1. Effect of the location on the quality of the curve
ABHINAV KUMAR VIGNESHWARAN VASANTHAKUMAR

2. HYPOTHESIS
The goal is to check whether there is any observable difference in the basic s,c fit when data used is from only the games played in a specific country/continent.
Based on the fit, we want to make inferences about the quality of players from different countries.

3. METHODOLOGY
We collected the data of the games played in 15 different countries spanning across 4 continents.
We used the EventCountryFilter available in the IR program to filter out games played in a specific country.
Then the obtained data was plotted to check the variation in the curve. We made two sets of plots.
One set is for each country and the other set is for a continent in whole.
For each country we obtained the data starting from the rating level 1950 to The ELO was increased in steps of We used SF7 engine.
We plotted the following graphs:
ELO, S
ELO, C
S, IPR
ASD, IPR

4. METHODOLOGY(cont’d)
We see the effect on the average error for different IPR values by plotting a bar plot between IPR and the corresponding ASD values.

5. Possible biases in the data
In the tournaments played in a specific country there could be certain foreign players which might affect the outcome.
But on closer examination this doesn’t seem to make much of an impact on the curve.

6. RESULTS
From the plots obtained on the s and IPR values, we see more linearity in European countries as compared to the rest .
The linearity metric for North American countries is pretty low as compared to others. It is hard to come to a conclusion as the data points obtained were only from USA and Canada.
The projected IPR values for USA is less than the corresponding ELO ratings for the ELO
From the final bar plot ,we see that as the IPR level increases ,the ASD value decreases.

7. RESUlts (cont’d) Elo vs c for Azerbaijan
Example s vs ELO and C vs ELO plots for different countries and variation in data :
Elo vs c for Azerbaijan

8. RESUlts (cont’d)
Elo vs s for China

9. RESUlts (cont’d) ASD vs IPR for Russia
Example ASD vs IPR plots for different countries and variation in data :
ASD vs IPR for Russia

10. ASD vs IPR for Argentina
RESUlts (cont’d)
ASD vs IPR for Argentina

11. ASD vs IPR for South America
RESULTS(CONT’D)
ASD vs IPR for South America

12. RESUlts (cont’d)
ASD Vs IPR plot for Germany
IPR
ASD

13. RESUlts (cont’d)
ASD Vs IPR plot for North America
IPR
ASD

14. RESUlts (cont’d)
ELO Vs C plot for
CANADA C
ELO

15. RESUlts (computed Average squared error)
Europe
North America
South America
Asia

16. CONCLUSIONS AND FURTHER HYPOTHESIS TESTING
From our observations it is clear that the projected values do not show a significant deviation from the actual ELO values. Even in the cases where the projected value is much higher or lower than the actual values we know that the it is due to certain one off games which have been magnified by the lesser number of datapoints.
The same process can be repeated with a dataset where we can obtain games tournaments played in a country without any foreign players. This will help in getting a more accurate understanding of the relation.
To sum up, the model follows the natural logistic curve even if tested for different countries/continents.