The effect of expertise on peak performance: the case of home-field advantage.

Adams, Richard David ; Kupper, Susan Jeanne

Irving and Goldstein (1990) described home-field advantage as a territorial effect, noted that home-field advantage appeared to increase as the superiority of performance increased, and found home-field advantage to have a statistically significant relationship with no-hit major league baseball games. In this study, we describe home-field advantage as an expertise deficiency, demonstrate that, in theory and in practice, home-field advantage decreases as superiority of performance increases, and demonstrate that the statistically significant relationship between home-field advantage and no-hit major league baseball games is not applicable for pitchers who either replicated performance by winning two or more no-hitters or amassed a large number of career wins. Our general finding is that home-field advantage is a metric for the inability to maintain performance independent of environment and that this metric is inversely related to variables of expertise.

This paper consists of six sections. The first section provides a review of the relevant expertise literature. The second section proposes and provides levels of the hypothesis of an inverse relationship between home-field advantage and performance. The third section provides a review of Irving and Goldstein (1990). The fourth section proposes tests of hypotheses of the expertise effect within no-hit performance. The fifth section reports the results of the tests of these hypotheses. The sixth section presents conclusions and suggestions for future research.

Review of Literature

Territorial superiority as described by Irving and Goldstein (1990) is a common phenomenon in nature. However, the requirement of multi-territorial competition creates problems when attempting to generalize this phenomenon to sports competition. Unlike organisms which are able to limit their competitive endeavors to territories in which they exhibit superiority, sport competitors are generally required to compete in multiple arenas under varying conditions. In these situations, what appears to be a territorial superiority may actually be an environmental dependency (i.e., a difficulty in maintaining performance independent of environment. Some examples of environmental dependencies in baseball are natural grass vs. astroturf, day-games vs. night-games, and playing at home vs. playing on the road. Environmental dependencies are expected to have a negative effect on all levels of individual performance (i.e., game, season, and career). In the absence of environmental dependencies, individual performance can be expected to optimize within the constraints of individual expertise.

Expertise

Hayes-Roth, Waterman, and Lenat (1983) described expertise as consisting of domain-relevant knowledge, a comprehension of domain-specific problems, and skills for solving those problems. This description was consolidated by Dreyfus and Dreyfus (1986) who described expertise as a competence level within an operative domain. Chase and Simon (1973) had previously demonstrated that the bounds of such a competence level could be constrained by domain-relevant knowledge and domain-relevant problem-solving skills, Arkes and Freedman (1984) expanded upon this when they demonstrated that the bounds of such a competence level could also be constrained by environmental dependencies.

The Effect of Expertise on Competition

Garland and Barry (1990) noted that when variables of expertise are considered, levels of competitive performance can be reliably differentiated along cognitive dimensions. This is, in fact, the general finding in studies of both intellectual and physical competition: Bridge (Keren, 1987), Go (Reitman, 1976), Basketball (Allard & Burnett, 1985), Field hockey (Starkes & Deakin, 1984), and Ice hockey (Bard & Fleury, 1981). Taylor (1987) demonstrated the effects of cognition on performance across six arenas of competition. The contribution of Irving and Goldstein (1990) is that rather than differentiating performance, they held performance constant and differentiated upon environment. We expand upon this contribution by differentiating upon both environment and expertise.

Home-Field Advantage as an Inverse Relationship

Defining Home-Field Advantage

Home-field advantage (HFA) can be used either as a random probability (historic HFA) or as a home/road performance differential (team-year HFA). Historic HFA answers the question: Given any major league baseball game, what is the probability the home-team won the game? Team-year HFA answers the question: Given a game won by a specific team in a specific year, what is the probability the game was played on their home-field?

[Mathematical Expression Omitted]

where t represents each major league team and y represents each major league season from 1900 through 1991.

For the 1724 team-year seasons from 1900 through 1991 for the American, National, and Federal Leagues, 133,560 games resulted in a won-lost decision (The Baseball Encyclopedia, 1990 and The Official Major League Baseball 1992 Stat Book, 1992). Of these, 72,468 were won by the home team. Thus, historic HFA is .5425876.

Team-Year HFA = ([Home.Wins.sub.ty]) / ([Total.Wins.sub.ty]) (2)

where T represents a specific major league team and y represents a specific major league season from 1900 through 1991.

While team-year HFA provides an accurate probability based on actual games played, it provides an accurate representation of home/road performance differential only for teams having played equal numbers of games at home and on the road. Since this occurred in slightly less than half of the actual team-seasons observed (i.e., 856/1724), equation (2) must be adjusted for differences in home games versus road games.

Adj. Team-Year HFA = (Home.WLP) / (Home.WLP + Road.WLP) (3)

where Home.WLP = Home.Wins / (Home.Wins + Home.Losses), and Road.WLP = Road.Wins / (Road.Wins + Road.Losses)

Defining Performance

Competitive performance at the team level, in the absence of tied games, is measured by won-lost percentage (WLP).

Team-Year WLP = (Games.Won) / (Games.Played) (4)

Just as team-year HFA was adjusted for differences in the numbers of home games and road games, team-year WLP must also be adjusted:

Adj. Team-Year WLP = (Home.WLP + Road.WLP) / 2 (5)

The Relationship between Home-Field Advantage and Performance

An analysis of equations (3) and (5) indicates the following:

(1) ADJ. TEAM-YEAR HFA varies directly with HOME.WLP and inversely with ROAD.WLP;

(2) ADJ. TEAM-YEAR WLP varies directly with both HOME.WLP and ROAD.WLP;

(3) When the maximum ADJ. TEAM-YEAR WLP of 1.000 is achieved by a team winning all its home games and all its road games, ADJ. TEAM-YEAR HFA is equal to .500;

(4) In order to achieve the minimum ADJ. TEAM-YEAR HFA of 0, a team must lose all of the home games and will, therefore, have an ADJ. TEAM-YEAR WLP less than or equal to .500; and

(5) In order to achieve the maximum ADJ. TEAM-YEAR HFA of 1, a team must lose all of its road games and will, therefore, have an ADJ. TEAM-YEAR WLP less than or equal to .500.

Evaluating the Relationship

The relationship between Adjusted Team-Year Home-Field Advantage and Adjusted Team-Year Won-Lost Percentage is constrained by the concave function of Maximum Adjusted Team-Year Home-Field Advantage. Irving and Goldstein (1990) noted that home-field advantage appeared to increase as the superiority of performance increased. If, as we propose, home-field advantage is a deficiency, then home-field advantage should decrease as the superiority of performance increases. In support of this proposition, we hypothesize that the slope of the following regression equation will be negative: ADJ. TEAM-YEAR WLP = ADJ. TEAM-YEAR HFA

H1.0: The slope of the regression equation will be equal to or greater than zero.

H1.1: The slope of the regression equation will be less than zero.

We also propose that high performance teams (i.e., teams with high adjusted team-year won-lost percentages) are able to maintain performance independent of environment while low performance teams (i.e., teams with low adjusted team-year won-lost percentages) are not. In support of this proposition, we hypothesize that, in a between-groups analysis, high performance teams will exhibit a lower variance for adjusted team-year home-field advantage than will low performance teams.

H2.0: The variance for adjusted team-year home-field advantage for high performance teams will be equal to or greater than the corresponding variance for low performance teams.

H2.1: The variance for adjusted team-year home-field advantage for high performance teams will be less than the corresponding variance for low performance teams.

Hypothesis 1

A simple linear regression of the 1724 team seasons produced the following regression equation:

ADJ. TEAM-YEAR WLP = 0.68692 - 0.34387 * ADJ. TEAM-YEAR HFA.

The 95% confidence interval for [Beta] is -0.25351 [is less than] [Beta] [is less than] -0.43424. Therefore, the slope of the regression equation is negative and the null hypothesis can be rejected at an alpha level of .05.

Hypothesis 2

For this hypothesis, we extracted a data set consisting of all team seasons where adjusted won-lost percentage was either less than 0.400 (n=230) or greater than 0.600 (n=211). First, a test of dispersion parameters (Moses, 1963) was applied to confirm the difference in variances were 0.001124 and 0.003676, respectively. This resulted in a z-score of 5.0636 and a corresponding p[is less than].0001. Second, a test of extreme values (Hollander, 1963) was applied to confirm the lower variance of the high performance teams could be attributed to central tendency. The result was a z-score of 4.8387 and a corresponding p[is less than].0001. Therefore, the null hypothesis can be rejected at an alpha level of .05.

A Review of Irving and Goldstein

Introduction

Irving and Goldstein (1990) collected data on no-hit games from The Sport Encyclopedia of Baseball (Neft & Cohen, 1988) and predicted that a significant number of no-hitters occurred on the home-field of the winning pitcher. They excluded no-hitters of less than nine innings and no-hitters which were lost in extra innings. They determined the number of no-hitters won at home versus on the road to be 111 to 64. They used a chi-square goodness of fit with an expected probability of .500. Their results are summarized in Table 1.

Table 1

Results per Irving & Goldstein (1990)

Where Expected Distribution [X.sup.2] p [is less than]
Won Probability Expected Actual

HOME .500 87.5 111 6.31
ROAD .500 87.5 64 6.31
TOTAL 1.000 175.0 175 12.62 .00039

Replicating Irving and Goldstein (1990)

When we replicated Irving and Goldstein (1990), differences were found in both data and choice of methods. First, home-team wins versus road-team wins were found to be 117 to 58 rather than 111 to 64. This difference was confirmed via multiple sources (i.e., Neft & Cohen, 1988; The Baseball Encyclopedia, 1990; Palmer, Thorn, & Reuther, 1989; Dickey, 1976). Second, the home-field advantage probability of .500 used by Irving and Goldstein (1990) was found to be inaccurate. The historic home-field advantage for major-league baseball, as previously shown, is .5426. Third, since the variable under observation is binomial (an event being won at home or won on the road), the binomial probability is known (.5426), and the events are independent of each other, a binomial probability distribution is more appropriate than a chi-square goodness of fit (Hays, 1988). The results, after corrections, are summarized in Tables 2 and 3. When reviewing these tables, please note that the results are still statistically significant.

Table 2

Results After Corrections

Where Expected Distribution
Won Probability Expected Actual [X.sup.2] p [is less than]

HOME .5426 94.95 117 5.12
ROAD .4574 80.05 58 6.07
TOTAL 1.0000 175.00 175 11.19 .00083
Table 3

Results Using Binomial Probability

No-hit At On Expected p [is less than]
Games Home Road Probability

175 117 58 .5426 .00048

The Effect of Expertise

Hypotheses

Two metrics, well-established in the expertise literature (Wallace, cited in Phelps & Shanteau, 1978; Trumbo, Adams, Milner, & Schipper, cited in Shanteau, 1988; Phelps & Shanteau, 1978; Shanteau, 1988) are proposed for classifying winning pitchers of no-hit games:

(1) the ability to replicate specific performance; and (2) the ability to sustain career performance.

Given a general hypothesis that home-field advantage and expertise have an inverse relationship when these metrics are applied to the data, two effects should be observable. We state them here in hypotheses 3 and 4:

H3.0: Home-field advantage will not be statistically significant for repeat performance pitchers.

H3.1: Home-field advantage will be statistically significant for repeat performance pitchers.

H4.0: Home-field advantage will not be statistically significant for high career performance pitchers.

H4.1: Home-field advantage will be statistically significant for high career performance pitchers.

Since our purpose is to demonstrate the contrary effect of an additional variable, rather than attempting to reject the null hypothesis at P = .05, we will attempt to fail to reject the null hypothesis at P = .15 (Greenwald, 1975).

Data and Method

The data set for these hypotheses was extracted from The Baseball Encyclopedia (1990), and career wins for current pitchers was updated from The Official Major League Baseball 1992 Stat Book (1992). The data set consists of all major league no-hitters from 1900 to 1988 using criteria set by Irving and Goldstein (1990) (i.e., no-hitters of less than nine innings and no-hitters which were lost in extra innings are excluded). Each observation included the league, the teams, the date of the game, the winning pitcher, his careerwins, whether the home team won or lost, and whether or not the winning pitcher won other no-hitters.

Since expertise is an effect rather than a correlation (Hayes-Roth, Waterman, & Lenat, 1983), the appropriate method is to test to the effect in homogeneous subsets of the data rather than to test for a correlation across full data sets (Arkes & Freedman, 1984). Therefore, two data sets were extracted, one for each hypothesis. The data set for repeat performance pitchers consists of 48 observations. The data sets for high career performance were created by rank ordering the data in descending order of careerwins of the winning pitcher and extracting the upper 20% (n=35) of the observation.

Results

Hypothesis 3

Forty-eight no-hitters were won by 21 pitchers who won two or more no-hitters. Of these, 28 games were won on the home-field of the winning pitcher. The null hypothesis cannot be rejected at an alpha level of .15 (p [is less than] .338).

Hypothesis 4

Thirty-five no-hitters were won by pitchers in the upper 20% of the rank ordered data set. Of these, 20 games were won on the home-field of the winning pitcher. The null hypothesis cannot be rejected at an alpha level of .15. (p [is less than] .434).

Table 4

Repeat Performance Pitchers

No-hit At On Expected p[is less than]
Games Home Road Probability

48 28 20 .5426 .3381
175 102 73 .5426 .1603
Table 5

High Career Performance Pitchers

No-hit At On Expected p[is less than]
Games Home Road Probability

35 20 15 .5426 .4338
175 100 75 .5426 .2461

Considering the Effect of Data Set Size

Nonparametric methods, in general, and the binomial probability, in particular, are sensitive to data set size. Given a constant ratio, the binomial probability will increase as the number of trials decreases. This raises the possibility that the loss of significance was due to the partitioning of the original data set into smaller data sets. Therefore, we questioned whether or not the null hypothesis would have been rejected had the size of the extracted data sets been equal to the size of the original data set (n = 175) at p = .15. Although linear transformations of the data are not viewed as statistically valid, rejection of the null hypothesis after a linear transformation would support an argument that the loss of significance had been due to data set size. Thus, we have provided a second entry on Tables 4 and 5 (p [is less than] .1603 and p [is less than] .2461, respectively) to indicate what the results would have been had the ratio of home wins to road wins remained constant for a data set with 175 observations and to demonstrate that such an argument is not supported by the data.

Conclusions and Future Research

The result of tests on our first two hypotheses support our position that home-field advantage is inversely related to won-lost percentage and that high performance teams exhibit lower variances in and a central tendency for home-field advantage. Failure to reject the second two hypotheses indicates that, based on the available data, the performance of the repeat no-hit pitchers with relatively high career wins were not significantly affected by home-field advantage.

These findings are consistent with the findings of Garland and Barry (1990) that when variables of expertise are considered, levels of competitive performance can be reliably differentiated along cognitive dimensions. They are also consistent with the findings of Irving and Goldstein (1990) that there is a significant relationship between home-field advantage and no-hit performance. However, these findings extend Irving and Goldstein by demonstrating that the relationship between home-field advantage and peak performance is inversely related to variables of expertise.

This study and Irving and Goldstein (1990) rely upon the no-hitter as a surrogate for peak performance. Whether or not a no-hitter is a valid surrogate for peak performance is an empirical question which neither study addressed. If the use of peak performance is essential to sports behavior research, then further research is necessary to develop well-calibrated metrics for peak performance.

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