (Sacheti et al. 2014). We collected data from 1,000 test matches played between 1986 and 2012 from ESPNCricInfo. The changes to regulations about neutral umpires provided us with an ideal ‘natural experiment’; in our sample, around 20% of matches were umpired by home officials, 35% by one home and one neutral official, and 45% by two neutral officials. We also controlled for the quality of team, venue (as each pitch may have distinct characteristics making it more or less conducive to enabling leg before wicket decisions than others), and even the experience of the umpires in the match, among other things. With these controls in place, we found striking results as shown in the Table 1 below.
  • During the period when there were two home umpires, home teams had a clear advantage.
Reading across the columns for the Home batting marginal effect in Table 1, batsmen in away teams were given out leg before wicket about 16% more often than batsmen in home teams.
  • However, with one neutral umpire, the bias against away teams receded to 10%, and in the matches with two neutral umpires there was no home advantage at all.
It would thus seem that having neutral officials is very important for a fair contest.

Table 1. Negative binomial model of number of leg before wicket (LBW) decisions per innings
Notes: (i) Robust standard errors in brackets, clustered by match; (ii) *Significant at the 10% level. **Significant at the 5% level. ***Significant at the 1% level; (iii) ‘Home marginal effect’ is calculated as the Average Marginal Effect (see Cameron and Trivedi 2010, p.576); (iv) Controls are umpire experience; log of overs; innings; country level dummies for each home team; batting team effects and bowling team effects; (v) For the full table of results and a battery of robustness checks see Sacheti et al. (2014).
So the next question is crowd pressure or favouritism?
An obvious question is whether the apparent bias in favour of home teams was caused by crowd pressure. We examined this by comparing results between the first two innings and the final two innings of test matches. The rationale is that crowds tend to be higher in the early stages of a test match and decline significantly later on (Hynds and Smith 1994). We found that the advantage to home teams from home umpires was strongest in the final two innings of the match. So, there is little evidence that bias towards home teams from home umpires was driven primarily by crowd pressure.
What, you may ask, of the decision review system (DRS)?
In our sample there were 71 matches in which the decision review system was in place. Leg before wicket appeals or decisions in these matches can be referred to a third umpire who has the benefit of watching a slow-motion replay of the appeal or decision. All these matches had two neutral umpires, so we cannot use these data to identify any effect of favouritism by home umpires. However, any differences between home and away teams in referred decisions could indicate favouritism by neutral umpires towards home (or away) teams. Out of the 389 referred leg before wicket decisions in our sample, almost exactly the same proportion went against the away team as against the home team. This is consistent with our main finding that neutral umpires do not display bias.
So, conscious or unconscious favouritism?
It is important to note that our results do not necessarily suggest that home umpires deliberately tended to favour their own team. It is possible that home umpires could favour home teams sub-consciously. Our research does not attempt to examine the motivations of umpires. It is clear, however, that the introduction of neutral umpires in test cricket overcame the problem of home bias. This finding is important given the continued presence of home umpires in One Day Internationals and also because some commentators are suggesting a return to home umpires in test cricket on the grounds that new technology such as the decision review system makes it easier to reduce poor decision making. However, whilst the decision review system offers a ‘check’ of umpires’ decisions, it still allows some subjective decisions to stay in favour of the on-field umpire’s call. So in the light of our results, any proposal to revert to home umpires in test cricket should be treated with some caution.
  • Cameron, A C and Trivedi, PK (2010), Microeconometrics using Stata, Texas: StataCorp LP.
  • Chedzoy, O B (1997), “The effect of umpiring errors in cricket”, The Statistician, 46, 529-540.
  • Crowe, S M and Middeldorp, J (1996), “A Comparison of Leg Before Wicket Rates Between Australians and Their Visiting Teams for Test Cricket Series Played in Australia, 1977-94”, The Statistician, 45, 255-262.
  • ESPNcricinfo (2010-12). Available from (First accessed on December 5 2010).
  • Hynds, M and Smith, I (1994), “The demand for test match cricket”, Applied Economics Letters, 1, 103-106.
  • Ringrose, T J (2006), “Neutral umpires and leg before wicket decisions in test cricket”, Journal of Royal Statistical Society: Series A (Statistics in Society), 169, 903-911.
  • Sacheti, A, Gregory-Smith, I and Paton, D (2014), “Home bias in officiating: evidence from international cricket”, Journal of the Royal Statistical Society: Series A (Statistics in Society).
  • Sumner, J and Mobley, M (1981), “Are cricket umpires biased?” New Scientist, 91, 29-31.

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