How to model a logistic regression with head to head data?

Question

Preface

I've looked at How should we convert sports results data to perform a valid logistical regression? and How to simulate head to head competition based on winning percentages? but I didn't get it to a 100%.

Question

We have 5 rows about head to head competition between elderly people playing bridge. We have competitor_home's age, competitor_visitor's age and the outcome (1 if home wins and 0 if visitor wins).

(trying to simulate a table below).

home_age visitor_age outcome
72       68          1 
75       63          1
78       74          1
79       77          1
71       71          1

The question is how I would create a logistic regression model that would be able to predict who the winner is depending on home and visitor age when the outcome is always 1. My idea is to duplicate the table and switch place with visitor_age and home_age so that we get 5 outcomes with zero. Is that a valid approach? Like below.

home_age visitor_age  outcome
72       68           1
75       63           1
78       74           1
79       77           1
71       71           1
68       72           0
63       75           0
74       78           0
77       79           0
71       71           0

The variance is still the same.

Answer 1

I can suggest to you 3 ideas:

• From your input data, you can create a new training set with only one feature: the age of the team. It almost the same idea that you suggest in your question. Your training set will look like:

age      outcome
72       1
75       1
78       1
79       1
71       1
68       0
63       0
74       0
77       0
71       0

• Maybe you prefer to use the difference of age between the two teams, so you can create this training set:

diff outcome 
4    1
-4   0 
12   1
-12  0 
4    1
-4   0 
2    1
-2   0 
0    1 
0    0

• The last idea is to use the Bradley-Terry model who is build to solve this kind of problem. Here is the documentation of the R package BreadleyTerry2.

However, I hope you have more than 5 rows as input data to build a relevant model. Also, I think it's totally useless to keep the "home/visitor" information because, at bridge, this information has no importance.

Answer 2

This approach is not correct because home_age and visitors_age are different variables. So their coefficients are also different. If you see that the car with 4 wheels and 0 engines can't drive you do not conclude that the car with 0 wheels and 4 drivers can drive).