Deal or No Deal - Investigating Shark Tank Deals Throughout the Show

Appendix to report

Data cleaning

This dataset largely already came in analysis-ready format. After downloading the data from Kaggle and converting the column names into snake case, our main job for cleaning was deciding which of the variables could be removed — both those that were not helpful for our research question and those that contained too many missing variables to be important. The ones that we decided to remove were pitchers_average_age (many missing values), company_website (missing values and unhelpful for analysis), business_description (redundant and less analyzable than industry), and notes (unhelpful for analysis). We also converted the character values of season_start, season_end, and original_air_date to dates using lubridate to make analysis easier. The last thing we reckoned with was that the original data set gives NA values for the columns like total_deal_amount if that pitch did not get a deal, and so we were questioning whether it would be better for analysis to change those NA values to 0. However, we decided that it is not clear in some cases whether this NA is from no deal or an actual missing value, and also that the primary tool of analysis for our research question will be the got_deal column which has no missing values. To analyze the amount of money given more specifically, we believe that analysis can be done just among the pitches that did get a deal.

library(tidyverse)
── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.4.0     ✔ purrr   1.0.0
✔ tibble  3.2.1     ✔ dplyr   1.1.2
✔ tidyr   1.2.1     ✔ stringr 1.5.0
✔ readr   2.1.3     ✔ forcats 0.5.2
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
library(skimr)

unwanted <- c('pitchers_average_age', 'company_website', 'business_description', 'notes')
shark_tank <- read_csv("data/shark_tank.csv") |>
  janitor::clean_names() |>
  select(!unwanted) |>
  mutate(season_start = lubridate::dmy(season_start),
         season_end = lubridate::dmy(season_end),
         original_air_date = lubridate::dmy(original_air_date))
Rows: 1038 Columns: 52
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (14): Season Start, Season End, Original Air Date, Startup Name, Industr...
dbl (38): Season Number, Episode Number, Pitch Number, Multiple Entrepreneur...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Warning: Using an external vector in selections was deprecated in tidyselect 1.1.0.
ℹ Please use `all_of()` or `any_of()` instead.
  # Was:
  data %>% select(unwanted)

  # Now:
  data %>% select(all_of(unwanted))

See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
skim(shark_tank)
Data summary
Name shark_tank
Number of rows 1038
Number of columns 48
_______________________
Column type frequency:
character 7
Date 3
numeric 38
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
startup_name 0 1.00 3 32 0 1036 0
industry 0 1.00 6 23 0 15 0
pitchers_gender 5 1.00 4 10 0 3 0
pitchers_city 540 0.48 3 18 0 250 0
pitchers_state 299 0.71 2 6 0 46 0
entrepreneur_names 557 0.46 8 60 0 479 0
guest_name 837 0.19 9 17 0 24 0

Variable type: Date

skim_variable n_missing complete_rate min max median n_unique
season_start 0 1.00 2009-08-09 2022-09-23 2015-09-25 14
season_end 7 0.99 2010-02-05 2022-05-20 2016-05-20 13
original_air_date 408 0.61 2009-08-09 2022-09-30 2014-01-13 154

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
season_number 0 1.00 6.76 3.11 1.00 4.00 7.00 9.00 1.400e+01 ▃▇▅▇▁
episode_number 0 1.00 12.12 7.74 1.00 5.00 11.00 18.00 2.900e+01 ▇▆▅▅▂
pitch_number 0 1.00 519.50 299.79 1.00 260.25 519.50 778.75 1.038e+03 ▇▇▇▇▇
multiple_entrepreneurs 487 0.53 0.35 0.48 0.00 0.00 0.00 1.00 1.000e+00 ▇▁▁▁▅
us_viewership 416 0.60 6.10 1.35 2.31 5.15 6.38 7.11 8.640e+00 ▁▃▅▇▃
original_ask_amount 0 1.00 281798.65 379843.24 10000.00 100000.00 200000.00 300000.00 5.000e+06 ▇▁▁▁▁
original_offered_equity 0 1.00 14.64 8.91 1.50 10.00 10.00 20.00 1.000e+02 ▇▁▁▁▁
valuation_requested 0 1.00 3163290.63 4804725.88 40000.00 600000.00 1485294.00 3333333.00 4.500e+07 ▇▁▁▁▁
got_deal 0 1.00 0.58 0.49 0.00 0.00 1.00 1.00 1.000e+00 ▆▁▁▁▇
total_deal_amount 436 0.58 290921.37 378899.37 0.00 100000.00 200000.00 300000.00 5.000e+06 ▇▁▁▁▁
total_deal_equity 436 0.58 25.51 16.18 0.00 15.00 25.00 33.00 1.000e+02 ▇▇▂▁▁
deal_valuation 436 0.58 2042821.14 3718413.81 0.00 336206.75 800000.00 2000000.00 3.600e+07 ▇▁▁▁▁
number_of_sharks_in_deal 436 0.58 1.32 0.63 1.00 1.00 1.00 2.00 5.000e+00 ▇▂▁▁▁
investment_amount_per_shark 436 0.58 245115.72 350301.99 0.00 75000.00 150000.00 300000.00 5.000e+06 ▇▁▁▁▁
equity_per_shark 436 0.58 21.55 15.17 0.00 10.00 20.00 25.00 1.000e+02 ▇▅▁▁▁
royalty_deal 987 0.05 1.00 0.00 1.00 1.00 1.00 1.00 1.000e+00 ▁▁▇▁▁
loan 1001 0.04 1.00 0.00 1.00 1.00 1.00 1.00 1.000e+00 ▁▁▇▁▁
barbara_corcoran_investment_amount 940 0.09 143520.41 137398.90 12500.00 50000.00 100000.00 200000.00 1.000e+06 ▇▂▁▁▁
barbara_corcoran_investment_equity 940 0.09 23.98 13.09 5.00 15.00 20.00 32.25 5.500e+01 ▇▇▂▂▂
mark_cuban_investment_amount 857 0.17 245649.17 278613.24 12500.00 75000.00 150000.00 300000.00 2.000e+06 ▇▁▁▁▁
mark_cuban_investment_equity 857 0.17 18.80 15.40 2.50 10.00 15.00 25.00 1.000e+02 ▇▃▁▁▁
lori_greiner_investment_amount 882 0.15 205993.59 198022.87 17500.00 75000.00 150000.00 250000.00 1.000e+06 ▇▂▁▁▁
lori_greiner_investment_equity 882 0.15 16.61 12.03 0.00 10.00 12.50 20.00 6.500e+01 ▇▅▁▁▁
robert_herjavec_investment_amount 938 0.10 290973.33 581148.81 5000.00 86458.33 150000.00 300000.00 5.000e+06 ▇▁▁▁▁
robert_herjavec_investment_equity 938 0.10 18.66 13.36 0.00 10.00 15.00 25.00 1.000e+02 ▇▃▁▁▁
daymond_john_investment_amount 943 0.09 186805.26 319390.55 5000.00 50000.00 100000.00 240000.00 3.000e+06 ▇▁▁▁▁
daymond_john_investment_equity 943 0.09 26.06 16.18 0.00 15.82 25.00 33.30 1.000e+02 ▇▇▁▁▁
kevin_o_leary_investment_amount 942 0.09 236276.04 315926.33 20000.00 80000.00 150000.00 250000.00 2.500e+06 ▇▁▁▁▁
kevin_o_leary_investment_equity 942 0.09 15.83 11.65 0.00 8.56 10.83 25.00 5.000e+01 ▇▃▂▁▁
guest_investment_amount 969 0.07 216606.28 239754.19 0.00 75000.00 125000.00 250000.00 1.250e+06 ▇▂▁▁▁
guest_investment_equity 969 0.07 16.71 15.52 0.00 10.00 11.25 20.00 1.000e+02 ▇▂▁▁▁
barbara_corcoran_present 143 0.86 0.56 0.50 0.00 0.00 1.00 1.00 1.000e+00 ▆▁▁▁▇
mark_cuban_present 142 0.86 0.90 0.30 0.00 1.00 1.00 1.00 1.000e+00 ▁▁▁▁▇
lori_greiner_present 142 0.86 0.75 0.43 0.00 0.75 1.00 1.00 1.000e+00 ▂▁▁▁▇
robert_herjavec_present 142 0.86 0.88 0.33 0.00 1.00 1.00 1.00 1.000e+00 ▁▁▁▁▇
daymond_john_present 143 0.86 0.66 0.47 0.00 0.00 1.00 1.00 1.000e+00 ▅▁▁▁▇
kevin_o_leary_present 143 0.86 0.96 0.21 0.00 1.00 1.00 1.00 1.000e+00 ▁▁▁▁▇
kevin_harrington_present 143 0.86 0.95 0.23 0.00 1.00 1.00 1.00 1.000e+00 ▁▁▁▁▇ 
glimpse(shark_tank)
Rows: 1,038
Columns: 48
$ season_number                      <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ season_start                       <date> 2009-08-09, 2009-08-09, 2009-08-09…
$ season_end                         <date> 2010-02-05, 2010-02-05, 2010-02-05…
$ episode_number                     <dbl> 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3,…
$ pitch_number                       <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, …
$ original_air_date                  <date> 2009-08-09, 2009-08-09, 2009-08-09…
$ startup_name                       <chr> "AvaTheElephant", "Mr.Tod'sPieFacto…
$ industry                           <chr> "Health/Wellness", "Food and Bevera…
$ pitchers_gender                    <chr> "Female", "Male", "Male", "Male", "…
$ pitchers_city                      <chr> "Atlanta", "Somerset", "Cary", "Tam…
$ pitchers_state                     <chr> "GA", "NJ", "NC", "FL", "MN", "CA",…
$ entrepreneur_names                 <chr> "Tiffany Krumins", "Tod Wilson", "K…
$ multiple_entrepreneurs             <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ us_viewership                      <dbl> 4.15, 4.15, 4.15, 4.15, 4.15, 5.59,…
$ original_ask_amount                <dbl> 50000, 460000, 1200000, 250000, 100…
$ original_offered_equity            <dbl> 15, 10, 10, 25, 15, 15, 10, 10, 20,…
$ valuation_requested                <dbl> 333333, 4600000, 12000000, 1000000,…
$ got_deal                           <dbl> 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1,…
$ total_deal_amount                  <dbl> 50000, 460000, NA, NA, NA, 500000, …
$ total_deal_equity                  <dbl> 55, 50, NA, NA, NA, 50, 100, NA, NA…
$ deal_valuation                     <dbl> 90909, 920000, NA, NA, NA, 1000000,…
$ number_of_sharks_in_deal           <dbl> 1, 2, NA, NA, NA, 2, 5, NA, NA, NA,…
$ investment_amount_per_shark        <dbl> 50000, 230000, NA, NA, NA, 250000, …
$ equity_per_shark                   <dbl> 55.0, 25.0, NA, NA, NA, 25.0, 20.0,…
$ royalty_deal                       <dbl> NA, NA, NA, NA, NA, NA, 1, NA, NA, …
$ loan                               <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA,…
$ barbara_corcoran_investment_amount <dbl> 50000, 230000, NA, NA, NA, NA, 5000…
$ barbara_corcoran_investment_equity <dbl> 55, 25, NA, NA, NA, NA, 20, NA, NA,…
$ mark_cuban_investment_amount       <dbl> NA, NA, NA, NA, NA, NA, 50000, NA, …
$ mark_cuban_investment_equity       <dbl> NA, NA, NA, NA, NA, NA, 20, NA, NA,…
$ lori_greiner_investment_amount     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA,…
$ lori_greiner_investment_equity     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA,…
$ robert_herjavec_investment_amount  <dbl> NA, NA, NA, NA, NA, 250000, 50000, …
$ robert_herjavec_investment_equity  <dbl> NA, NA, NA, NA, NA, 25.0, 20.0, NA,…
$ daymond_john_investment_amount     <dbl> NA, 230000, NA, NA, NA, NA, 50000, …
$ daymond_john_investment_equity     <dbl> NA, 25, NA, NA, NA, NA, 20, NA, NA,…
$ kevin_o_leary_investment_amount    <dbl> NA, NA, NA, NA, NA, 250000, 50000, …
$ kevin_o_leary_investment_equity    <dbl> NA, NA, NA, NA, NA, 25.0, 20.0, NA,…
$ guest_investment_amount            <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA,…
$ guest_investment_equity            <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA,…
$ barbara_corcoran_present           <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ mark_cuban_present                 <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ lori_greiner_present               <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ robert_herjavec_present            <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ daymond_john_present               <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ kevin_o_leary_present              <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ kevin_harrington_present           <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ guest_name                         <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA,…

Other appendicies (as necessary)

Data exploration: industry breakdown of Sharks

From these plots, we can see the investment in industries does slightly differ between sharks but it’s not a drastic difference like we anticipated. For example, Lori Greiner and Daymond John have never invested in Business Services. However, we think it’s more important to observe the overall relationship in investments over the course of the show instead of focusing on sharks on a case by case basis.

Evaluation of Significance 2: Multiple Pitchers and Getting Deals

Helps answer Analysis 2 from Pre-Registration

We want to see if the relationship between having multiple pitchers and getting a pitch is random or significant. To do this, we will use a hypothesis test and focus on singular vs. multiple pitchers.

Null hypothesis: Pitcher groups with one member and multiple members percentages of getting deals are equal.

\[ H_0 = p_m -p_f = 0 \]

Alternative hypothesis: Pitcher groups with one member and multiple members percentages of getting deals are not equal.

\[ H_A = p_m -p_f ≠ 0 \]

set.seed(123)

shark_tank_hypo <- shark_tank |>
  mutate(deal = if_else(got_deal == 1, 'yes', 'no')) |>
  mutate(multiple = if_else(multiple_entrepreneurs == 1, 'multiple', 'singular')) |>
  select(deal, multiple) |>
  drop_na()

shark_tank_hypo
# A tibble: 551 × 2
   deal  multiple
   <chr> <chr>   
 1 yes   singular
 2 yes   singular
 3 no    singular
 4 no    singular
 5 no    singular
 6 yes   singular
 7 yes   singular
 8 no    singular
 9 no    singular
10 no    singular
# ℹ 541 more rows
point_estimate <- shark_tank_hypo |>
  specify(multiple ~ deal, success = 'multiple') |>
  calculate(stat = "diff in props", order = c('yes','no'))

null_dist <- shark_tank_hypo |>
  specify(multiple ~ deal, success = 'multiple') |>
  hypothesize(null = "independence") |>
  generate(1000, type = "permute") |>
  calculate(stat = "diff in props", order = c('yes','no'))

visualize(null_dist) +
 shade_p_value(obs_stat = point_estimate, direction = "two sided")

null_dist |>
  get_p_value(obs_stat = point_estimate, direction = "two sided")
# A tibble: 1 × 1
  p_value
    <dbl>
1   0.134

This analysis gives us a P-value of 0.134, which is too large (>0.05) to reject the null hypothesis. Hence, we fail to reject the null hypothesis and do not find that there is a non-random difference in the success of pitcher groups with multiple pitchers and the pitcher groups of a singular pitcher.