Opponent left-handedness does not affect fight outcomes for Ultimate Fighting Championship hall of famers

This paper is a commentary on Pollet et al. (2013), where both the incidence of left-handedness and its effect on outcomes were analyzed. One of the drawbacks is that these analyses were largely cross-sectional with only a small number of fights for any given fighter. Here, we explore the effects of left-handedness on fight outcomes in a small sample of elite UFC fighters with multiple fights from the same fighter. All UFC fights by the current 10 UFC hall of fame fighters were coded by the second author B.R. (with assistance of Thomas V. Pollet) from a variety of online sources (www.ufc.com; www.sherdog.com; www.mmajunkie.com; www.wikipedia. com) (N = 182 fights). The UFC hall of fame list consists of the most successful UFC fighters of all time and currently one non-fighter (UFC, 2014). For each fight we coded the outcome and handedness of the hall of famer and his opponent, if available. There were nine right-handed hall of famers and one left-hander (Royce Gracie). As there is only one left-hander we excluded his fights. Our analyses also exclude duplicate fights (i.e., hall of famers fighting one another). Central to our analyses is that we examine the effects of right-handers fighting left-handers, this is why we also exclude fights by Mark Coleman, who in our dataset, as a righthander only fought right-handers. This leaves 75 fights with complete data on both fighters’ handedness for analysis. The most straightforward test is a simple χ2 test for the 2 × 2 table. However, such a test does not take into account the nested structure of the data (i.e., fights belonging to the same hall of famer). Therefore, we also ran a Cochran-Mantel-Haenszel test (Agresti, 2002) and a Generalized Linear Mixed Model with binomial link (GLMM; McCulloch, 2006; Verbeke and Molenberghs, 2009), using the lme4 procedure in R 3.0.1 (R Development Core Team, 2008; Bates et al., 2012). If we find some indication for a fixed effect of opponent handedness in a GLMM, after accounting for the nested structure of the data (random intercept), then this suggests that the opponent’s handedness significantly influences the outcome. We also test a model whereby we model a random intercept for the opponent, In order to account for multiple appearances of an opponent, as well as a random intercept for the hall of famer (see Hox, 2010). The lme4 package does not allow fitting quasibinomial models, we therefore also tested a GZLM with quasibinomial link, as over/underdispersion could affect the result from the GLMM. Given that our sample is (very) small we report one-tailed tests in favor of the hypothesis that left-handedness has an effect. Hall of famers were not significantly less likely to win from left-handers (Figure 1; χ2 test = 0.17; Monte Carlo bootstrapped one-tailed p-value based on 10,000 samples = 0.39). The CochranMantel-Haenszel test also does not support the conclusion that handedness affects outcomes in our sample (CMH test, one-tailed p = 0.44; estimate of common odds ratio = 0.813; 95%CI(odds ratio) = < 00.01 to 2.188). In the GLMM, with a random intercept for hall of famer, we found no evidence for a handedness effect (B = −0.214(±0.520); Z = −0.412, one-tailed p = 0.34). Accounting, for multiple appearances of the opponent or analyzing the data via a GZLM with quasi-binomial link does not alter this conclusion (respectively: B = −0.454(±0.628); Z = −0.723, onetailed p = 0.235; B = −0.214(±0.527); t = −0.407, one-tailed p = 0.342). Our analyses further support the conclusion that currently there is little evidence for an advantage of left-handers in mixed martial arts (MMA) based on wins. Across all tests there is little suggestion that Hall of Famers were more inclined to lose from left-handers. A much larger sample by Baker and Schorer (2013) also found that, while left-handers are overrepresented in MMA, there is no relationship between handedness and fight outcomes. One of the drawbacks of the Baker and Schorer (2013) study, however, is that Simpson’s Paradox (Simpson, 1951) could not be ruled out (see Kievit et al., 2013). The pattern between fighters could be markedly different than that within fighters. While the win ratios analyzed by Baker and Schorer (2013) could be similar between left-handed and right-handed fighters, it is possible that the pattern within fighters is markedly different. It should also be noted that some evidence from other combat sports suggests that handedness