It's a common assumption that neutral court games should be treated differently from games played at one team's home court, but is that really true? The SI article that looked at home court advantage concluded that it was primarily due to the referees treating the home team differently. That jibes with something I found -- that large home dogs don't get a HCA.
Presumably the refs don't give the benefit of the doubt when they know the home team is overmatched.
I did some other experiments (prior to starting the blog, so they aren't documented here) where I trained a predictor on regular season games using just a strength measure for each team, so that the prediction equation looked like this:
MOV = (C1 * Strength of Home Team) + (C2 * Strength of Away Team) + C3
C2 was negative, and C3 (along with any C1/C2 ratio) was the "home court advantage".
I then tested the accuracy of this predictor on NCAA tournament games, first treating the higher seed as the home team, then the lower seed as the home team, and then washing out HCA altogether by dropping C3 and forcing C1 & C2 to be equal.
What I found was that the best prediction was made treating the higher seed as the home team. This makes some intuitive sense -- the refs are giving the benefit of the doubt to the team that they "know" is the better team. So I'm a little dubious that there's really no "HCA" in tournament games, although I don't know that anyone else has looked at it.
Showing posts with label home court advantage. Show all posts
Showing posts with label home court advantage. Show all posts
Tuesday, March 20, 2012
Friday, April 15, 2011
The Home Court Advantage
In the previous post, we started looking at RPI and found that it was a considerably better predictor than the 1-Bit Predictor. However, RPI has several obvious shortcomings. Will fixing these improve its performance as a predictor? Let's see!
The first area we can look at improving is accounting for Home Court Advantage. Recall that previously we showed HCA to give the home team about a 4.5 point advantage, or overall a +30% chance of winning. In 1981, the NCAA added a correction to the RPI formula to account for this advantage. The correction weights a team's wins and losses differently depending upon where they were played. A home win is only worth 0.6 "wins", while a road win is worth 1.4 "wins". Conversely, a home loss costs 1.4 "losses", while a road loss is only 0.6 "losses".
There are a couple of potential problems with this approach. First, the RPI formula applies this weighting only to the winning percentage calculation of the team being rated. It is not used in calculating the opponents' winning percentage (OWP) or the opponents' opponents' winning percentage (OOWP). So the OWP and OOWP are potentially biased by the HCA. Second, the weighting chosen (0.6/1.4) doesn't appear to reflect the actual home court advantage, which is closer to 30% than 40%.
Let's see if changing the weightings in the calculation of WP to 0.7/1.3 (closer to the HCA I measured) results in any improvement. Making this change and testing gives this result:
A very slight improvement. This is not too surprising -- this change only has a small effect on Winning Percentage, which is only 25% of a team's RPI. Perhaps the NCAA's approach to HCA doesn't have much impact at all?
I should have learned my lesson last time, let's pause a moment to run a test to make sure that the HCA really is a problem. To do this, we'll run a quick experiment using no weighting (e.g., 1.0/1.0) to see how much improvement this approach to HCA is actually providing. Performance with no weighting gives these results:
Surprise! The NCAA's correction for the home court advantage seems to have actually made the RPI's performance worse. Hence the value of testing everything -- sometimes intuitively correct notions turn out to be incorrect. Further experimenting with a variety of weightings confirms that the unweighted RPI actually performs better than any weighted variety.
A different approach to accounting for HCA is to adjust game outcomes using the HCA in points. That is, we'll subtract the HCA (say, 4.5 points) from the home team before determining who "won" the game. So when Duke wins by 3 at home against North Carolina, that game will count as a win for North Carolina when calculating RPI. (And we'll carry this through all levels of the RPI calculation to avoid that possible shortcoming.) This is the equivalent of moving every game to a neutral site (but cheaper).
That change provides this performance:
This is not an improvement over RPI with no weighting. Experiments with other values for the HCA also do not improve performance (HCA=3.5 does the best, though). So it appears that the RPI does not benefit from adjustments to eliminate the HCA -- a somewhat surprising result!
My vague intuition about this result is that the HCA is essentially "washed out" of the RPI because the majority of teams play home-and-home series within their conferences. So any home advantage is gained equally by every team, and any attempt to compensate within the RPI formula just adds error.
We'll return in a bit to an alternative approach for HCA suggested by Dick Vitale. But since HCA doesn't appear to be a significant problem, first we'll detour into a couple of other possible improvements to RPI.
The first area we can look at improving is accounting for Home Court Advantage. Recall that previously we showed HCA to give the home team about a 4.5 point advantage, or overall a +30% chance of winning. In 1981, the NCAA added a correction to the RPI formula to account for this advantage. The correction weights a team's wins and losses differently depending upon where they were played. A home win is only worth 0.6 "wins", while a road win is worth 1.4 "wins". Conversely, a home loss costs 1.4 "losses", while a road loss is only 0.6 "losses".
There are a couple of potential problems with this approach. First, the RPI formula applies this weighting only to the winning percentage calculation of the team being rated. It is not used in calculating the opponents' winning percentage (OWP) or the opponents' opponents' winning percentage (OOWP). So the OWP and OOWP are potentially biased by the HCA. Second, the weighting chosen (0.6/1.4) doesn't appear to reflect the actual home court advantage, which is closer to 30% than 40%.
Let's see if changing the weightings in the calculation of WP to 0.7/1.3 (closer to the HCA I measured) results in any improvement. Making this change and testing gives this result:
| Predictor | % Correct | MOV Error |
|---|---|---|
| 1-Bit | 62.6% | 14.17 |
| RPI | 73.2% | 11.62 |
| RPI (1.7/0.3) | 73.4% | 11.58 |
A very slight improvement. This is not too surprising -- this change only has a small effect on Winning Percentage, which is only 25% of a team's RPI. Perhaps the NCAA's approach to HCA doesn't have much impact at all?
I should have learned my lesson last time, let's pause a moment to run a test to make sure that the HCA really is a problem. To do this, we'll run a quick experiment using no weighting (e.g., 1.0/1.0) to see how much improvement this approach to HCA is actually providing. Performance with no weighting gives these results:
| Predictor | % Correct | MOV Error |
|---|---|---|
| 1-Bit | 62.6% | 14.17 |
| RPI | 73.2% | 11.62 |
| RPI (1.7/0.3) | 73.4% | 11.58 |
| RPI (1.0/1.0) | 74.6% | 11.53 |
Surprise! The NCAA's correction for the home court advantage seems to have actually made the RPI's performance worse. Hence the value of testing everything -- sometimes intuitively correct notions turn out to be incorrect. Further experimenting with a variety of weightings confirms that the unweighted RPI actually performs better than any weighted variety.
A different approach to accounting for HCA is to adjust game outcomes using the HCA in points. That is, we'll subtract the HCA (say, 4.5 points) from the home team before determining who "won" the game. So when Duke wins by 3 at home against North Carolina, that game will count as a win for North Carolina when calculating RPI. (And we'll carry this through all levels of the RPI calculation to avoid that possible shortcoming.) This is the equivalent of moving every game to a neutral site (but cheaper).
That change provides this performance:
| Predictor | % Correct | MOV Error |
|---|---|---|
| 1-Bit | 62.6% | 14.17 |
| RPI (unweighted) | 74.6% | 11.53 |
| RPI (HCA=4.5) | 73.6% | 11.61 |
This is not an improvement over RPI with no weighting. Experiments with other values for the HCA also do not improve performance (HCA=3.5 does the best, though). So it appears that the RPI does not benefit from adjustments to eliminate the HCA -- a somewhat surprising result!
My vague intuition about this result is that the HCA is essentially "washed out" of the RPI because the majority of teams play home-and-home series within their conferences. So any home advantage is gained equally by every team, and any attempt to compensate within the RPI formula just adds error.
We'll return in a bit to an alternative approach for HCA suggested by Dick Vitale. But since HCA doesn't appear to be a significant problem, first we'll detour into a couple of other possible improvements to RPI.
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