Summary: Building A Better Fantasy Baseball Team
STATISTICS
Building a Better Fantasy Baseball Team by I. Elaine Allen, Kirill Kustov and George Recck
F
antasy baseball has grown to be a popular social activity for ambitious sports fans eager to display their baseball expertise in competition with their peers. The nature of fantasy baseball fosters meticulous planning and research in the hopes of outsmarting rival teams, contributing to the burgeoning market of readily available
In 50 Words Or Less
• Fantasy baseball is a competition that pits the performance statistics of Major League Baseball players against one another. • Applying multivariate and univariate analysis to players’ statistics can show which players have the potential to be the most valuable on a fantasy baseball …show more content…
team.
sports data and analysis tools that assist team owners in their roster decisions. For those not familiar with fantasy baseball, here’s a brief explanation: A group of people (usually eight to 12) get together and form a fantasy baseball league; each of these people becomes the owner of a mock baseball team. The first step is to hold a “draft” before the Major League Baseball (MLB) season begins. At the draft, each owner selects a number of MLB players to form his or her fantasy team. Each player can only be picked (drafted) by one team. When the MLB season begins, the owners compare performance statistics of their players. At the end of the season, the owner who assembled the best fantasy team—as determined by the agreed upon scoring system—is the winner. Owners can drop and add players and trade players with other teams throughout the season. The owners agree on rules and limitations regarding such transactions before the season begins. Each year, most fantasy leagues start anew, giving participants the opportunity to tinker and plan in the quest for the perfect team that can outplay all opponents. It seems reasonable to assume that, given a constant rule set in the fantasy league as
24
I APRIL 2007 I www.asq.org
well as constant record keeping in MLB, one could accurately measure the most effective drafting technique. By looking at fantasy performance of players in various positions and leagues and applying statistical methods, we can find the most effective drafting strategy to maximize overall fantasy team performance.
Fantasy League Structure
A fantasy league can set up its roster and scoring system however participants want, but for this article, the template we will use is ESPN’s Fantasy Baseball default rule set and rotisserie-style scoring. It is a relatively simple structure that is the basis for many other fantasy league structures. The rule set centers around five scoring statistics that measure batting performance: runs scored (R), home runs (HR), runs batted in (RBI), stolen bases (SB) and batting average (BA). The fantasy team’s score is the sum of its players’ performances in each of these five categories on the previous day. The team itself consists of an active batting roster of 13 players, allowing openings based on position and forcing fantasy teams’ positions to be consistent with those of real-life teams. The starting lineup must include: • One player for every infield position: catcher (C), first base (1B), second base (2B), third base (3B) and shortstop (SS). • One corner infielder (CI), which is someone who can play either 1B or 3B. • One middle infielder (MI), which is someone who can play either 2B or SS. • Five outfielders (OF), regardless of whether they actually play left field (LF), center field (CF) or right field (RF). • One utility slot (UTIL), available to a player of any position. In rotisserie scoring, each fantasy team in the league is ranked weekly in the five scoring categories (R, HR, RBI, SB, BA) and allocated points accordingly. In a 10-team league, the team with the most runs that week receives 10 points, the team with the second most runs receives nine points, the team with the third most runs receives eight points, and so on. This is repeated for the other four scoring categories.
By looking at fantasy performance of players in various positions and leagues and applying statistical methods, we can find the most effective drafting strategy to maximize overall fantasy team performance.
So, in a 10-team league with five scoring categories, a team could obtain 50 points in a week—if it led all five categories for that week. Even if a team ranks last in each category, that team still receives five points—one point for each category.
Drafting a Team
These rules dictate somewhat how a team should be selected to maximize performance: • The scoring emphasizes individual player statistics over actual team success, meaning that a player’s team is irrelevant in a fantasy league sense. It is often the case that the best players are on the most successful teams, but the fantasy rule set calls for the focus to be on individual rather than collective contribution. • The rules select five specific performance categories out of dozens available, negating other statistics, such as on-base percentage (OBP), strikeouts (K) and walks, also known as base on balls (BB). Though these categories might have an indirect correlation with performance in the five major categories, we will assume it is most prudent to select players primarily based on their success in the five categories. • Basing active roster slots on position forces the owner to draft players based on eligibility to be in the starting lineup rather than on overall
QUALITY PROGRESS
I APRIL 2007 I 25
STATISTICS
performance. For example, an owner wouldn’t want to draft 13 shortstops because he or she could only fill three roster positions (SS, MI, UTIL). This adds a strategic element to the draft process. At times, an owner must consider drafting a far worse overall performer just to make sure he or she will have enough players to fill the weekly roster, while keeping in mind such a player might drag down the statistic totals of the team. • Given rotisserie’s scoring distribution based on comparative weekly ranking, the amount a team leads by in any category is irrelevant beyond the fact that it is leading. For instance, the team that leads the HR category gets 10 points, whether the team leads by one HR or 20 HRs over the next team. • Given that each of the five criteria is weighted equally in awarding points, it is useless to
FIGURE 1
Fantasy Pe r formance By League
12 10 8 6 ESPN index 4 2 0 -2 -4 -6 -8 AL Count Median Mean 124 0.1 0.7 NL 154 -1.4 -0.6
“stack” an individual category and neglect others.
This requires a team to have players performing well in each of the five categories to be successful. These preliminary conclusions come as a result of the conditions imposed by the ESPN fantasy league and are only the tip of the iceberg in relation to the findings the data will provide. The dataset used in this article is comprehensive statistics of MLB players during the 2005 season. The data contain 21 different batting criteria that are continuous variables and three categorical variables that group the players by position, team and league. The criteria are specifically batting oriented and do not reflect any pitching or defensive statistics, gearing the focus of this article to the offensive side of a fantasy team. The 21 continuous variables include the aforementioned five criteria used directly in calculating fantasy performance, leading initial analysis to be focused primarily on them. There are 278 separate player entries in the data with no missing values per player. All players are batters; no pitchers are included regardless of whether they batted during the season. There are some difficulties with these data based on the different league rules pertaining to the American League’s (AL’s) designated hitter (DH) position. DHs are classified as LFs, making the number of LFs twice as large as any other position and possibly skewing results because characteristics of DHs and LFs differ …show more content…
slightly.
TABLE 1
Pe r formance Diff e rences B e t we e n L e a g u e s
F-statistic R HR RBI SB BA 15.992 5.757 13.148 0.412 0.398 p-value 0.000 0.017 0.000 0.522 0.562
League AL = American League NL = National League
26
R = runs scored HR = home runs RBI = runs batted in SB = stolen bases BA = batting average
I APRIL 2007 I www.asq.org
Univariate Analysis
The first step in observing and determining the potential of fantasy players is to create an index that combines the five major scoring criteria into a single value. To this end, each variable was astandardized and then added together to create a composite index of a player’s relative success. The median (-0.5) is below the mean (0 by standardization), showing the data are slightly skewed high and that there are outliers from better performers pulling the mean higher. The impact that this has on the selection of fantasy players is that the best performers (the ones who will be drafted first) will have a disproportionately significant impact on the overall scoring of the team. Based on this assertion, the first round of drafting will play the largest role in predicting the future success of the team. Breaking down the fantasy index by
The first step in observing and determining the potential of fantasy players is to create an index that combines the five major scoring criteria into a single value.
FIGURE 2
Fantasy Pe r formance by Position
12 10 8 6 ESPN index 4 2 0 -2 -4 -6 -8 1B 31 0.7 0.9 2B 38 -0.8 -0.7 3B 31 -0.9 -0.1 C 30 -2.1 -2.1 CF 33 0.1 0.5 LF 53 -0.1 0.6 RF 30 -0.1 -0.1 SS 32 -0.2 0.7
Count Median Mean
Position
1B = first baseman 3B = third baseman CF = center fielder RF = right fielder
2B = second baseman C = catcher LF = left fielder SS = shortstop
league illustrates the commonly held assumptions about the differences between play styles and player performance in MLB’s two leagues. The National League (NL) is most often associated with “small ball,” its players having higher OBP, SB and sacrifice hits, while the AL, with its DHs, has players with higher slugging averages, HRs, Ks and sacrifice flies. Examining boxplots by league (Figure 1) shows the AL has a higher mean (0.7) and median (0.1) fantasy index than the NL (-0.6 and -0.14). This implies that AL players are better overall contributors to a fantasy team’s success, further supported by the fact that the range and inter-quartile range are smaller among AL players. That means there is also less variability among players from an already higher mean value than among players in the NL. One explanation of this is ESPN’s choice of scoring categories. The AL has a higher mean in each of the five, with three (R, HR, RBI) significantly higher (p < 0.05), as shown in Table 1. Judging by these descriptive statistics, prioritizing AL players over NL players is a rational choice for fantasy team owners. Examining the fantasy index breakdown by position (Figure 2) shows the variability by position to be relatively constant, with the exception of catchers. While their overall
QUALITY PROGRESS
I APRIL 2007 I 27
STATISTICS
ESPN index is lower than that of the other positions, knowing that the variability in this position is also small indicates catchers can be drafted last because most of them will have the same performance on the five categories overall.
Notice shortstops have the most variation. For drafting order, simply ranking positions by their average or median index score does not take into account the roster restrictions, requiring further exploration to decide which positions to draft early. Looking at the standardized values of each of the five components of the index adds further information for drafting players. The boxplots in Figure 3 indicate the variability in HR and SB, with many outliers, offers the best opportunity for drafting a player that can consistently add value (and index points) to a fantasy
team.
TABLE 2
C o r r e l a t i o n B e t we e n t h e E S P N I n d ex C o m p o n e n t s
Correlations R 1 HR .663** .000 278 278 .663** 1 .000 278 278 RBI .761** .00 278 .897** .000 278 SB .429** .000 278 -.106 .079 278 -.023 .707 278 1 278 BA .535** .000 278 .283** .000 278 .397** .000 278 .183** .002 278
R
HR
Pearson correlation Significance (2-tailed) N Pearson correlation Significance (2-tailed) N
RBI Pearson correlation .761** .897** 1 Significance (2-tailed) .000 .000 N 278 278 278 SB Pearson correlation .429** -.106 Significance (2-tailed) .000 .079 N 278 278 -.023 .707 278
BA
Pearson correlation .535** .283** .397** .183** 1 Significance (2-tailed) .000 .000 .000 .002 N 278 278 278 278 278
R = runs scored HR = home runs RBI = runs batted in SB = stolen bases BA = batting average ** Correlation is significant at the 0.01 level (2-tailed).
FIGURE 3
O v e r a l l R , H R , R B I , S B a n d B A P e r fo r m a n c e
3 3.5 3 2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 HR (normalized) 278 Count Median -0.2 0.0 Mean (None) R (normalized) 3 2 1 0 -1 R (normalized) 278 Count Median -0.1 -0.0 Mean (None) SB (normalized) Count 278 Median -0.3 Mean 0.0 (None) RBI (normalized) HR (normalized) SB (normalized) 1 0.5 0 2.5 2 1.5 4 5 3.5 3 2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -1.5 -2 RBI (normalized) Count 278 Median -0.1 Mean -0.0 (None)
3 2.5 2 1.5 1 BA (normalized) 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3 BA (normalized) Count 278 Median -0.0 Mean 0.0 (None)
-0.5 -1
BA = batting average
28
HR = home runs
R = runs scored
SB = stolen bases
RBI = runs batted in
I APRIL 2007 I www.asq.org
Multivariate Analysis
Analyzing correlations between the five categories shows their overlap. For example, an increase in HR mandates an increase in R, RBI and BA but is negatively related to SB. In fact, most power hitters are not good base stealers. The correlations shown in Table 2 support that the five scoring categories overlap significantly and that leaders in one category will most likely be doing well in others. Finally, to assess the impact of the five categories on the ESPN index, a multiple regression model was fit with the five fantasy categories as predictors of the ESPN index to examine the strength of their relationship overall. These variables (doubles, K, BB, caught stealing, sacrifice hits) collectively are able to explain 68% of the variability in the fantasy index of all players in the database (Table 3). This is not as high as you would hope but indicates there are other (unmeasured) factors in performance.
TABLE 3
R e g ression of Variables O n t h e E S P N I n d ex
Coefficientsa
Unstandardized Standardized coefficients coefficients Standard error Model B Beta t Significance 1 (Constant) -7.802 .425 -18.376 .000 Doubles .172 .017 .457 10.354 .000 Caught stealing .214 .042 .199 5.122 .000 Walks .053 .007 .326 7.160 .000 Strikeouts .011 .005 .094 2.111 .036 Sacrafice hits -.101 .042 -.095 -2.389 .018
a. dependent variable: ESPN index
Tips for Fantasy Owners
Based on exploring the ESPN index’s components and the player performance variability, several conclusions can be made on how to select the best possible fantasy team: • A player’s real-life team is irrelevant, but AL players perform better than NL players. • The early draft picks have the most impact on a fantasy team’s success. • The SB statistic is the easiest to dominate. • Leaders in one statistic will most likely be doing well in others. • Run scorers create the most balanced and successful team. • HR hitters have the most impact on a team’s success. Also, certain positions outperform others. So, when drafting, keep in mind: • 1B should fill the CI slot. • SS should fill the MI slot. • LF or CF should fill the OF slots. • 1B or OF should fill the UTIL slot. These conclusions serve as an introduction to drafting success, though by no means are they exhaustive. Plenty of avenues exist for continuing the pursuit of the perfect fantasy team, such as
including pitching statistics and analyzing the many possible fantasy league rule sets. And while almost all fantasy leagues have already held their 2007 drafts, team owners can still use these conclusions to give them an edge in trading players and preparing for next year’s draft.
I. ELAINE ALLEN is an associate professor of statistics and
entrepreneurship at Babson College in Babson Park, MA. She has a doctorate in statistics from Cornell University in Ithaca, NY. Allen is a senior member of ASQ.
KIRILL KUSTOV is an undergraduate studying statistics at
Babson College.
GEORGE RECCK is the director of the math resource center at Babson College, where he earned a master’s degree in business management.
Please comment
If you would like to comment on this article, please post your remarks on the Quality Progress Discussion Board at www.asq.org, or e-mail them to editor@asq.org.
QUALITY PROGRESS
I APRIL 2007 I 29
Building a Better Fantasy Baseball Team by I. Elaine Allen, Kirill Kustov and George Recck
F
antasy baseball has grown to be a popular social activity for ambitious sports fans eager to display their baseball expertise in competition with their peers. The nature of fantasy baseball fosters meticulous planning and research in the hopes of outsmarting rival teams, contributing to the burgeoning market of readily available
In 50 Words Or Less
• Fantasy baseball is a competition that pits the performance statistics of Major League Baseball players against one another. • Applying multivariate and univariate analysis to players’ statistics can show which players have the potential to be the most valuable on a fantasy baseball …show more content…
team.
sports data and analysis tools that assist team owners in their roster decisions. For those not familiar with fantasy baseball, here’s a brief explanation: A group of people (usually eight to 12) get together and form a fantasy baseball league; each of these people becomes the owner of a mock baseball team. The first step is to hold a “draft” before the Major League Baseball (MLB) season begins. At the draft, each owner selects a number of MLB players to form his or her fantasy team. Each player can only be picked (drafted) by one team. When the MLB season begins, the owners compare performance statistics of their players. At the end of the season, the owner who assembled the best fantasy team—as determined by the agreed upon scoring system—is the winner. Owners can drop and add players and trade players with other teams throughout the season. The owners agree on rules and limitations regarding such transactions before the season begins. Each year, most fantasy leagues start anew, giving participants the opportunity to tinker and plan in the quest for the perfect team that can outplay all opponents. It seems reasonable to assume that, given a constant rule set in the fantasy league as
24
I APRIL 2007 I www.asq.org
well as constant record keeping in MLB, one could accurately measure the most effective drafting technique. By looking at fantasy performance of players in various positions and leagues and applying statistical methods, we can find the most effective drafting strategy to maximize overall fantasy team performance.
Fantasy League Structure
A fantasy league can set up its roster and scoring system however participants want, but for this article, the template we will use is ESPN’s Fantasy Baseball default rule set and rotisserie-style scoring. It is a relatively simple structure that is the basis for many other fantasy league structures. The rule set centers around five scoring statistics that measure batting performance: runs scored (R), home runs (HR), runs batted in (RBI), stolen bases (SB) and batting average (BA). The fantasy team’s score is the sum of its players’ performances in each of these five categories on the previous day. The team itself consists of an active batting roster of 13 players, allowing openings based on position and forcing fantasy teams’ positions to be consistent with those of real-life teams. The starting lineup must include: • One player for every infield position: catcher (C), first base (1B), second base (2B), third base (3B) and shortstop (SS). • One corner infielder (CI), which is someone who can play either 1B or 3B. • One middle infielder (MI), which is someone who can play either 2B or SS. • Five outfielders (OF), regardless of whether they actually play left field (LF), center field (CF) or right field (RF). • One utility slot (UTIL), available to a player of any position. In rotisserie scoring, each fantasy team in the league is ranked weekly in the five scoring categories (R, HR, RBI, SB, BA) and allocated points accordingly. In a 10-team league, the team with the most runs that week receives 10 points, the team with the second most runs receives nine points, the team with the third most runs receives eight points, and so on. This is repeated for the other four scoring categories.
By looking at fantasy performance of players in various positions and leagues and applying statistical methods, we can find the most effective drafting strategy to maximize overall fantasy team performance.
So, in a 10-team league with five scoring categories, a team could obtain 50 points in a week—if it led all five categories for that week. Even if a team ranks last in each category, that team still receives five points—one point for each category.
Drafting a Team
These rules dictate somewhat how a team should be selected to maximize performance: • The scoring emphasizes individual player statistics over actual team success, meaning that a player’s team is irrelevant in a fantasy league sense. It is often the case that the best players are on the most successful teams, but the fantasy rule set calls for the focus to be on individual rather than collective contribution. • The rules select five specific performance categories out of dozens available, negating other statistics, such as on-base percentage (OBP), strikeouts (K) and walks, also known as base on balls (BB). Though these categories might have an indirect correlation with performance in the five major categories, we will assume it is most prudent to select players primarily based on their success in the five categories. • Basing active roster slots on position forces the owner to draft players based on eligibility to be in the starting lineup rather than on overall
QUALITY PROGRESS
I APRIL 2007 I 25
STATISTICS
performance. For example, an owner wouldn’t want to draft 13 shortstops because he or she could only fill three roster positions (SS, MI, UTIL). This adds a strategic element to the draft process. At times, an owner must consider drafting a far worse overall performer just to make sure he or she will have enough players to fill the weekly roster, while keeping in mind such a player might drag down the statistic totals of the team. • Given rotisserie’s scoring distribution based on comparative weekly ranking, the amount a team leads by in any category is irrelevant beyond the fact that it is leading. For instance, the team that leads the HR category gets 10 points, whether the team leads by one HR or 20 HRs over the next team. • Given that each of the five criteria is weighted equally in awarding points, it is useless to
FIGURE 1
Fantasy Pe r formance By League
12 10 8 6 ESPN index 4 2 0 -2 -4 -6 -8 AL Count Median Mean 124 0.1 0.7 NL 154 -1.4 -0.6
“stack” an individual category and neglect others.
This requires a team to have players performing well in each of the five categories to be successful. These preliminary conclusions come as a result of the conditions imposed by the ESPN fantasy league and are only the tip of the iceberg in relation to the findings the data will provide. The dataset used in this article is comprehensive statistics of MLB players during the 2005 season. The data contain 21 different batting criteria that are continuous variables and three categorical variables that group the players by position, team and league. The criteria are specifically batting oriented and do not reflect any pitching or defensive statistics, gearing the focus of this article to the offensive side of a fantasy team. The 21 continuous variables include the aforementioned five criteria used directly in calculating fantasy performance, leading initial analysis to be focused primarily on them. There are 278 separate player entries in the data with no missing values per player. All players are batters; no pitchers are included regardless of whether they batted during the season. There are some difficulties with these data based on the different league rules pertaining to the American League’s (AL’s) designated hitter (DH) position. DHs are classified as LFs, making the number of LFs twice as large as any other position and possibly skewing results because characteristics of DHs and LFs differ …show more content…
slightly.
TABLE 1
Pe r formance Diff e rences B e t we e n L e a g u e s
F-statistic R HR RBI SB BA 15.992 5.757 13.148 0.412 0.398 p-value 0.000 0.017 0.000 0.522 0.562
League AL = American League NL = National League
26
R = runs scored HR = home runs RBI = runs batted in SB = stolen bases BA = batting average
I APRIL 2007 I www.asq.org
Univariate Analysis
The first step in observing and determining the potential of fantasy players is to create an index that combines the five major scoring criteria into a single value. To this end, each variable was astandardized and then added together to create a composite index of a player’s relative success. The median (-0.5) is below the mean (0 by standardization), showing the data are slightly skewed high and that there are outliers from better performers pulling the mean higher. The impact that this has on the selection of fantasy players is that the best performers (the ones who will be drafted first) will have a disproportionately significant impact on the overall scoring of the team. Based on this assertion, the first round of drafting will play the largest role in predicting the future success of the team. Breaking down the fantasy index by
The first step in observing and determining the potential of fantasy players is to create an index that combines the five major scoring criteria into a single value.
FIGURE 2
Fantasy Pe r formance by Position
12 10 8 6 ESPN index 4 2 0 -2 -4 -6 -8 1B 31 0.7 0.9 2B 38 -0.8 -0.7 3B 31 -0.9 -0.1 C 30 -2.1 -2.1 CF 33 0.1 0.5 LF 53 -0.1 0.6 RF 30 -0.1 -0.1 SS 32 -0.2 0.7
Count Median Mean
Position
1B = first baseman 3B = third baseman CF = center fielder RF = right fielder
2B = second baseman C = catcher LF = left fielder SS = shortstop
league illustrates the commonly held assumptions about the differences between play styles and player performance in MLB’s two leagues. The National League (NL) is most often associated with “small ball,” its players having higher OBP, SB and sacrifice hits, while the AL, with its DHs, has players with higher slugging averages, HRs, Ks and sacrifice flies. Examining boxplots by league (Figure 1) shows the AL has a higher mean (0.7) and median (0.1) fantasy index than the NL (-0.6 and -0.14). This implies that AL players are better overall contributors to a fantasy team’s success, further supported by the fact that the range and inter-quartile range are smaller among AL players. That means there is also less variability among players from an already higher mean value than among players in the NL. One explanation of this is ESPN’s choice of scoring categories. The AL has a higher mean in each of the five, with three (R, HR, RBI) significantly higher (p < 0.05), as shown in Table 1. Judging by these descriptive statistics, prioritizing AL players over NL players is a rational choice for fantasy team owners. Examining the fantasy index breakdown by position (Figure 2) shows the variability by position to be relatively constant, with the exception of catchers. While their overall
QUALITY PROGRESS
I APRIL 2007 I 27
STATISTICS
ESPN index is lower than that of the other positions, knowing that the variability in this position is also small indicates catchers can be drafted last because most of them will have the same performance on the five categories overall.
Notice shortstops have the most variation. For drafting order, simply ranking positions by their average or median index score does not take into account the roster restrictions, requiring further exploration to decide which positions to draft early. Looking at the standardized values of each of the five components of the index adds further information for drafting players. The boxplots in Figure 3 indicate the variability in HR and SB, with many outliers, offers the best opportunity for drafting a player that can consistently add value (and index points) to a fantasy
team.
TABLE 2
C o r r e l a t i o n B e t we e n t h e E S P N I n d ex C o m p o n e n t s
Correlations R 1 HR .663** .000 278 278 .663** 1 .000 278 278 RBI .761** .00 278 .897** .000 278 SB .429** .000 278 -.106 .079 278 -.023 .707 278 1 278 BA .535** .000 278 .283** .000 278 .397** .000 278 .183** .002 278
R
HR
Pearson correlation Significance (2-tailed) N Pearson correlation Significance (2-tailed) N
RBI Pearson correlation .761** .897** 1 Significance (2-tailed) .000 .000 N 278 278 278 SB Pearson correlation .429** -.106 Significance (2-tailed) .000 .079 N 278 278 -.023 .707 278
BA
Pearson correlation .535** .283** .397** .183** 1 Significance (2-tailed) .000 .000 .000 .002 N 278 278 278 278 278
R = runs scored HR = home runs RBI = runs batted in SB = stolen bases BA = batting average ** Correlation is significant at the 0.01 level (2-tailed).
FIGURE 3
O v e r a l l R , H R , R B I , S B a n d B A P e r fo r m a n c e
3 3.5 3 2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 HR (normalized) 278 Count Median -0.2 0.0 Mean (None) R (normalized) 3 2 1 0 -1 R (normalized) 278 Count Median -0.1 -0.0 Mean (None) SB (normalized) Count 278 Median -0.3 Mean 0.0 (None) RBI (normalized) HR (normalized) SB (normalized) 1 0.5 0 2.5 2 1.5 4 5 3.5 3 2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -1.5 -2 RBI (normalized) Count 278 Median -0.1 Mean -0.0 (None)
3 2.5 2 1.5 1 BA (normalized) 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3 BA (normalized) Count 278 Median -0.0 Mean 0.0 (None)
-0.5 -1
BA = batting average
28
HR = home runs
R = runs scored
SB = stolen bases
RBI = runs batted in
I APRIL 2007 I www.asq.org
Multivariate Analysis
Analyzing correlations between the five categories shows their overlap. For example, an increase in HR mandates an increase in R, RBI and BA but is negatively related to SB. In fact, most power hitters are not good base stealers. The correlations shown in Table 2 support that the five scoring categories overlap significantly and that leaders in one category will most likely be doing well in others. Finally, to assess the impact of the five categories on the ESPN index, a multiple regression model was fit with the five fantasy categories as predictors of the ESPN index to examine the strength of their relationship overall. These variables (doubles, K, BB, caught stealing, sacrifice hits) collectively are able to explain 68% of the variability in the fantasy index of all players in the database (Table 3). This is not as high as you would hope but indicates there are other (unmeasured) factors in performance.
TABLE 3
R e g ression of Variables O n t h e E S P N I n d ex
Coefficientsa
Unstandardized Standardized coefficients coefficients Standard error Model B Beta t Significance 1 (Constant) -7.802 .425 -18.376 .000 Doubles .172 .017 .457 10.354 .000 Caught stealing .214 .042 .199 5.122 .000 Walks .053 .007 .326 7.160 .000 Strikeouts .011 .005 .094 2.111 .036 Sacrafice hits -.101 .042 -.095 -2.389 .018
a. dependent variable: ESPN index
Tips for Fantasy Owners
Based on exploring the ESPN index’s components and the player performance variability, several conclusions can be made on how to select the best possible fantasy team: • A player’s real-life team is irrelevant, but AL players perform better than NL players. • The early draft picks have the most impact on a fantasy team’s success. • The SB statistic is the easiest to dominate. • Leaders in one statistic will most likely be doing well in others. • Run scorers create the most balanced and successful team. • HR hitters have the most impact on a team’s success. Also, certain positions outperform others. So, when drafting, keep in mind: • 1B should fill the CI slot. • SS should fill the MI slot. • LF or CF should fill the OF slots. • 1B or OF should fill the UTIL slot. These conclusions serve as an introduction to drafting success, though by no means are they exhaustive. Plenty of avenues exist for continuing the pursuit of the perfect fantasy team, such as
including pitching statistics and analyzing the many possible fantasy league rule sets. And while almost all fantasy leagues have already held their 2007 drafts, team owners can still use these conclusions to give them an edge in trading players and preparing for next year’s draft.
I. ELAINE ALLEN is an associate professor of statistics and
entrepreneurship at Babson College in Babson Park, MA. She has a doctorate in statistics from Cornell University in Ithaca, NY. Allen is a senior member of ASQ.
KIRILL KUSTOV is an undergraduate studying statistics at
Babson College.
GEORGE RECCK is the director of the math resource center at Babson College, where he earned a master’s degree in business management.
Please comment
If you would like to comment on this article, please post your remarks on the Quality Progress Discussion Board at www.asq.org, or e-mail them to editor@asq.org.
QUALITY PROGRESS
I APRIL 2007 I 29