RPI: Home/Away/Neutral Issues

Updated March 2017

As discussed on the "RPI Formula" page, in general the NCAA computes the RPI for Division I women’s soccer without regard to game locations.  The one exception is in the bonus and penalty adjustments the NCAA makes to the Unadjusted RPI in order to produce the Adjusted RPI.  The adjustments award bonuses for good wins and ties and impose penalties for poor ties and losses, with the bonus and penalty amounts depending in part on whether a team receiving an adjustment played the game at home, at a neutral site, or away.

There is a reasonable question whether the RPI formula, apart from the bonus and penalty adjustments, should make a distinction between home, away, and neutral site games.  Some critics have asserted, in particular, that the top teams and teams from the strong conferences have leverage that enables them to play more non-conference games at home than away and that this unfairly skews the RPI in their favor.

For Division I men's basketball, the RPI formula makes a game site distinction:  In its Element 1 (Team's winning percentage) computation, it treats a home win as 0.6 of a win and an away win as 1.4 wins; and an away loss as 0.6 of a loss and a home loss as 1.4 losses.  In baseball, there is a similar distinction except that the weights are 0.7 and 1.3, since home field advantage is statistically less in baseball than in basketball.  The question is whether Division I women's soccer should convert to a comparable system.

HOME/AWAY IMBALANCES

In order to test whether teams play balanced home/away schedules, I looked at conferences and regions over the 2007 to 2016 seasons to determine whether they have game location imbalances.  I found that they do.  I also found a pattern to the imbalances:  Conferences and regions with higher average Adjusted RPIs tend to have favorable home game imbalances and conferences and regions with lower average Adjusted RPIs tend to have unfavorable home game imbalances.  This is not true in all cases, but it is true on average.

The following table shows the relationship, for the 2007 through 2016 seasons, between conferences’ average NCAA ARPIs and conferences’ home game imbalances.  It is in order from the conference with the highest average ARPI to the conference with the lowest.


Conference Home Game Imbalances Table


The following chart, derived from the above table, shows the relationship between conference strength and game locations:

Conference Home Game Imbalances Chart



As the trend lines show -- pink for percent of non-neutral games at home and yellow for percent of non-neutral non-conference games at home -- there is a correlation between conference average strength and percent of games at home: Stronger conferences' teams tend to play a higher percent of games at home than weaker conferences' teams.

The following table shows the relationship, for the 2007 through 2016 seasons, between the regional playing pools’ average NCAA ARPIs and the pools’ home game imbalances.  It is in order from the region with the highest average ARPI to the region with the lowest.


Region Home Game Imbalances Table


The following chart, derived from the above table, shows the relationship between region strength and game locations:

Region Home Game Imbalances Chart



As the trend lines show -- pink for percent of non-neutral games at home and yellow for percent of non-neutral non-region games at home -- there is a correlation between regional playing pool average strength and percent of games at home: Stronger regions' teams tend to play a higher percent of games at home than weaker regions' teams.

In summary, there are home/away imbalances.  Further, stronger conferences and regions tend to have favorable home game imbalances and weaker conferences and regions tend to have unfavorable home game imbalances.

HOME FIELD ADVANTAGE

IS THERE A HOME FIELD ADVANTAGE IN DIVISION I WOMEN'S SOCCER?

Given that there are home/away imbalances, the next question is whether there is a home field advantage and, if so, its extent.

In order to determine whether there is a home field advantage in relation to RPI ratings, I use my Correlator and performance percentage method of analysis applied to data for the ten seasons from 2007 through 2016.  (See the "RPI: Measuring the Correlation Between Teams' Performance and Their Ratings" page for information on the Correlator and performance percentage method of analysis.)  In a performance percentage analysis, a percentage of 100% means that a group of teams, on average, is performing in accord with its ratings; a percentage above 100% means that the group of teams, on average, is outperforming its ratings; and a percentage below 100% means that the group is under-performing its ratings.

To understand home field advantage, I use the Correlator to compare teams' performance percentage in home games as compared to their performance percentage in away games.  I do this for all games regardless of the rating difference between opponents, and also for the most closely rated 5%, 10%, and 15% of games.  In the table below, I show the results of this analysis for the Unadjusted RPI.  I've chosen the URPI because it is "uncluttered" by the bonus and penalty adjustments and thus gives the cleanest picture of the extent of home field advantage:


Home Game Advantage for URPI


As the two left-hand columns indicate, this shows home and away teams' performance percentages for the URPI with no adjustment for home field advantage.  Looking first at the two right-hand columns in the table, they say that for the most closely rated 5% of games, home teams perform better than their ratings say they should -- their performance percentage is 121.5% rather than the norm of 100.0% -- and away teams perform more poorly than their ratings say they should -- at the 78.5% level rather than at 100%.  The same is true looking at the most closely rated 10% and 15% of games, as well as for all games.  The impact of home field advantage is best measured by the 5% number.  Those are the games in which teams are closely rated enough that the impact of home field advantage is most likely to show up.  (For games with large rating differences, the higher rated team is likely to win regardless of game location.)  And, the 5% number covers 1,500 games, which is a sufficient-sized data sample.

Although the exact numbers vary from one rating system variation to another, the above pattern is the same for every rating system.  Simply put, there is a home field advantage in Division I women's soccer; and the advantage affects results in a significant number of games.  This, of course, is not surprising.

WHAT IS THE EXTENT OF HOME FIELD ADVANTAGE?

Knowing that there are home field imbalances and that home field advantage affects game results in a significant number of games, the next step is to measure the effect.  Since home teams perform as though their ratings are higher than their NCAA RPI ratings and away teams perform as though their ratings are lower, this suggests that there should be an upward RPI adjustment one could add to teams’ ratings when they host games and a matching downward adjustment to teams’ ratings when they are visitors, such that, with those game-by-game adjustments, the teams then would perform as a whole in accord with their "Home/Away/Neutral (or HAN) Corrected" ratings -- in other words, their performance percentages would be right around 100% for both home and away games.  With that in mind, for the ten years 2007 through 2016, for each rating system, I test a series of HAN corrections to teams' ratings, to see what level of HAN correction will produce correlations teams have 100% performance percentages for  both home and away games.

When I test a series of HAN correction amounts for a rating system, the results converge on a particular value of matching upward and downward corrections at which teams’ performances, as corrected game by game based on game location, match their ratings in closely rated games.  For corrections of lesser amounts, home teams still outperform and away teams under-perform their ratings; and for corrections of greater amounts, home teams under-perform and away teams outperform their ratings.

The following table illustrates how this process works, using the Unadjusted RPI as an example:


Home Game Correction for URPI


In this table, what I look for is the correction amount at which home and away team performance percentages are closest to 100% for the 5% most closely rated games.  The correction amount, highlighted in yellow, is 0.0065.   A lesser correction leaves the home teams outperforming and the away teams under-performing their ratings; and a greater correction leaves the home teams under-performing and the away teams outperforming their ratings.  Based on this approach, for the URPI rating system, a home team on average performs as though its rating is 0.0065 higher and an away team performs as though its rating is 0.0065 lower than the rating actually assigned by the URPI.  In other words, the effect of home field advantage is a cumulative change in two opponents' relative ratings of 0.0065 + 0.0065 = 0.0130.  (Note:  Although the home and away performance percentages together add up to 200%, in this particular case they don't due to rounding.)

Each rating system, including each RPI variation, has its own home/away correction amount. This is because each rating system has its own spread between teams' ratings as it moves through the ranks.  For some systems, teams ratings are quite compact and for other systems, their ratings are more spread out.  The amount of the home/away correction depends on this spread.  That being the case, when I evaluate a rating system using the Correlator, my first step is to go through the above kind of analysis to determine the appropriate home/away correction for that system.  On the "RPI: Modified RPI?" page, where I report on the performance of each of a number of rating systems, I include the home/away correction amount for each of those systems.

SHOULD THERE BE A CHANGE TO THE RPI FORMULA FOR WOMEN'S SOCCER TO TAKE HOME FIELD ADVANTAGE INTO CONSIDERATION?

Although it might seem that the NCAA should change the RPI formula for women's soccer to take home field advantage into consideration, in my view it. shouldn't.  Why?  As I have shown on other pages of this website, the RPI discriminates in favor of weaker conferences and regions and against stronger conferences and regions.  What is happening is that the stronger conferences' and regions' favorable home field imbalances are partially balancing out the RPI's discrimination against them.  But, they don't balance it out completely, as evidenced by the discrimination I've demonstrated after taking home field advantage into consideration.  If the NCAA were to change the RPI formula to take home field advantage into consideration, it would eliminate this "partial balancing out" effect of the favorable home field imbalances and the RPI's discrimination against stronger conferences and regions would be even greater than it already is.
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