2019-01-22

1 Introduction

2 Definitions

2.1 Competitive Games

3 Data

3.1 Forfeits

3.2 Non-IA Games

3.3 Limited Data

4 Analysis

4.1 Linear Regression

4.2 Visualizing Regression

4.3 Performing the Analysis

4.4 Post-analysis Elements

5 Questions

5.1 Head-to-Head

5.2 Personnel

5.3 Playing up a Class

5.4 Running up the Score

5.5 Team Schedules questions

2 Definitions

2.1 Competitive Games

3 Data

3.1 Forfeits

3.2 Non-IA Games

3.3 Limited Data

4 Analysis

4.1 Linear Regression

4.2 Visualizing Regression

4.3 Performing the Analysis

4.4 Post-analysis Elements

5 Questions

5.1 Head-to-Head

5.2 Personnel

5.3 Playing up a Class

5.4 Running up the Score

5.5 Team Schedules questions

The following handbook is meant to help the reader understand BCMoore Rankings.

I’m happy to augment and improve this guide. Questions and thoughts are very welcome: bcmoore87@bcmoorerankings.com.

Deviation: difference between the observed score - the predicted score

Game margin: Home score - visitor score.

Upset: a game outcome where the stronger team loses

The analysis strongly believes in the idea of competitive games. Competitive games happen when both teams perform at their full strength and ability.

In a non-competitive game, the favorite can ”pick the score”. Thus the actual game margin for this game may not add much value to evaluating both teams. If a team is expected to win by 30 and actually wins by 50, did we learn anything from this game? On the other side, if expectation is 30 and the actual score is 20, did the favorite put in non-starters to help them gain experience?

A competitive game is one where the winner is believed to be less than 2.5 standard deviations better than the loser. The number, 2.5, is a discovered value that improves the predictive power of the model.

All data comes from official sources. Boys data comes from www.iahsaa.org. Girls data comes from the partnership of www.ighsau.org and www.quikstatsiowa.com. During a sports season, data is synced five times per day.

If you see an error in the data, please work with the upstream sources identified in this section.

The analysis handles the game based on when the forfeit was declared.

Pre-game forfeit: This game is not used in the calculation of team strengths. This game is included on team outputs and records.

Mid-game forfeit: This game is treated the same as a pre-game forfeit.

Post-game forfeit: If the score is “Alpha 20, Beta 7” AND Alpha forfeits, then:

- This game is used in the calculations of team strengths.
- The on-field OR on-court game score will be included in the analysis and all output reports.
- This game will be displayed as a loss for Alpha and a win for Beta.
- When compiling the record of Alpha, this game will increment the loss total.
- When compiling the record of Beta, this game will increment the win total.

Commentary:

In the case of a pre-game forfeit, a score of 1-0 does not add value to the analysis; this is a made-up score. This game is not used in the regression analysis.

In the case of a mid-game forfeit, the score is not for a completed game. Thus, this score is only partially “true”. This game is not used in the regression analysis.

In the case of a post-game forfeit, the rankings assume that all coaches and authorities are making a good-faith effort to follow rules and guidelines. The rankings believe that the on-field data is generally an unbiased representation of the relative abilities of the two teams. Additionally, the score of the field has a certian historical value (independent of the subsequent forfeit).

Games with non-Iowa opponents are fundamentally treated the same as any other game. Because of the regression nature of the analysis, keep these two things in mind.

- If a non-Iowa team plays only one game in the score database, then this game score is assumed to have no error. Thus, this game will have no impact on the rating of any Iowa team.
- If a non-Iowa team plays two or more games in the score database, then these games will have an impact on the analysis (just like any Iowa team).

Week 1: Alpha 20, Beta 10; Gamma 14, Delta 7.

Week 2: Alpha plays Delta and Beta plays Gamma.

After week 1, how can we make a prediction?

The early season is always a period of revelation. With each game, new clues are revealed. And at some point, teams become connected (except for comparing 8-man football teams to the rest of the state).

The rankings will use last year’s strength scores as a starting point for connecting teams. When each team has played about 3-4 games, real connections will be present, old strength scores will be removed, and the analysis becomes unbiased.

Linear Regression is a statistical process for finding meaning from inexact data. Inexact data arises when randomness is present.

Randomness is always present is sports. Without randomness, there would be no reason to play the game: we would already know the outcome.

Linear regression is a process for isolating randomness.

Linear regression is an iterative process where deviations are minimized.

How can we think about the statistical regression process as we apply it to sports?

The regression model minimizes the square of the difference between its predictions and the observed game results. Non-technically: the model strives for its predictions to be as close as they can be to the observed game results.

Let’s pretend Alpha and Beta are playing tonight at Beta, and Beta is a 10-point favorite. The game is played and Beta wins by 8.

The deviation is -2, (8 - 10 = -2). In general, this is a good prediction. The model is predicting generally well.

If Beta is a 10-point favorite and loses by 10, then the deviation is -20, (-10 - 10 = -20), and we have a bad prediction. In this case the regression model will attempt to lower the rating of Beta and raise the rating of Alpha to attempt to better predict this specific result.

Changing the rating of Alpha and Beta will have an effect on all games that Alpha and Beta have played; new game deviations are calculated and minimized.

The computer model uses two major inputs: game margin and location.

Step 1: Linear regression is then used to discover two important outputs: relative team strengths and home-field advantage.

Step 2: After relative team strengths are discovered, a modification is done to attempt to minimize the effect of non-competitive games. This modification assigns the relative team strength as the average of all game strengths of competitive games played by the team.

Notes: (very explicitly)

- Class membership is not an input to this model. At the time of calculating team strengths, the model does not know anything about the class of teams.
- District/conference membership is not an input to this model. At the time of calculating team strengths, the model does not know anything about the district/conference of teams.
- A team’s record (W/L) is not an input to this model. Whether the team is 10-4, 5-2, 7-13, 5-20; the record of the team is not important. What is important to the analysis is the individual games. Consequently, there is no positive or negative effect of playing a different number of games. If Alpha plays 5 games, those are the 5 games used to analyze the team. If Beta plays 20 games, those of the 20 games used to analyze the team. An analysis involving both Alpha and Beta will be perfectly valid (assumes connecting games between the teams).
- Strength of schedule (SOS) is not an input to this model. In the analysis, SOS is calculated as the average opponent strength. Thus, this calculation can only be done after we have discovered the team strengths. SOS calculations may be used to understand “what is the model thinking?”. However, and again, this is a model output, not an input.

After team strengths and home-field advantage are discovered, many different reports are generated. These reports (1) use the discovered team strengths AND (2) add other pieces of information: class membership, district/conference membership, schedule information.

Question: My team won the head-to-head matchup. However, the other team is ranked above us. Thoughts?

This can, and very definitely does, occur. Team strengths are based on all competitive games (and indirectly based on all games). Again, remember the model is trying set team strengths such that it is predicting all games accurately, not just this one.

This is a very wonderful attribute of the model: the ability to recognize upsets.

This can be a fun one to think about. If the teams played again, would the teams have the same score? If you say “of course not, that never happens”, then you readily admit that there was randomness in that game too.

Question: The season is about half over, and my best player missed the first half of the season. However, he/she is back in action in an Alpha uniform. How correctly is the analysis ranking my team, Alpha?

The analysis rates all games equally. This fact conflicts with the fact that your team, Alpha, is now fundamentally different than the Alpha team that played the first half of the season.

As such, the analysis will underestimate your team.

It is possible to make an estimate of your new team strength. In your team schedule report, find the “Stren” column and find the average of all game strengths since your best player is back. Then compare this number to the team strength numbers in the class rankings.

Question: I’d like everyone to fully realize how wonderful my 1A team is. I’ve heard that if I play 2A teams, then the model will love my team no matter what the result. Thoughts?

As noted above, class membership is not an input to this model.

At the time of discovering team strengths, the computer model does not know the classification of the teams that play the games. As explicitly noted above, class membership is not an input to this model.

Note:

It is easy to see how this idea can occur.

After 2500 scores into the 2019 boy’s basketball season (about 4000 games):

Class N Mean Stdev

4A 48 101.65 11.86

3A 64 87.49 13.36

2A 96 79.22 16.07

1A 147 62.80 20.73

4A 48 101.65 11.86

3A 64 87.49 13.36

2A 96 79.22 16.07

1A 147 62.80 20.73

The average 2A team is believed to be about 16.4 points better than the average 1A team.

Question: I’ve heard that running up the score will help everyone fully realize how wonderful my team is. Thoughts?

If a team consistently (1) runs up the score AND (2) never plays a competitive game, the computer will output a relatively high strength score. No adjustment is possible, because no competitive games were played.

This is rarely the situation. Typically a team has a mix of both competitive and non-competitive games, and the computer will make its evaluation based on the competitive games. A season full of non-competitive games is essentially boring (my opinion).

Minor note: Alpha plays a mix of both competitive and non-competitive games. If Alpha runs up the score against a weak opponent (* in the team outputs, modified column), the effect this particular game seems to slightly lower the estimate of Alpha’s strength.

Question: In a team’s season report, why do some games have a “*” in the modifications, M, column?

If a team is expected to win by 2.5 standard deviations (about 22 points in boy’s basketball), then the computer attempts to minimize the effect of the game. In some/many/most of these types of games, the favorite can “pick the score”. Thus, the actual game margin for this game may not add much value to evaluating both teams.

Question: In a team’s season report, why do some games have a “X” in the modifications, M, column?

If a team has a pre-game forfeit, and an “X” in the modifications column, this means that this game is not included in the dataset used to create team strengths.