Rabid Crowd Theory 2: Parity Index
07.29.05
The last post about home court advantage by conference generated quite a bit of e-mail traffic. It was actually only three people that responded, but that represents half of my readership at this time of year. The point raised in the e-mails was that [major conference] was at a disadvantage because dominant teams at the top of the conference artificially bring the home winning percentage down by winning almost all of their road games. While I intended this post to be about why the future of possession-based stats is dependent upon Utah State winning the WAC this season, I feel duty-bound to slog through another post about the randomness of home court advantage.
Let me say first that part of the theory is sound. A team going unbeaten (or winless) will naturally drive the conference home record towards .500. However, a couple of points need to be made before we do any semi-serious analysis of this. One, this domination on the road says something about the ability to win in those road venues, and two, even the little conferences have their dominant teams. The only conference unbeatens in '04 were from the Big West and SoCon.
To dig in further, I created a measure of parity in each conference. The Parity Index goes like this: take the standard deviation of each team's conference wins and divide it by the length of the conference schedule.
So as an example, the 2005 Big South would be
SD(15,11,8,7,7,7,7,3)/16 = .2202
I don't like small numbers, so I multiplied every result by 100. The Parity Index for the Big South was 22.02. It turns out this is about average among conferences. Here's the complete list for last season...
CAA 26.96 Big Ten 26.95 Big West 25.79 Patriot League 25.61 Mountain West 25.61 MEAC 24.85 America East 24.71 Southland 24.53 Big East 24.28 SEC 23.99 Atlantic 10 22.77 WAC 22.53 SoCon 22.41 MidCon 22.32 West Coast 22.26 Big South 22.02 Sun Belt 21.76 ACC 21.10 OVC 20.92 Ivy League 20.56 Big XII 20.47 Horizon League 20.01 Conference USA 19.87 Big Sky 19.84 Pac 10 19.60 Missouri Valley 18.52 NEC 18.43 Atlantic Sun 18.03 MAC 17.27 MAAC 16.56 SWAC 14.81
The PI is a simple measure of how close each conference is to Paul Tagliabue's utopia. If every team finished .500, the conference PI would be zero. (For the record, the 2004 NFL had a PI of 19.25.) In the SWAC's 18 game schedule, every team had at least 5 wins and 6 losses. In the CAA, only one of the ten teams finished within 3 games of .500. The Parity Index may not be the most scientific way to do it, but it appears to be a reasonable way to measure the competitiveness of a conference.
It turns out there isn't much connection to conference parity and home court winning percentage. The correlation between home winning percentage and parity index is negligible. The five conferences with the most parity ranked 25th, 9th, 2nd, 30th and 22nd in home court record last season. The five with the least parity ranked 23rd, 8th, 9th, 15th, and 7th. Historically, the 2003 Ivy League had the least parity since 2000, with the help of one unbeaten and one winless team among their eight. They tied for the worst home record (28-28) in 2003. The 2004 Big Sky had the most parity since 2000, with six of its eight members going 7-7 or 6-8. They finished that season third-to-last in home record.
How does this happen? Probably because that while a team running the table drags the home winning percentage towards .500, those teams in the middle can drag a winning percentage below .500.
OK, let's move on. Now about that WAC race...
Rabid Crowd Theory
07.12.05
There's nothing like an unsubstantiated assertion to motivate me to post.
The principal difference between the ACC and the Big East is the level of home-court advantage. Sure, there are a few dominant courts in the Big East, but you'd be hard-pressed to find a weak one anywhere in the ACC. Even traditional bottom-feeders, such as Clemson and Florida State, can pack 'em in and chase away road teams. - Andy Katz, ACC Summer Session
I've had this theory that I don't think I have expressed here yet: home court advantage isn't much different between, say playing at Duke, as compared to playing at Savannah State. Most of the home court advantage is the result of simply being able to maintain one's normal routine, play in familiar confines, etc. Sure, it's harder to win at Cameron Indoor, but that has much more to do with the team you have to play there than any intimidation by the fans. So even though Katz's comment falls into the common-sense category, it was with skepticism that I read it.
And any skepticism I have can be easily addressed by tallying up how each conference's home teams did in conference play. Here's the list for the 2005 season...
1 Big Sky 42-14 .750 2 MAC 83-34 .709 3 Ivy 38-18 .679 4 Missouri Valley 61-29 .678 5 SEC 65-31 .677 6 Ohio Valley 59-29 .670 7 Patriot 37-19 .661 8 Big Ten 58-30 .659 9 WAC 59-31 .656 9 Big West 59-31 .656 9 MAAC 59-31 .656 12 SoCon 62-34 .646 13 America East 58-32 .644 14 Big XII 61-35 .635 15 Mountain West 35-21 .625 15 ACC 55-33 .625 15 Big South 45-27 .625 15 Sun Belt 50-30 .625 15 West Coast 35-21 .625 20 Pac 10 56-34 .622 21 Conference USA 69-43 .616 22 NEC 60-39 .606 23 CAA 54-36 .600 24 Horizon 43-29 .597 25 SWAC 53-37 .589 26 Big East 56-40 .583 26 Atlantic 10 56-40 .583 26 MidCon 42-30 .583 29 Southland 50-38 .568 30 Atlantic Sun 62-48 .564 31 MEAC 54-45 .545
So yeah, the ACC (15th) was tougher on road teams than the Big East (26th), but what is striking is how random this list seems to be. If a coach takes a job in the Big Sky, he's not going to be complaining about how difficult it will be to play in Pocatello, Missoula, and Cheney. Which means if you buy into this data, then it's hard to support the traditional view of home-court advantage. And if you don't believe the data, then you probably shouldn't be reading this blog. If the "rabid crowd theory" has any validity then there must be a lot of noise contained in the 2005 numbers.
To weed out the noise, let's look at the aggregate conference home records for the last five years combined.
1 Mountain West 192- 88 .686 2 SEC 320-160 .667 2 Big XII 320-160 .667 4 Big Ten 293-147 .666 5 Missouri Valley 296-154 .658 6 MAC 384-201 .656 7 ACC 245-131 .652 8 CAA 271-145 .651 9 WAC 281-151 .650 10 Big South 220-120 .647 11 Big Sky 191-105 .645 12 Ohio Valley 251-141 .640 13 Horizon 219-125 .637 14 Patriot 169- 99 .631 15 Conference USA 343-201 .631 16 SWAC 280-170 .622 17 Southland 311-195 .615 18 SoCon 295-185 .615 19 Big West 265-167 .613 20 Big East 333-211 .612 21 NEC 332-214 .608 22 Atlantic 10 285-185 .606 23 Pac 10 271-179 .602 24 Sun Belt 250-166 .601 25 America East 248-166 .599 26 Atlantic Sun 308-208 .597 27 MidCon 195-133 .595 28 MAAC 267-183 .593 29 Ivy 163-117 .582 30 MEAC 288-207 .582 31 West Coast 155-125 .554
This list should make a little more sense to the folks that think the intensity of the crowd is what matters. Four of the six power conferences hold spots in the top seven for home court advantage. But there are still some oddities like the Big East and Pac 10 being ranked so low, and the respectable WCC being the worst conference for home teams.
So what does this mean? You can take from it what you want. But when I see the Big South with a better home record than the Big East, I have to wonder how much of an impact an intense crowd has. Sure, it has some impact, since there is a general trend for the conferences with the more avid following to be near the top. But the fact that it took five years of data to uncover a weak trend, and that there isn't much consistency for a given conference from year-to-year*, tells me that factors that affect basketball as a whole (travel, change in routine, etc.) have more impact than factors specific to any conference (size/intensity of crowds, or "dominant courts").
*Some support for that idea - the average year-to-year correlation of conference rank in home court win% over the past 5 years is .24. Compare that to the average correlation of RPI rank over the same time of .92. Or looking at it more simply - the average change in RPI rank from year-to-year for a particular conference is 2.7, and for home court rank it's 8.6.
The Value of Ben Gillery
07.05.05
After John Thompson said goodbye to Patrick Ewing and before he said hello to Alonzo Mourning, he had a void at the center position. In light of the quality of the aforementioned players, it was a huge void. In 1987, Thompson brought seven-footer Ben Gillery to Georgetown from the junior college ranks. Gillery, in a word, was a "project" and he never quite panned out. What I remember about him was that he would start a game, be pulled at the first stoppage, and never return. I marveled at box scores where he was listed as a starter, played 2 minutes, and the rest of his line was filled with zeroes. It was like his only purpose was to win the jump ball.
In truth, my memory can't be too accurate, since according to Jazzy J's site, Gillery averaged about eight minutes a game during his career. So the two-minute games must have been rare. Nonetheless, I want to test how important a Ben Gillery as I remembered him would be. How important is it to win the opening tip?
Actually, what I really want to know is this: how important is it to have one more possession that your opponent? When computing possession statistics, by convention it's assumed that each team has an equal number of possessions. But in reality, this doesn't have to be true. Because teams alternate possessions, if one team starts and ends a half with the ball, they can have one more possession than the opponent in each half. This happens in roughly 50% of all games. Winning the opening tip doesn't guarantee you an extra possession for the game, but it certainly increases your chances.
To demonstrate how much of an advantage this is, I'll use the Pythagorean formula. As regular readers have figured out by now, I think this formula can be used to solve any of college basketball's great mysteries. And here's another example.
Let's say teams A and B both average a point per possession. In a 70 possession game, you'd expect each team to score 70 points (totally ignoring defense). So A's expected winning percentage against B would be...
70^10 / ( 70^10 + 70^10 ) = .500
We didn't need to work through this formula to know that Team A has a 50% chance to beat a team equal to it. But what if Team A gets an extra possession? They would be expected to score 71 points in their 71 possessions. Their expected winning percentage in this scenario would be...
71^10 / ( 71^10 + 70^10 ) = .535
So the Gillery effect results in an increased chance of winning of 3.5% in this case. As I said before, winning the tip does not guarantee an extra possession. But in the long haul, teams winning the tip will average about a half a possession more than their opponent. (Actually, for reasons I won't get into it's probably slightly less than that.) Since losing the tip results in a loss of a half possession, it's accurate to say that the tip itself is worth a possession.
Naturally, in a game with fewer possessions, the tip is more valuable. Here's a list of the increased chance of winning in games with various tempos.
Incr. in Poss Win% 85 2.9 80 3.1 75 3.3 70 3.5 65 3.8 60 4.1 55 4.5 50 4.9
So in those methodical Horizon League games, the tip means more than in the relatively frenetic ACC games.
But this is the best case scenario. As teams become more unequal, the extra possession means less. If All-American Team is playing Intramural Scrubs, it doesn't matters who gets the extra possession, All-American Team will win all of the time.
For a more realistic example, let's use teams that average 1.1 and 0.9 points per possession. With each team getting 70 possessions, Team A wins 88.1% of the time...
77^10 / ( 77^10 + 63^10 ) = .881
Give Team A an extra possession and that figure improves to 89.6...
78.1^10 / (78.1^10 + 63^10 ) = .896
That's a difference of only 1.5%, compared to 3.5% for the game between equal teams.
This is more than we really needed to know on the impact a seldom used Georgetown center had on the game over 15 years ago. Nonetheless, this exercise illustrates that the jump ball is more than a ceremonial start to the game.
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