Participants
A total of 43 professional male cricket players (mean age 29.6 years, standard deviation [SD] 5.6) and 93 inexperienced male cricketers (mean age 24.1 years, SD 7.2) participated in the study. The professional group were all members of a first-class and/or international cricket team: 26 had played at international level (ten had played test cricket) and 17 had played at first-class level. The professional players were all selected in their team based on their skill as a batsman (i.e., as a specialist batsman, a wicketkeeper/batsman, or as an all-rounder—someone who bats and bowls). Participants in the inexperienced group had less than five years’ cricket experience (mean 1.2 years, SD 1.4), with most not actively participating in organized cricket at the time of testing. The experimental procedure conformed to the ethical standards of the Declaration of Helsinki and was approved by the Ethics Committee of the Faculty of Human Movement Sciences at Vrije Universiteit Amsterdam. Participants were informed about the nature of the study and signed informed consent forms prior to testing.
Procedure
We determined the hand dominance, eye dominance, and batting stance of all participants.
Hand Dominance
To determine hand dominance, participants completed the Edinburgh Handedness Inventory—Short Form [10]. This validated questionnaire provides a measure of handedness by testing the hand used during four activities of daily living: writing, throwing, using a toothbrush, and using a spoon. For each of the four activities, participants rated whether they use their right or left hand for that activity on a scale from one (always right) to five (always left). According to the questionnaire guidelines, participants whose average score across all four tasks was greater than three were classed as left-hand dominant, those whose score was below three were classed as right-hand dominant, and those with a score equal to three were classified as mixed dominance [10]. One professional and one inexperienced player had mixed hand dominance and were therefore excluded from all analyses. Handedness surveys were unavailable for five of the professional players. Consistent with previous studies [1], for those players we assumed the hand they used when bowling was their dominant hand (classifying one as reversed and four as conventional). In support, the hand used for bowling is almost always that used for throwing,Footnote 1 and there was 96 % agreement (124/129 participants) between the dominant hand established by the questionnaire and that used for throwing.
Eye Dominance
Eye dominance can change depending on the conditions in which it is tested [11–13]. To account for this, three different tests of eye dominance were performed (Fig. 2). All three tests were based on a modified version of the Porta test [14], with a camera used to produce material evidence of eye dominance. For each test, participants stood three meters from a camera positioned at the participant’s eye level. Two of the three tests were performed using a front-on stance. In the right-hand front-on test, participants stood front-on to the camera, raised their right arm, and pointed directly at the center of the camera lens with both eyes open. When the participant confirmed that he was pointing at the center of the lens, a photograph was taken. This procedure was repeated for the left-hand front-on test when pointing with the left arm. The third test was one of batting eye dominance, where participants adopted their side-on batting stance and looked towards the camera. All inexperienced participants knew the stance they would typically adopt as they were from cricket-playing countries and had at some time played the game (formally or informally). From the batting stance, participants were asked to raise the arm nearest the camera and point towards the center of the lens with both eyes open. A photograph was taken when the participant confirmed he was ready.
Eye dominance was established by viewing the photographs of the participants. In each of the three tests, the dominant eye was determined by selecting the eye participants used to align themselves with the camera. If the finger/thumb was aligned with one of the eyes then that eye was deemed to be the dominant eye (e.g., if the right eye was in any way obscured by the finger/thumb, the participant was deemed to be right-eye dominant and vice versa). If the finger/thumb was placed between the two eyes rather than in any way obscuring an eye then the dominance was deemed to be mixed. The dominant eye established during the batting eye dominance test was expected to be the one most likely to be preferred during batting, so it was the eye used as the ‘dominant eye’ for further analyses. One of the professional players was found to have mixed eye dominance with this test; however, it was the same participant who had mixed handedness and had already been excluded from all analyses (the player was a relatively inexperienced and less accomplished all-rounder who had played only two first-class matches, and who bats and bowls left handed).
We checked the agreement between the three different tests of eye dominance. The agreement between the two front-on tests was 85 %, that between the batting eye dominance test and the right-hand front-on test was 87 %, and that between the batting and left-hand front-on test was 91 %. However, the best agreement was between the result for the test of batting eye dominance and that found during the corresponding front-on test using the same hand (95 %; i.e., if batting right handed, we compared the batting test with the left-hand front-on test and vice versa). This suggests it was the hand used during the test that caused most of the variability between the tests.
Batting Stance
Batting stance was determined on the basis of the stance that participants adopted in the test of batting eye dominance; a stance with the left foot closer to the camera was classified as a right-handed batting stance, and a stance with the right foot nearer the camera was classified as a left-handed batting stance.
Additional Data
A preliminary check of the handedness data revealed very high agreement between the dominant hand determined by the questionnaire and the hand used when throwing (96 % agreement). Given that the throwing hand is generally also the hand used for bowling, we decided to use the bowling hand as a proxy for the dominant hand and to perform further analysis to check whether the proportion of professional batters who adopted a reversed stance in our sample was representative of that in the wider population of international-level batsmen. To do so, we collected additional data on the bowling hand and batting stance of (1) the 100 highest-ranked batsmen in the world, and (2) batsmen at the 2003 Cricket World Cup (matching the sample from the aforementioned study by Brooks et al. [4]). Data on the bowling hand and batting stance were collected from the match records of first-class and international cricket matches available on the website of ESPN Cricinfo (http://www.espncricinfo.com/ci/content/stats/index.html). If a player had not bowled in a match (typically wicketkeepers), we excluded that player from all analyses, as we had no way of determining their dominant hand.
Highest-Ranked International Batsmen
The International Cricket Council (ICC) ranks the 100 best-performing batsmen on an on-going basis for those who play in international tests, 1-day, and T20 matches (the three different formats of the game). We chose to use the rankings for the test batsmen, as this represents what is typically considered the most challenging form of the game. The rankings we used were accessed from the ICC website (http://www.icc-cricket.com/player-rankings/mens-test) on 15 November 2014. Data about the bowling hand were unavailable for seven batsmen, so only 93 batsmen were included in the final analysis.
Batsmen at the 2003 Cricket World Cup
Brooks et al. [4] reported, based on their analysis of batsmen taking part in the 2003 Cricket World Cup, that left-handed batsmen benefit from a negative frequency-dependent effect. We re-analyzed these data to determine whether the benefits experienced by the left-handed batsmen were better explained by an advantage for those who adopt a reversed stance. Of the 205 players reported to have batted at the 2003 World Cup (data retrieved from http://www.espncricinfo.com/ci/content/stats/index.html), we excluded those for whom we could not establish the bowling hand (n = 12). For consistency with the data from Brooks et al. [4], we excluded those who had not been dismissed at least once in the group matches (n = 33). As a result, a total of 160 batsmen were included in our analysis.
Statistical Analyses
Chi-squared testing was used to establish whether proportions (e.g., proportion of batsmen who adopted a reversed stance) differed across two groups. Odds ratios (ORs) were used to calculate the size effects using Eq. (1):
$$ {\text{OR}} = \frac{{\left( n \right){\text{Exposed cases }} \times \left( n \right){\text{Unexposed noncases}}}}{{\left( n \right){\text{Exposed noncases}} \times \left( n \right){\text{Unexposed cases}}}} $$
(1)
where, for example, when interested in the proportion of professional batsmen who bat using a reversed stance (when compared with the proportion of the inexperienced group): (n)Exposed cases = number of professional batsmen who bat with a reversed stance, (n)Exposed non-cases = number of inexperienced batsmen who bat with a reversed stance, (n)Unexposed cases = number of professional batsmen who bat with a conventional stance, (n)Unexposed non-cases = number of inexperienced batsmen who bat with a conventional stance.
In two cases, we pooled the players in our professional group with the 100 highest-ranked international batsmen and the players in the 2003 Cricket World Cup. Eight batsmen were in at least two of the three pooled groups, so their data were included only once. The data for the pooled group were then compared with those of the participants in our inexperienced group. To compare the advantages afforded to professional left-handed batsmen who used a conventional or reversed stance to those in the inexperienced group, we used a goodness-of-fit test because the number of inexperienced batsmen who did so was very low (three and two respective participants) and this would have violated the assumptions of a normal chi-squared test (needing a minimum of five observations in each cell of the contingency table). ORs were reported as a measure of effect size for the goodness-of-fit test (comparing the observed and expected frequencies).
We calculated 95 % confidence intervals (CIs) for each of the ORs using Eq. (2). Results were considered significant to p < 0.05 if the CI did not pass through the null value of one.
$$ 95 \,\, \% \,\,{\text{CI}} = e^{{\left( {\ln \left( {\text{OR}} \right) \pm 1.96\sqrt {\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d}} } \right)}} $$
(2)
where a, b, c, and d, respectively, refer to the number of exposed cases, exposed non-cases, unexposed cases, and unexposed non-cases.