2025 Ratings

Your rating is adjusted based on who you compete against in each race, the margin of victory/loss against them and how surprising those victories/losses are based upon everyone's pre-race ratings.

Beating a stronger opponent gives you a bigger rating boost, while beating a weaker opponent changes it little. Losing to someone with a much lower rating will lower your rating.

Over time, these corrections help refine everyone's rating, making it more accurate as more races are completed.

Champions

At the start of each season, it’s a level playing field, with everyone starting at a rating of 100. At the end of the season, the overall leaders will be those with the highest rating that have completed at least 5 events. There will be 2 club champions in the open/women category for the Macclesfield Wheelers squad, then 2 guest champions for all other riders.

The ratings are like fitness adaptations!

Think of your rating like your current fitness level. Every hillclimb gives you multiple opponents and every opponent you face can be seen as a "training session".

• Racing someone at your own level is like doing a workout at your usual intensity - it keeps you sharp, but doesn't move the needle much.
• Beating someone much stronger than you is like doing a breakthrough workout - it gives your system a shock, and your "fitness" (rating) jumps up.
• Beating someone much weaker is like doing an easy recovery ride - your body doesn't adapt much, and your rating barely changes.
• Losing to a much weaker rider? That's like failing at a basic workout - your system actually degrades, and your rating drops.

Now, imagine everyone is constantly "training" by racing others. All the opponents you face give you wins and losses: we take each one, look at the margin of victory/loss and that "shock factor" mentioned above.

We add up all these wins/losses and change your rating after each hillclimb by that amount... just like how your fitness goes up or down by a given amount determined by the net effect of your last 50 rides.

Your rating is shaped by the network of opponents you face, not just direct matchups. You don't need to do every possible workout to infer your fitness level, so you don't need to compete directly against everyone to reveal your rating. However, the more events you take part in, the more accurate all ratings become because more opportunities arise for everyone to be compared.

Champions

At the start of each season, it’s a level playing field, with everyone starting at a rating of 100. At the end of the season, the overall leaders will be those with the highest rating that have completed at least 5 events. There will be 2 club champions in the open/women category for the Macclesfield Wheelers squad, then 2 guest champions for all other riders.

This document describes a rating system designed to rank cyclists based on their performance in a series of uphill time trial events. It adapts the principles of the Elo rating system, commonly used in chess, to handle events with multiple participants and performance measured by speed rather than simple win/loss outcomes.

1. Performance Measurement and Normalization

For each hillclimb event, raw performance is typically measured by the average speed achieved by each cyclist. These were the "leaderboard points" from previous editions of the race series, but applied to everyone, rather than individual gender categories.

• Benchmark: The highest average speed achieved in the event (i.e., the winner's speed) is used as the benchmark for that specific race. Let's denote this as Speed_max.
• Normalized Score: Each participant i in the event receives a normalized performance score, let's call it P_i. This score is calculated relative to the winner's speed:

• This results in a score P_i between 0 and 100, where the winner always scores 100.
• This score effectively represents how close a rider's performance was to the best performance achievable in that specific event context (considering course, conditions, etc.).

2. Adapting Elo for Multi-Participant Events: Pairwise Comparisons

The standard Elo system evaluates pairs of competitors. To apply this to an event with N cyclists, the system decomposes the event into a series of virtual one-on-one "battles" between all possible unique pairs of participants.

• For an event with N riders, there are N * (N - 1) / 2 unique pairs to compare.
• Each pair (e.g., Rider i vs. Rider j) is evaluated independently using Elo logic.

3. Calculating Performance Outcomes for Pairs

Within each virtual matchup between Rider i and Rider j, the system needs a way to represent their relative performance in that specific event, analogous to a win/loss/draw outcome in traditional Elo.

3.1. Actual Score (S)

An Actual Score is calculated for each rider in the pair based on their normalized performance scores (P_i, P_j) from the event:

• S_i represents Rider i's "share" of the combined performance score for that pair.
• Note that S_i + S_j always equals 1.
• If Rider i performed better (P_i > P_j), then S_i > 0.5. If they performed equally, S_i = 0.5.
• This S_i value serves as the observed outcome for the pairwise comparison.

3.2. Expected Score (E)

An Expected Score is calculated based solely on the riders' Elo ratings before the event. Let R_i and R_j be the pre-race ratings of Rider i and Rider j, respectively.

• This is the standard Elo probability formula derived from the logistic curve.
• E_i represents the predicted probability that Rider i would outperform Rider j, based purely on their rating difference.
• D is a divisor constant that scales the impact of rating differences. A common value in chess Elo is 400, but this system uses a different value (specifically 40), making expected scores more sensitive to smaller rating differences.
• Similar to the Actual Score, E_i + E_j always equals 1.

4. Calculating Rating Adjustments

The core of the Elo update lies in comparing the Actual Score (S) with the Expected Score (E) for each pairwise interaction.

• K is the K-factor, a constant determining the maximum possible rating change per event (or per comparison, depending on how it's applied). It controls the system's volatility. A higher K means ratings change faster. This system uses a K-factor of 3.20, suggesting relatively small, gradual rating adjustments.
• If a rider performs better than expected (S_i > E_i), their rating change (ΔR_i) for this comparison is positive.
• If they perform worse than expected (S_i < E_i), their rating change is negative.
• Because S_i + S_j = 1 and E_i + E_j = 1, it holds that ΔR_i = -ΔR_j. The rating exchange within each pair is zero-sum.

5. Aggregating Changes and Updating Ratings

Each rider participates in N-1 pairwise comparisons within a single event. Their total rating change for the event is the sum of the individual rating changes from all their comparisons.

• Total Event Change: For a Rider k, the total change is Σ ΔR_{k_vs_m} for all other riders m in the event.
• This summation is performed for every rider who participated.
• Final Update: The rider's new rating (R_{k, new}) is calculated by adding this total event change to their pre-race rating (R_{k, old}):

This new rating becomes their starting rating for the subsequent event.

6. Championship Determination and Data Integrity

At the conclusion of the season (comprising 16 races), final rankings are determined, and champions are identified based on specific criteria designed to ensure fairness and statistical validity.

6.1. Qualification Criteria

• Minimum Participation Threshold: Only riders who have participated in 5 or more events throughout the season are eligible for the final season rankings and championship consideration.
• Championship Categories: Four distinct champions are recognized based on their final calculated Elo rating after the last event. They are the highest-rated:
  • Macclesfield Wheeler (Cat: Open)
  • Macclesfield Wheeler (Cat: Women)
  • Guest of any/no team (Cat: Open)
  • Guest of any/no team (Cat: Women)
• Selection is based strictly on the final Elo rating among eligible participants within each category.

6.2. Rationale for Minimum Participation Requirement (≥ 5 Events)

The requirement for a minimum number of event participations is crucial for several reasons related to the nature of Elo rating systems and statistical reliability:

• Rating Stability and Convergence: Elo ratings require a sufficient number of data points (i.e., competitive interactions across multiple events) to converge towards a statistically stable representation of a rider's relative strength. Ratings based on only one or two events are highly susceptible to noise, luck, and the specific composition of the field in those few events. They may not accurately reflect the rider's true ability compared to the broader pool over time.
• Mitigation of Outlier Effects: A rider might achieve an unusually high or low rating in a single event due to exceptional circumstances (e.g., a particularly favorable matchup, unusual conditions, mechanical issues). Requiring multiple performances helps average out such outliers, ensuring the final rating is based on more consistent demonstrated ability.
• Preventing Strategic Non-Participation: Without a minimum threshold, a rider could potentially achieve a high rating early in the season against a limited or weaker field and then cease participation to "protect" that rating. The 5-event minimum ensures that contenders must demonstrate performance across a significant portion of the season, fostering continuous competition and fairer comparisons.
• Ensuring Representativeness: A champion selected from riders who have competed consistently throughout the season provides a more meaningful representation of season-long performance and standing within the established competitive hierarchy. The threshold ensures the ranking reflects sustained engagement rather than isolated results.

In essence, the 5-event minimum acts as a data quality filter, increasing confidence that the final Elo ratings accurately reflect the relative abilities of the consistently participating riders, thereby ensuring a fairer determination of season champions.

Summary of Key Characteristics

• Uses normalized speed (% of winner) as the performance input.
• Applies Elo logic by breaking events into all pairwise comparisons.
• Calculates an "Actual Score" based on relative performance within a pair (mapped to 0-1).
• Calculates an "Expected Score" based on pre-race ratings using the logistic Elo formula (with D=40).
• Adjusts ratings based on the difference between Actual and Expected scores, scaled by a K-factor (K=3.20).
• Rating exchange within each pair is zero-sum.
• Total rating change per rider is the sum of changes from all their pairwise comparisons in the event.