Oakland Athletics Baseball Club (A’s) was one of 28 professional teams divided into 4 leagues. A’s ranking in his own league was 2nd and Mark Nobel was one of his star player, who was arguing to raise his salary from $40,000 p.a to $600,000 p.a by taking the plea that in addition to his contribution to success of A’s in 1980, he had also been attraction at the box office. Further Nobel had won Gold Glove Award as best fielding pitcher and finished 2nd in the balloting for the Cy Young Award which reinforced his claims.
In order to verify the Nobel’s claims and to give a judicious advice to Mr. Steward Roddey, general manger A’s baseball team, various mathematical and statistical analysis have been performed. Further a model has been developed to forecast the future tickets sale based on certain parameters.
As per our analysis, Nobel claim regarding major attraction at box office was not right. Further he was not the major factor in success of A’s. No doubt, A’s success rate was high when Nobel played but Nobel played most of his matches against low ranking teams’ resulting in high success rate. Further, average tickets sale for the matches when Nobel played is high because of one outlier, Detroit match. Actually that was double header match and, A’s position, at that time, was one and Detroit team “game behind” position was also zero. This phenomenon lead to high average of Nobel matches.
Keeping in view all these points and arguments, it is recommended to convince the Nobel to review its stance and revised salary package may be negotiated accordingly.
Detailed Study and Analysis
Two separate worksheets have been created by filtering the data in to Nobel’s game and non Nobel’s games using the filtering command and then copying the data one by one to separate sheets for further analysis. Both sheets are available as exhibit 1 & exhibit 2 in the end of this report.
If we analyze the data available in exhibit 1 &2 using different Ms Excel techniques i.e sum, count, countif, and percentage, we come across the inferences mentioned in exhibit 3.
It is quite evident from exhibit-3, Nobel’s matches tickets sale is 8% higher (54%) as compare to no Nobel’s matches (46%). Nobel itself may be the one factor but there may be other factors contributing to this attraction as well. If we carefully examine exhibit 3, we can easily deduce, Nobel played most of the games in night time (56%) where it might be more chance of attendance. Further, only 22% matches were televised, so likely more chances of viewer in the ground. Moreover, noble played more matches at weekends which might also be a factor having more average tickets sold in Nobel games.
On the other hand, very less promos have been used for Nobel’s games, only (23%) and despite this Nobel attracts the crowed.
For two other important factors, team position and games behind, average is same for bother Nobel’s games and Non Nobel’s games.
Let us focus our analysis on two parameters for sales break down i.e on opposing teams and games in which Nobel played (exhibit 4). Luckily a very useful tool pivot table is available is Ms Excel. We notice again the same result i.e average tickets for Nobel played matches is higher but when closely probe the table, we witnesses that Nobel is not the only criteria. The major factor affecting the average of attendance is opponent team. For example, overall attendance average for Yankees is 40,445, Boston 13,023, Baltimore 11,753 and Kansas City 11,652 despite Noble played very few matches against these team i.e only two out of three matches against Yankees and two out of four against Boston. Further Nobel did’t play even single match against Baltimore and Kansas City despite their tickets sold are above average.
From the table, another thing which we figured out is the league against you play. If you play matches against opponent league i.e Eastern Division, that attract more spectators instead of teams of Western Division. There are three teams from Eastern Division league having tickets sale above average.
Even, decrease in tickets sale was witnessed for matches against Yankees, Milwaukee, Boston and Cleveland by 6%, 27%, 7% &33% respectively when Nobel plays. However, increase in tickets sale have been witnessed in the matches played against Seattle, Detroit, White Sox and Texas by 22%, 42%, 30% and 14% respectively. Actually these are low ranking teams and presence of Nobel might create attraction for the public (exhibit 5).
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Let us apply the regression analysis to determine the importance of various factors in the attendance that happened, but before doing this exercise it is necessary to refine the data and eliminate / add the factors that are irrelevant / relevant to our analysis. During exploration of mess to find out the problem and opportunities, we stumble upon the inference, that opposing team number don’t have any sense and Ms excel would not be able to develop correlation with the opposing team numbers and tickets sold, rather it would be much better to allot ranking on the basis of percent of success for regression analysis. Because team success rate and spectators’ interest in the game might have some relationship.
There is team in the data “White Sox” whose ranking / percent of success is not available in the provided data. It is assumed that “White Sox” did not play in any league and hence least ranking has been allocated to “White Sox”
There are six double header entries in the 75 entries. It means, Oakland A’s played two consecutive games on the same day between the same teams. One ticket at the same price as a single game ticket, provided admission to both games. It is obvious that attendance in double header matches should be more because one can watch two games in one ticket. To add this factor, another column was added in the data with “double header” name.
Before searching for solution and to know the importance of various factors in the attendance, let us 1st comprehend the problem little bit more by drawing an influence chart.
Oakland Position
Avg. Temp
Game Behind
Weather
Day of Week
Promo
Double Header
Opponent Team
Tickets Sale
Day and Time
Time of day
Televised
TV & Promo
Precipitations
Nobel
Opp. Team Ranking Success
To understand the relationship, let us 1st determine the correlation of individual factor with the tickets sale.
Correlation of No. of Tickets Sold with the other Factors
Opp. Team Ranking.
Game Behind
Position
Day of Week
Avg. Temp.
Precip
Time of Game
Double Header
Televised
Promo
Nobel
-50.90%
7.48%
-11.49%
-0.70%
-6.08%
-9.74%
12.87%
20.63%
-9.79%
26.66%
7.65%
From above table, it is quite obvious that opposing team ranking on the basis of success percentage is most relevant factor, then promo, double header, time of game, televised, precipitations and then Nobel respectively.
Relationship among response variable (tickets sold) and explanatory variables can also be established through multiple regressions (exhibit 6):
If we look at the coefficients values & P values, it give us almost the same end results as we deuced from correlations i.e ranking of opponent team is the most relevant factor then d. header, promo, time of game, precipitations and then Nobel respectively. Over and above, P Values give us the probability that a & b we determined as coefficients were by luck i.e how likely the coefficients we calculated would be wrong. Hence lesser the P Value, greater will be surety of of each factor relationship with attendance.
R square and adjusted R square tells us that how well regression equation fits data. 41.44% R square means that probability of fitness of regression line is 41.44%. As we are using multiple regression, hence it is better to use adjusted R. Further significance of F tells us the chance that R square we got was luck. As our significance of F is very low (0.0171%) hence we are 99.98% confident that regression equation/ line is not through by just luck.
Keeping in view the above discussion, one can easily establish the opinion that most important factor influencing the ticket sale is opponent team. If Oakland A’s plays against strong team will attract more crowed and vice versa. No doubt, A’s own performance also matters, and A’s performance is not merely dependent on Mr. Nobel (exhibit 7). Nobel games win % is 67% (22/33%), it means, out of 16 home games played by Nobel, 11 would have been won by A’s. As A’s overall success rate is 51.2 %, hence out of total 75 home games, A’s would have won 38 games. 11 (67%) when Nobel was playing and 27 (46%) when Nobel was not playing). Hence we can say that A’s team does not win because of Nobel, however it is true that success rate increases when Nobel plays.
It is recommended that all the points mentioned in above paragraphs one (1) to three (3) may be explained to Mr. Nobel while negotiating the salary. Further, Roddey should keep the following things in mind while deciding the salary of Nobel.
Nobel played only 16 matches out of 75 home matches, hence he may affect only 21% matches.
If we normalize the outlier of Detroit match, Nobel average comes down to 11,988 instead of 12,664 leaving difference of only 1,129 per match. As Noble played 16 matches, total difference would be 18,058, multiplied by the average ticket price $3.66; total resulting figure will $ 66,093 instead of 105,650 as claimed by Nobel.
As Nobel correlation to attract the crowed is just 7.65%.
In team success, there is significant contribution of Billy Martin as evident from history.
Promotions also played vital role in attraction of spectators.
Part II.
Before developing a model for future forecasting, input parameters (explanatory) having high P value for their respective coefficients have been eliminated from data and revised multiple regression applied. Following parameters were eliminated:-
Position
Game behind
Average Temperatures
Televised
Revised regression chart is attached as exhibit 8
Trend chart on the basis of projected values and actual values is attached as exhibit 9
Model Snapshot is attached as exhibit 10. (Complete model is available in corresponding Ms Excel File)
Exhibit 1-non Nobel Games’ Data
Date
Tickets Sold
Opp. Team
Position
G. Behind
D.o. Week
Temp.
Precipitation
Time of Game
Televised
Promotions
Nobel
4/10
24,415
2
5
1
4
57
0
2
0
0
0
4/11
5,729
2
3
1
5
66
0
2
0
0
0
4/12
5,783
2
7
1
6
64
0
1
0
0
0
4/13
6,300
2
5
1
7
62
0
1
0
0
0
4/15
2,140
1
6
1
2
60
0
2
0
0
0
4/16
2,418
1
4
1
3
61
0
1
0
0
0
4/18
6,570
3
3
1
5
58
0
2
0
0
0
4/20
9,014
3
1
0
7
57
1
1
1
0
0
5/2
8,636
5
1
0
5
57
0
2
0
0
0
5/3
7,062
5
1
0
6
59
0
1
1
0
0
5/5
12,605
11
1
0
1
60
0
2
0
0
0
5/6
24,272
11
1
0
2
60
0
2
0
1
0
5/7
4,731
11
1
0
3
60
0
1
0
0
0
5/10
4,929
7
1
0
6
55
1
1
0
0
0
5/23
4,141
12
4
2
5
56
0
2
0
0
0
5/24
5,061
12
3
2
6
55
0
1
1
0
0
5/26
21,882
13
4
2
1
58
0
1
1
0
0
5/27
4,488
13
4
3
2
58
0
2
0
0
0
5/28
4,094
13
3
2
3
59
0
1
0
0
0
6/7
12,990
9
3
6
6
61
0
1
0
0
0
6/8
18,753
9
3
7
7
63
0
1
0
0
0
6/9
20,162
10
3
7
1
61
0
2
0
0
0
6/10
3,873
10
3
7
2
59
0
2
0
0
0
6/11
5,628
10
3
7
3
60
0
1
0
1
0
6/13
47,768
4
3
7
5
60
0
2
0
0
0
6/15
46,294
4
3
8
7
64
0
1
0
1
0
6/23
17,666
6
3
9
1
62
0
2
0
1
0
6/24
4,899
6
4
10
2
62
0
2
0
0
0
6/25
6,856
6
4
11
3
63
0
1
0
0
0
6/28
5,204
8
4
12
6
69
0
1
1
0
0
6/29
7,369
8
4
12
7
63
0
1
0
0
0
7/11
7,696
3
5
12
5
62
0
2
0
0
0
7/16
7,413
5
5
13
3
65
0
2
0
0
0
7/17
6,370
5
3
12
4
65
0
1
0
0
0
7/19
6,506
11
3
11
6
65
0
1
1
0
0
7/20
10,606
11
3
11
7
65
0
1
1
1
0
7/21
14,588
7
3
12
1
65
0
2
0
1
0
7/23
4,765
7
3
12
3
64
0
1
0
0
0
8/4
16,741
2
2
12
1
65
0
2
0
0
0
8/5
4,651
2
2
12
2
67
0
2
0
0
0
8/6
6,697
2
2
12
3
63
0
1
0
0
0
8/8
6,283
1
2
13
5
62
0
2
0
0
0
8/10
13,062
1
2
13
7
63
0
1
0
0
0
8/19
11,934
9
2
15
2
67
0
2
0
0
0
8/21
10,947
9
2
15
4
61
0
1
0
0
0
8/22
11,532
10
2
15
5
62
0
2
0
0
0
8/23
10,578
10
2
16
6
64
0
1
0
1
0
8/24
18,745
10
2
17
7
63
0
1
0
1
0
8/26
32,905
4
2
17
2
62
0
2
0
1
0
9/8
9,731
12
3
19
1
65
0
2
0
0
0
9/9
2,443
12
3
18
2
63
0
1
0
0
0
9/12
17,440
13
2
17
5
62
0
2
0
0
0
9/13
11,253
13
2
16
6
61
0
1
0
0
0
9/14
10,756
13
2
17
7
63
0
1
0
0
0
9/23
3,069
8
2
15
2
70
0
2
0
0
0
9/24
3,836
8
2
14
3
69
0
2
0
0
0
9/25
3,180
8
2
14
4
64
0
1
0
0
0
9/27
4,581
6
2
13
6
62
0
1
0
0
0
9/28
10,662
6
2
12
7
65
0
1
0
1
0
Exhibit 2- Nobel Games’ Data
Date
Tickets Sold
Opp. Team
Position
G. Behind
Day of Week
Temp.
Prec
Time of Game
Televised
Promotions
Nobel
4/14
5,260
1
7
2
1
60
0
2
0
1
1
4/19
5,239
3
2
1
6
59
0
1
1
0
1
5/4
18,217
5
1
0
7
58
0
1
0
0
1
5/11
7,839
7
1
0
7
57
0
1
0
0
1
5/25
10,549
12
5
3
7
57
0
1
0
0
1
6/6
15,947
9
3
6
5
59
0
2
0
0
1
6/14
27,312
4
3
7
6
63
0
1
0
0
1
6/27
8,482
8
4
11
5
69
0
2
0
1
1
7/10
11,337
3
5
12
4
66
0
2
0
0
1
7/18
5,949
11
3
12
5
60
1
2
0
0
1
7/22
8,645
7
3
12
2
63
0
2
0
0
1
8/9
13,629
1
2
12
6
63
0
1
0
1
1
8/20
7,569
9
2
15
3
65
0
2
1
0
1
8/25
47,946
4
2
17
1
62
0
2
0
0
1
9/10
3,598
12
2
17
3
64
0
1
0
0
1
9/26
5,099
6
2
14
5
64
0
2
0
0
1
Exhibit 3
Description
Nobel Game
%
No Nobel Games
%
Total
Total Tickets
202,617
24%
640,702
76%
843,319
Average Tickets
12,664
54%
10,859
46%
23,523
Games Count
16
21%
59
79%
75
Day Games
7
44%
32
54%
39
Night Games
9
56%
27
46%
36
Televised
2
22%
7
78%
9
Promotion
3
23%
10
77%
13
Precipitations
1
33%
2
67%
3
Avg. Temp
62
50%
62
50%
124
Avg. Game Behind
9
50%
9
50%
18
Average Position
3
51%
3
49%
6
Average Day of Week
5
52%
4
48%
9
Exhibit 4
Avg Sale Breakdown (Team no. as per original data)
Teams No./ Nobel
Count of Sold
Average of Sold
Sum of Sold
Total Count of Sold
Total Average of Sold
Total Sum of Sold
0
1
0
1
0
1
1
4
2
5,976
9,445
23,903
18,889
6
7,132
42,792
2
7
10,045
70,316
7
10,045
70,316
3
3
2
7,760
8,288
23,280
16,576
5
7,971
39,856
4
3
2
42,322
37,629
126,967
75,258
5
40,445
202,225
5
4
1
7,370
18,217
29,481
18,217
5
9,540
47,698
6
5
1
8,933
5,099
44,664
5,099
6
8,294
49,763
7
3
2
8,094
8,242
24,282
16,484
5
8,153
40,766
8
5
1
4,532
8,482
22,658
8,482
6
5,190
31,140
9
4
2
13,656
11,758
54,624
23,516
6
13,023
78,140
10
6
11,753
70,518
6
11,753
70,518
11
5
1
11,744
5,949
58,720
5,949
6
10,778
64,669
12
4
2
5,344
7,074
21,376
14,147
6
5,921
35,523
13
6
11,652
69,913
6
11,652
69,913
Grand Total
59
16
10,859
12,664
640,702
202,617
75
11,244
843,319
Exhibit 5
Ranking of Opponent team, Nobel Plays and Double Header Matches
Total Average of Sold
Teams as per new Ranking
No D. Header
D. Header
Total Sum of Sold 2
Average of Sold
Sum of Sold 2
Average of Sold
Sum of Sold 2
No Nobel
10,194
570,858
23,281
69,844
10,859
640,702
1
39,600
79,199
47,768
47,768
42,322
126,967
2
11,753
70,518
11,753
70,518
3
11,652
69,913
11,652
69,913
4
8,933
44,664
8,933
44,664
5
10,513
84,105
10,513
84,105
7
11,744
58,720
11,744
58,720
8
10,045
70,316
10,045
70,316
9
5,344
21,376
5,344
21,376
10
8,094
24,282
8,094
24,282
11
7,133
14,266
9,014
9,014
7,760
23,280
12
3,614
10,841
13,062
13,062
5,976
23,903
13
4,532
22,658
4,532
22,658
Nobel
12,648
164,418
12,733
38,199
12,664
202,617
1
37,629
75,258
37,629
75,258
4
5,099
5,099
5,099
5,099
5
11,758
23,516
18,217
18,217
13,911
41,733
7
5,949
5,949
5,949
5,949
9
7,074
14,147
7,074
14,147
10
7,839
7,839
8,645
8,645
8,242
16,484
11
5,239
5,239
11,337
11,337
8,288
16,576
12
9,445
18,889
9,445
18,889
13
8,482
8,482
8,482
8,482
Grand Total
10,656
735,276
18,007
108,043
11,244
843,319
Exhibit 6
Regression Statistics
Multiple R
64.37%
R Square
41.44%
Adjusted R Square
31.21%
Df
F
Significance F
Regression
11
4.0522964
0.0171%
Coefficients
P-value
Lower 95%
Upper 95%
Intercept
17,251
48.78%
(32,144)
66,646
Team Ranking.
(1,297)
0.00%
(1,863)
(731)
Position
(177)
81.51%
(1,685)
1,331
G. Behind
(9)
96.86%
(459)
441
D.o.Week
297
60.49%
(843)
1,436
Temp.
(68)
87.32%
(921)
785
Precip
(3,882)
46.69%
(14,481)
6,717
T.o.Game
3,111
19.02%
(1,583)
7,806
Tele
(350)
90.93%
(6,469)
5,769
D.Header
10,002
0.81%
2,699
17,306
Promo
6,119
1.97%
1,009
11,230
Nobel
1,421
55.28%
(3,336)
6,178
Exhibit 7
Nobel Success Rate vs. Total Success Rate
No. of Matches
%
Total Nobel Games (Home/Road)
33
Win
22
67%
Total Noble Games (Home)
16
Success (by applying success rate)
11
69%
Total Oakland As Home Games
75
Success rate of Oakland
51.2%
Total Wins (Oakland A’s Home)
38
No Noble Wins
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