Analyzing Golf Scores: Rank Calculation with Average Position for Tied Scores

Analyzing Golf Scores: Rank Calculation with Average Position for Tied Scores#

Introduction#

In this article, we explore a method for ranking golf scores. The challenge is to assign ranks based on the lowest scores while accounting for ties in scores. If two or more players have the same score, they receive the same rank, and the rank positions they occupy are averaged to determine their final standing.

Problem Overview#

The main goal is to assign ranks in a sequence where a lower score corresponds to a better rank. However, if players score the same, they must receive the same rank, and the average position of all tied players must be computed accordingly.

Example#

Given a set of sample scores, we can observe the following:

  • Scores: 67, 68, 68, 70, 70, 70, 74

When sorted, we can see:

  1. 67 gets 1st place.

  2. The two 68 scores will share the average of 2nd and 3rd places to get 2.5.

  3. The three 70 scores will share the average of 4th, 5th, and 6th places to get 5.

  4. The 74 score gets 7th place.

We can represent these scores in APL:

s ← 67 68 68 70 70 70 74

General Approach#

To resolve this, a computational approach is employed:

  1. Sorting: The scores need to be sorted in ascending order.

  2. Ranking: Use a method that accounts for ties and averages their ranks.

In APL, this could be accomplished by:

⍋s ⍝ Sort scores to get ranks

Implementation Strategies#

Method 1: Grading and Grouping#

  • Grading: First, identify the sequence of scores and their corresponding indices.

  • Grouping: Group scores that are the same, calculate their averages, and use those for ranking.

For example, we can find the unique ranks and their frequencies:

s ← 67 68 68 70 70 70 74
(≢⍴ +⌿ ÷ ≢)¨ s ⊆ ⍳ ≢ s

Method 2: Stable Sorting and Averaging#

By creating indices and sorting them accordingly, we can utilize a stable sort to maintain the original order of scores, aiding in identifying ties. The APL approach might look like this:

F ← {∊(≢⍴ +⌿ ÷ ≢)¨ ⍵ ⊆ ⍳ ≢ ⍵}
F s ⍝ Calculate the ranks based on scores

Method 3: Using Functions in APL#

In APL (A Programming Language), we can implement various functions:

  1. A function to compute the average of scores and occurrences.

  2. A group function that is capable of handling indices, which will ensure that duplicate scores are grouped together correctly.

Here’s how one would create a proper function:

g ← {
  ⍵ ← → `group` result of grouping function
}

Handling Edge Cases#

When applying functions to single values, adjustments may be necessary to ensure that scalar cases are handled without error. For instance, returning values as arrays allows functions that are meant to group and average to work seamlessly.

G ← ∊(⊂≢⍴ +⌿ ÷ ≢)⍤⊢⌸
G 5 ⍝ RANK ERROR

Performance Comparison#

We can compare the execution times of different methods using random score generation to assess how well each ranks scores:

cmp ← { 
  // Comparison logic here
}

When conducting tests with a dataset of 5000 scores in the range of 10,000, we find that certain methods yield significantly faster results. For instance, using the grade method that sorts both ways (ascending and descending) was identified as the fastest for the given input size:

t ← ?5E3⍴1E4
t ← t[⍋t]

Conclusion#

The process of ranking golf scores while accounting for ties can be complex, but through careful methodology and leveraging of APL functions, we can arrive at an elegant solution. The different methods employed not only provide accurate rankings but also perform efficiently across varied dataset sizes.

Thank you for reading! Feel free to share your thoughts or questions regarding golf score ranking in the comments below.

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