Empirical study on relationship between sports analytics and success in regular season and postseason in Major League Baseball

3.1Conditional probabilities

3.1.1BELIEVERS/NON-BELIEVERS

The last four teams in the postseason of 2014-2017, respectively, were Baltimore Orioles (BELIEVER), St. Louis Cardinals(BELIEVER), Kansas City Royals(BELIEVER, advanced to World Series), and San Francisco(NON-BELIEVER, the champion of World Series); Chicago Cubs(BELIEVER), Toronto Blue Jays(BELIEVER), New York Mets(BELIEVER, advanced to World Series), and Kansas City Royals(BELIEVER, the champion of World Series); Los Angeles Dodgers(BELIEVER), Toronto Blue Jays(BELIEVER), Cleveland Indians(BELIEVER, advanced to World Series), and Chicago Cubs (BELIEVER, the champion of World Series); Chicago Cubs(BELIEVER), New York Yankees(BELIEVER), Los Angeles Dodgers(BELIEVER, advanced to World Series), and Houston Astros(BELIEVER, the champion of World Series). The distribution of BELIEVERS and NON-BELIEVERS teams in no playoffs and playoffs for 2014-2017 is displayed in Fig. 1.

Fig. 1.

Distribution of BELIEVERS and NON-BELIEVERS teams in no playoffs and playoffs for 2014-2017.

Based on Fig. 1, the conditional probabilities below show the chances of getting into playoffs if the team is a BELIEVER or a NON-BELIEVER. Once the team is in playoffs, the conditional probabilities show its chances of advancing to different stages of playoffs. The entries in the parentheses are the corresponding conditional probabilities occurred in 2014-2017.

P(Playoffs | BELIEVERS) ≈ (44%, 56%, 50%, 44%)

P(Playoffs | NON-BELIEVERS) ≈ (21%, 7%, 14%, 21%)

P(Last 4 teams of playoffs | BELIEVERS and playoffs) ≈ (43%, 44%, 50%, 57%)

P(Last 4 teams of playoffs | NON-BELIEVERS and playoffs) ≈ (33%, 0%, 0%, 0%)

P(Last 2 teams of playoffs | BELIEVERS and playoffs) ≈ (14%, 22%, 25%, 29%)

P(Last 2 teams of playoffs | NON-BELIEVERS and playoffs) ≈ (33%, 0%, 0%, 0%)

P(Champion of World Series | BELIEVERS and playoffs) ≈ (0%, 11%, 13%, 14%)

P(Champion of World Series | NON-BELIEVERS and playoffs) ≈ (33%, 0%, 0%, 0%)

Through the data of 2014-2017, we can see that the chances (44%, 56%, 50%, 44%) of advancing to playoffs for a BELIEVER team were higher than those (21%, 7%, 14%, 21%) for a NON-BELIEVER team. Once the team was in playoffs, the chances (43%, 44%, 50%, 57%) of advancing to the last 4 teams of playoffs for a BELIEVER team were also higher than those (33%, 0%, 0%, 0%) for a NON-BELIEVER team. Similar patterns remain for the data of 2015-2017, when comparing a BELIEVER team and a NON-BELIEVER team for advancing to the last 2 teams of playoffs and for becoming the champion of World Series. The data of 2014, however, shows the opposite pattern that a NON-BELIEVER team had a higher chance of advancing to the last 2 teams of playoffs than a BELIEVER team (33% vs 14%) and had a higher chance of becoming the champion of World Series (33% vs 0%). This happened because of the fact that the champion of World Series in 2014 was San Francisco which was categorized as a NON-BELIEVER team.

To test the relationship between a team’s category of analytics belief (BELIEVER or NON-BELIEVER) and whether it advances to the postseason, we apply the chi-square test for testing the independence of these two characteristics. We obtain the observed chi-square value = 1.674, 8.105, 4.286, 1.674 and p-value = 0.196, 0.004, 0.038, 0.196 for 2014-2017, respectively. Notice that both p-values for 2014 and 2017 are 0.196. Therefore, with 5% level of significance, there is insufficient evidence to reject the null hypothesis that these two characteristics were independent for these two years, i.e., a team advancing to the postseason of 2014 and 2017 was unrelated to the category of its analytics belief. However, opposite conclusion occurred for 2015 and 2016 as the corresponding p-values (0.004 and 0.038) are less than 0.05. The opposite conclusion obtained is related to the fact that 30% (higher percentage) of the playoffs teams were NON-BELIEVERS in 2014 and 2017, while there were only 10% in 2015 and 20% in 2016.

3.1.2Analytics staff

According to the information listed in the Baseball America Directories, the distribution of teams having analytics staff = 0, 1, 2 or more, in no playoffs and playoffs for 2014-2017 is presented in Fig. 2. It appears that teams having no analytics staff were in much higher proportion than teams having 1 or at least 2 analytics staff in both no playoffs and playoffs for these four years. The following conditional probabilities show the chances of getting into playoffs and the chances of advancing to different stages of playoffs for teams having different numbers of analytics staff.

P(Playoffs | Analytics Staff (A) = 0) ≈ (30%, 40%, 40%, 39%)

P(Playoffs | A = 1) ≈ (33%, 11%, 33%, 0%)

P(Playoffs | A ≥ 2) ≈ (100%, 100%, 0%, 20%)

P(Last 4 teams of playoffs | Playoffs and A = 0) ≈ (29%, 38%, 38%, 44%)

P(Last 4 teams of playoffs | Playoffs and A = 1) ≈ (50%, 0%, 50%, 0%)

P(Last 4 teams of playoffs | Playoffs and A ≥ 2) ≈ (100%, 100%, NA, 0%)

P(Last 2 teams of playoffs | Playoffs and A = 0) ≈ (14%, 13%, 25%, 22%)

P(Last 2 teams of playoffs | Playoffs and A = 1) ≈ (0%, 0%, 0%, NA)

P(Last 2 teams of playoffs | Playoffs and A ≥ 2) ≈ (100%, 100%, NA, 0%)

P(Champion of World Series | Playoffs and A = 0) ≈ (14%, 0%, 13%, 11%)

P(Champion of World Series | Playoffs and A = 1) ≈ (0%, 0%, 0%, NA)

P(Champion of World Series | Playoffs and A ≥ 2) ≈ (0%, 100%, NA, 0%)

Fig. 2.

Distribution of teams having analytics staff = 0, 1, 2 or more, in no playoffs and playoffs for 2014-2017.

If there was no team under the condition of the conditional probability, then NA (not applicable) would be given. There were many MLB teams having no analytics department and hence no analytics staff for 2014-2017. Kansas City Royals, with four analytics staff, was a very successful team in 2014 and 2015. It advanced to the World Series but lost in 2014. Nevertheless, it became the champion of World Series in 2015. Other than Kansas City Royals, all other teams advanced to the World Series from 2014-2017 didn’t have any analytics staff. Among those last four teams of playoffs from 2014 to 2017, only Baltimore Orioles and Toronto Blue Jays each had one analytics staff. Besides the extraordinary performance of Kansas City Royals in 2014 and 2015, teams having analytics staff indicated no higher percentage of success in advancing to playoffs or during postseason in almost all conditional probabilities shown above.

3.1.3Research staff

Again from the Baseball America Directories, we compile the list of research staff (including analytics staff) employed by teams. The distribution of teams having research staff = High(7-5), Medium(4-3), Low(2-1), None(0), in no playoffs and playoffs for 2014-2017 is given in Fig. 3. The conditional probabilities below show the chances of getting into playoffs and the chances of advancing to different stages of playoffs for teams having different numbers of research staff.

P(Playoffs | Research Staff (R) = High) ≈ (0%, 50%, 20%, 50%)

P(Playoffs | R = Medium) ≈ (67%, 75%, 20%, 63%)

P(Playoffs | R = Low) ≈ (40%, 20%, 43%, 20%)

P(Playoffs | R = None) ≈ (20%, 33%, 33%, 0%)

P(Last 4 teams of playoffs | Playoffs and R = High) ≈ (NA, 0%, 0%, 67%)

P(Last 4 teams of playoffs | Playoffs and R =  Medium)≈(100%, 67%, 100%, 20%)

P(Last 4 teams of playoffs | Playoffs and R = Low) ≈ (33%, 67%, 33%, 50%)

P(Last 4 teams of playoffs | Playoffs and R = None) ≈ (0%, 0%, 50%, NA)

P(Last 2 teams of playoffs | Playoffs and R = High) ≈ (NA, 0%, 0%, 0%)

P(Last 2 teams of playoffs | Playoffs and R = Medium)≈(50%, 33%, 100%, 20%)

P(Last 2 teams of playoffs | Playoffs and R = Low) ≈ (17%, 33%, 17%, 50%)

P(Last 2 teams of playoffs | Playoffs and R = None) ≈ (0%, 0%, 0%, NA)

P(Champion of World Series | Playoffs and R = High) ≈ (NA, 0%, 0%, 0%)

P(Champion of World Series | Playoffs and R = Medium) ≈ (0%, 33%, 0%, 20%)

P(Champion of World Series | Playoffs and R = Low) ≈ (17%, 0%, 17%, 0%)

P(Champion of World Series | Playoffs and R = None) ≈ (0%, 0%, 0%, NA)

Fig. 3.

Distribution of teams having research staff = High(7-5), Medium(4-3), Low(2-1), None(0), in no playoffs and playoffs for 2014-2017.

Three years out of four from 2014 to 2017, teams with research staff = Medium had higher percentages of advancing to playoffs than teams with research staff = High, Low, or None. Once teams were in playoffs, similar pattern occurred (3 years out of four) that teams with research staff = Medium had the same or higher percentages of advancing to the last 4 teams as well as the last 2 teams of playoffs than teams with research staff in other groups. Two years out of four from 2014 to 2017, teams with research staff = Medium had higher percentages of becoming the champion of World Series than teams with research staff in other groups. It appears that teams with 3 or 4 research staff (Medium group) performed most consistently than teams in other groups.

3.2Correlation coefficients

To study the correlations between different variables, we define the following notation:

The Pearson sample correlation coefficients for various pairs of variables for 2014-2017 are computed and displayed in Table 1. For example, r(W and P) = 0.38 (0.04) means that the Pearson sample correlation coefficient for assessing the linear relationship between W (number of games won in a regular season) and P (team payroll) is 0.38 with p-value = 0.04. Hence, the correlation between W and P is positive and significant at α = 5%. We are mostly interested in those pairs of variables whose correlations are significant (i.e., p-values < 0.05).

The number of games won in a regular season (W) and levels of playoffs towards the championship of World Series (C) were moderately to strongly positively correlated (r= 0.67, 0.71, 0.75, 0.83) for 2014-2017. It was because teams of fewer wins would likely not advance to playoffs and hence their value of C would be zero. Because of the zero value of C mostly coming from teams of fewer wins, the correlation between W and C tends to be positive. To see the actual effect of the number of games won in a regular season on the success in the postseason, we need to consider only those teams in the postseason, i.e., removing those teams with zero value of C. After ignoring all zeros of C (i.e., considering C*), W and levels of playoffs towards the championship of World Series in the postseason (C*) show no significant correlation at α = 5% for 2014 and 2015, but a significantly positive correlation (r= 0.71, 0.68) for 2016 and 2017. It seems that once a team is in playoffs, its standing in the regular season has a random effect on its success in the postseason. Teams of higher standings in the regular season might not generate any advantages to move forward in the postseason.

W and categories of analytics belief (B) were significantly positively correlated (r= 0.61, 0.44, 0.43) for 2015-2017.

B and C show positive correlations (r  =  0.37, 0.37, 0.37) for 2015-2017. This might indicate that the categorization of analytics belief on teams could reflect the commitment made by teams that, in turn, would contribute some positive impact on the success of winning a championship of World Series. To see the actual effect of the categories of analytics belief on the success in the postseason, we consider only those teams in the postseason. B and C* show no significant correlations for 2014-2017 as all p-values are greater than 0.05. It seems that once a team is in playoffs, the analytics belief and commitment made by a team has no effect on its success in the postseason.

B and number of research staff (R) indicate a positive correlation as demonstrated by r= 0.48, 0.38, 0.39 for 2014-2016 and r= 0.35 (p-value = 0.06) in 2017.

The number of analytics staff (A) and R display some positive correlation (r= 0.46, 0.44) for 2014-2015 and r= 0.33 (p-value = 0.07) for 2016, but not for 2017.

A and C had a positive correlation (r= 0.39) in 2014, but not in 2015-2017. A and C* had a positive correlation (r= 0.66) in 2015, but not in the other three years.

R, however, does not show any significant positive or negative correlation with C or C*. R and W had a positive correlation (r= 0.39) in 2017 and r= 0.31 (p-value = 0.09) in 2015.

It is interesting to note that the team payroll (P) and W were positively correlated (r= 0.38, 0.61) in 2014 and 2016, and had r= 0.35 (p-value = 0.06) in 2017. In addition, P and C had a positive correlation (r= 0.43, 0.45) in 2016-2017 and had r= 0.34 (p-value = 0.07) in 2014. This might reflect that financial resources did have some positive impact on the journey of winning a championship of World Series. To see the actual effect of the team payroll on the success in the postseason, we need to consider C*. P and C* do not show any significant positive correlation for 2014-2017. It seems that once a team is in playoffs, its team payroll has no linear effect on its success in the postseason.

3.3Binary logistic regression models

We employ binary logistic regression models to assess the relationship between the success of advancing to playoffs and the use of sports analytics (categories of analytics belief, number of analytics staff, and number of research staff) for the data of 2014-2017. The response variable Y is the advancement to playoffs, which has the value of 1 if the team advances to playoffs and 0 if not. The continuous explanatory variable X₁ is the categories of analytics belief, which has the value of 4 if the team is All-in, 3 if Believers, 2 if One-foot-in, 1 if Skeptics, and 0 if Non-believers. The variables X₂ and X₃ represent the number of analytics staff and number of research staff, respectively. The equation of the binary logistic regression model is

We can see from Table 2 that the p-values are both 0.03 for 2015 and 2016. Therefore there is sufficient evidence, with 5% level of significance, that the categories of analytics belief, numbers of analytics staff and research staff employed were associated with the success of a team advancing to playoffs for 2015 and 2016. However, there is insufficient evidence to indicate this association for 2014. The evidence is less convincing for 2017 as p-value = 0.09 is greater than 5% but slightly less than 10%.

The associated goodness-of-fit tests give the corresponding p-values in Table 3.

With the p-values of the goodness-of-fit tests shown in Table 3, there is insufficient evidence (with 5% level of significance) to claim that the binary logistic regression models do not fit the data adequately for 2014-2017. However, the p-value of Hosmer-Lemeshow test for 2016 is slightly less than 10%.

3.4Multiple linear regression models

We also apply multiple linear regression models to assess the relationship between the number of games won in a regular season and the use of sports analytics (categories of analytics belief, number of analytics staff, and number of research staff) for the data of 2014-2017. The response variable Y is the number of games won in a regular season. The categories of analytics belief are treated as a categorical explanatory variable, using four indicator variables X₁, X₂, X₃ and X₄ for the first four categories of analytics belief (All-in, Believers, One-foot-in, and Skeptics with Non-believers as the baseline). X₅ is the number of analytics staff, and X₆ is the number of research staff. The equation of the multiple linear regression model is

Minitab yielded the estimated values of parameters β_i, i = 0, 1, 2, . . . , 6, with their standard error, observed F value, and p-value of the model for the data of 2014-2017. These results are presented in Table 4.

More games won in a regular season should increase the chances of moving forward to playoffs. Consequently, the number of games won in a regular season should very likely relate to the success of advancing to playoffs. By comparing 0.05 with the p-values in Table 4, we obtain the same conclusions as those in the previous section for 2014, 2015 and 2017. For 2016, the binary logistic regression model shows that, with α = 5%, the set of explanatory variables was useful for predicting the chances of advancement to playoffs. But the same set of explanatory variables was not useful for predicting the number of games won in that regular season, as shown in the multiple linear regression model. As advancing to playoffs is an important goal for teams, it seems that the binary logistic regression model is more appropriate to formulate the relationship between the success in a regular season and those explanatory variables.

3.5Ordinal logistic regression models

To assess the relationship between the success of a team in the postseason and the use of sports analytics, we apply ordinal logistic regression models. Since there are only ten teams competing in playoffs each year, we have combined four years’ data together for data analysis. The response variable Y is the levels of playoffs in the postseason towards the championship of World Series, which is defined previously as C* (i.e., C without considering the value of 0). It is because those teams in playoffs have nonzero values of C. Consequently, there are five different values (5, 4, 3, 2, 1) for five different levels of playoffs towards the championship of World Series. This response variable has a natural order (i.e., champion(5) > third round(4) > second round(3) > first round(2) > wild card(1)) and can be classified as an ordinal variable. The continuous explanatory variable (or predictor) X is either (1) categories of analytics belief, (2) number of analytics staff, or (3) number of research staff. When X is the categories of analytics belief, it is defined as 4 if the team is All-in, 3 if Believers, 2 if One-foot-in, 1 if Skeptics, and 0 if Non-believers. As the response variable Y has five levels, Minitab used level 5 as the reference and formulated only four logit equations. Each equation has a unique constant, but the parameter of the predictor X is the same for all equations. The ordinal logistic regression model is

To assess the relationship between the response variable and the predictor in the ordinal logistic regression model, we test the null hypothesis that β is zero. All p-values in Table 5 are greater than 0.05. Therefore, with 5% level of significance, we conclude that no significant relationship exists between the success of a team in the postseason and any of the three analytics indicators (categories of analytics belief, number of analytics staff, and number of research staff) for the combined data of 2014-2017. Note that the evidence is less convincing when X = number of analytics staff as the p-value = 0.07.

The associated goodness-of-fit tests give the corresponding p-values in Table 6.

Based on the p-values shown in Table 6, there is insufficient evidence, with 5% level of significance, to claim that the ordinal logistic regression models do not fit these combined four years’ data adequately.

4.1Partial correlation coefficients

4.2Partial F tests

When the team payroll is used in the regression model as an explanatory variable to predict the number of games won in a regular season, does the addition of the information of (1) categories of analytics belief, (2) number of analytics staff, or (3) number of research staff significantly improve the predictability of the regression model?

4.3Model utility F test

To test if both the team payroll and the use of sports analytics are good predictors of the success in playoffs towards the championship of World Series, we apply the model utility F test to the combined postseasonal data of 2014-2017. Thus there are altogether forty data points for analysis, instead of ten data points in each year. The response variable Y is the levels of playoffs in the postseason towards the championship of World Series: 5(Champion), 4(Third round game but lost), 3(Second round game but lost), 2(First round game but lost), 1(Wild card game but lost). For simplicity, we assume that Y is a continuous variable. The four continuous explanatory variables are the team payroll (logarithmic value) X₁, categories of analytics belief X₂, number of analytics staff X₃, and number of research staff X₄. The variable X₂ has the values: 4(All-in), 3(Believers), 2(One-foot-in), 1(Skeptics), and 0(Non-believers); it is assumed to be a continuous variable. The equation of the multiple linear regression model is

Minitab calculated the estimated values of the regression parameters β_i’s with their standard error, observed F value, and p-value of the model for the combined data of 2014-2017. The results are given in Table 8.

Fig. 4.

Decision tree for binary target variable with Wins as an input variable.

The model utility F test is to test the null hypothesis that β₁ = β₂ = β₃ = β₄ = 0 . As the p-value is 0.12, we conclude (with 5% level of significance) that the team payroll, categories of analytics belief, number of analytics staff, and number of research staff are not good predictors in the multiple linear regression model for the success in playoffs. This conclusion agrees with Schwartz and Zarrow (2009) that the success in October (i.e., playoffs) can be viewed as a truly random event.

5.1Wins as an input variable available

5.1.2Ordinal target variable

With all the input variables given in Section 5.1.1, the target variable is considered to be the levels of playoffs towards the championship of World Series. The target variable has 6 levels: 0(No playoffs), 1(Wild card game but lost), 2(First round game but lost), 3(Second round game but lost), 4(Third round game but lost), and 5(Champion). It will be treated as an ordinal variable. The outcome of a decision tree is displayed in Fig. 5.

In Node 1, all 120 teams are randomly divided approximately 50-50 into the training and validation models according to their stages towards the championship of World Series. In fact, 59 teams and 61 teams go to the training and validation models, respectively. The input variable Wins with the same test condition (< 86.5 or ≥ 86.5 games) is first chosen among all the given input variables to split the decision tree. Among the 59 teams in the training model, 40 teams go to Node 3 as their wins are less than 86.5 games and 19 teams go to Node 4 as their wins are 86.5 games or more. Likewise, among the 61 teams in the validation model, 41 teams go to Node 3 and 20 teams go to Node 4. Wins less than 86.5 games in a regular season is an excellent predictor to classify 100% of the teams in training model and 95.12% of the teams in validation model as target 0 (i.e., no playoffs). There is only one team (2.44%) in the validation model having target 1 (i.e., wildcard game but lost), and also only one team having target 2 (i.e., first round game but lost).

Node 4 shows that none of the 19 teams in the training model and only 1 team out of 20 teams (5%) in the validation model has target 0(no playoffs). It means that 38 of 39 teams (97.4%) with 86.5 wins or more in a regular season go to playoffs. As four teams out of the ten playoffs teams go to the first round game but lost, target 2 in Node 4 has the highest percentage for both models, 42.11% of teams in the training model and 35% of teams in the validation model. Apart from this observation, however, both training and validation models do not display any distinct patterns on different stages towards the championship of World Series.

Fig. 5.

Decision tree for ordinal target variable with Wins as an input variable.

Fig. 6.

Decision tree for binary target variable without Wins as an input variable.

The input variable All_in is then chosen to further split Node 4. In Node 5 (when teams are not All_in), it looks like more teams have lower target values (1 and 2) in the training model and teams spread evenly with slightly higher target values in the validation model. In Node 6 (when teams are All_in), however, it seems that teams spread more widely across the targets with three spikes at targets 1, 3, 5 in the training model, and teams have lower targets (1 and 2) in the validation model.

Afterwards, the input variable pitchers’ salary with the test condition (< 55,764,782 or ≥ 55,764,782) is used to split Node 5 further. For not All_in teams winning at least 87 games in a regular season and pitchers’ salary at least $55.7 million (approximately), Node 8 shows that they have higher targets (2-5) in the validation model and concentrate on target 2 in the training model. Node 7, however, shows that these not All_in teams with pitchers’ salary less than $55.7 million (approximately) spread more evenly across the targets in both the validation and training models.

The misclassification rates for the training and validation models are 11.86% and 31.15%, respectively. The average squared errors for the training and validation models are 0.0232 and 0.0752, respectively. This decision tree yields moderately accurate predictions for classifying MLB teams into different stages of playoffs towards the championship of World Series.

5.2Wins as an input variable not available

At the beginning of a MLB season in late March, the information of the number of games won in a regular season is certainly not available. In this situation, one may still wish to build a decision tree to classify teams into no playoffs (target 0) or playoffs (target 1). As the target variable is binary, we can use the same procedure as shown in Section 5.1.1 but without Wins as an input variable. The decision tree is presented in Fig. 6.

Node 1 shows that the data are randomly selected into the training model (60 teams) and validation model (60 teams). The first input variable chosen is pitchers’ salary with the test condition (< 29,766,607 or ≥ 29,766,607). Under this test condition, the 60 teams in each of the training and validation models are separated into 23 teams in Node 3 and 37 teams in Node 4 in their respective model. In Node 3 (pitchers’ salary < ≈ $29.7 million), none of the 23 teams in the training model and 17.39% of the 23 teams in the validation model advanced to playoffs. In Node 4 (pitchers’ salary ≥ ≈ $29.7 million), however, 54.05% of the 37 teams in the training model and 43.24% of the 37 teams in the validation model advanced to playoffs. Consequently, pitchers’ salary with a threshold of approximately $29.7 million played an important role to identify whether or not the team had a higher chance of moving on to playoffs.

Under Node 4, further classification takes place. The second input variable chosen is All_in with the test condition: 1(yes) or 0(no). Under this test condition, the 37 teams in the training model are separated into 11 teams in Node 5 and 26 teams in Node 6. Likewise, the 37 teams in the validation model are separated into 7 teams in Node 5 and 30 teams in Node 6. For teams that were All_in, Node 5 shows that 72.73% of the 11 teams in the training model and 71.43% of the 7 teams in the validation model advanced to playoffs. However, Node 6 shows that 46.15% of the 26 teams in the training model and 36.67% of the 30 teams in the validation model advanced to playoffs. In addition to spending at least $29.7 million on pitchers’ salary, the All_in teams would significantly increase their chances of advancing to playoffs. For teams that were not All_in but were Believers instead, Node 7 indicates that their chances of advancing to playoffs were 66.67% and 61.54% in the training and validation models, respectively. These percentages were much higher than those (35.29% and 17.65%) in Node 8 for teams that were not Believers either.

The misclassification rates for the training model and the validation model are 20% and 23.33%, respectively. The average squared errors produce 0.1344 and 0.1923 for the training and validation models, respectively. This decision tree yields moderately accurate predictions for classifying MLB teams into no playoffs or playoffs.