[Lax] Designing a lacrosse-specific PWR

I'm starting this discussion here rather than on laxpower because I wanted to clarify some of the discussion of appropriate criteria without being buried in the rants going on over the Hofstra-Duke discussion. The current PWR-for-lax page just uses the hockey selection criteria, but the lacrosse handbook spells out its own selection criteria, and we could build a system around that. Here are the primary and secondary criteria, in the order listed:

1. Record vs teams ranked 1-5, 6-10, 11-15, etc. This is the infamous "quality wins" criterion, and I've been trying to find a way of handling it which is more even-handed to teams playing a smaller number of games against the top teams. My idea for a compromise of reasonableness without being too complicated is this: compare winning percentages against the top 5 teams in the RPI; if that's a wash, look at the top 10; if that's still a wash, look at the top 15, etc. There are some fine details to be worked out, like is 1-2 considered equivalent to 2-4, how does 0-0 get considered, and so forth. To throw a bone to the NCAA's apparent focus on wins over losses, how about looking at number of wins if winning percentage is tied, and number of losses if both teams are winless. That way 2-0 > 1-0 > 3-1 > 4-2 > 2-1 > 3-2 > 3-3 > 2-2 > 1-1 > 2-3 > 2-4 > 1-2 > 1-3 > 0-0 > 0-1 > 0-2. This also ensures that the only way teams can be tied is if they have identical records, which avoids the situation where team A is 2-4 against the top five and 2-1 against the next five, while team B is 1-2 against the top five and 3-2 against the next five, so top five is a wash and there's the question of whether to compare them on record vs 6-10 (so 2-1 > 3-2) or record vs 1-10 (so 4-5 < 4-4).
2. Strength of schedule, as measured by opponents' average winning percentages vs other teams. I really hate this criterion, since it's not there to balance any bias towards teams with good winning percentages against tough schedules, and the RPI already takes strength of schedule into account, some say too much. I would prefer to drop it, or perhaps use strength of schedule rather than RPI as the tie-breaker in unresolved PWCs.
3. Ratings Percentage Index. For lacrosse purposes, we should use the NCAA's default 25:50:25 weighting.
4. Head-to-head results. As I mentioned over on laxpower, this is effectively more heavily weighted in hockey where a team can go 3-0 against a conference opponent, making head-to-head count as multiple criteria. On the other hand, the lack of ties means a single game will always produce a result, and many season seried in hockey will end up 2-1, 1-0-1, 2-1-1, etc. Also, if we drop strength of schedule and only have four criteria, this one becomes worth more.
5. Common opponents.

So for example, here are some sample PWCs in my best first cut at this system:

Duke/Hofstra:
Record vs quality opponents: Duke 1-3 > Hofstra 0-2
RPI: Hofstra .6394 > Duke .6299
Head-to-head: Hofstra W
Common Opponents: Hofstra 1-2 > Duke 0-3
RESULT: HOFSTRA 3 > Duke 1

Cornell/Hofstra:
Record vs quality opponents: Cornell 1-2 > Hofstra 0-2
RPI: Hofstra .6394 > Cornell .6380
Head-to-head: N/A
Common Opponents: Hofstra 0-1 = Cornell 0-1
RESULT: CORNELL 1 + .6115 SOS > Hofstra 1 + .6394 SOS

Yale/Hofstra:
Record vs quality opponents: Yale 1-0 > Hofstra 0-2
RPI: Hofstra .6394 > Yale .6219
Head-to-head: N/A
Common Opponents: Hofstra 4-1 = Yale 4-1
RESULT: YALE 1 + .6155 SOS > Hofstra 1 + .6394 SOS

Loyola/Hofstra:
Record vs quality opponents: Hofstra 0-2 > Loyola 0-3
RPI: Hofstra .6394 > Loyola .6110
Head-to-head: Loyola W
Common Opponents: Hofstra 6-1 = Loyola 6-1
RESULT: HOFSTRA 2 > Loyola 1

Yale/Georgeotown:
Record vs quality opponents: Yale 1-0 > Georgetown 0-1
RPI: Georgetown .6644 > Yale .6219
Head-to-head: N/A
Common Opponents: Georgetown 3-1 > Yale 1-3
RESULT: GEORGETOWN 2 > Yale 1

Thoughts?

Looks great John!

However, I honestly need to ask if it is worth the effort. Rather what is the point of the effort?

If the point is to model the behavior of the committee, it probably isn't worth the effort given the post-hoc coaches ranking clause in the handbook that allows the committee to toss the statistical results if they don't like them.

Given that, on the whole, the lax criteria suck sweaty monkey balls, is it worth designing a rational model for a system that is based on illogical criteria?

Personally, I'd rather use the hockey PWR as a way to illustrate how messed up the lacrosse selection process is. Admittedly, with this goal, fixing known PWR flaws might be a good idea. Namely, replacing L8 with a declining function and maybe fixing the now I'm a TUC, now I'm not problem.

If you truly want to implement this system, the primary criteria should get 2 pts while the secondary criteria get 1 point.

Primary
* record against ranked opponents
* SoS
* RPI

Secondary
* common opponents
* head to head

Of course, the handbook wording makes it sound like secondary criteria are to be used as tiebreakers.

Yes, the criteria themselves are poor, but weighing the two secondary criteria along with two of the primary ones, using winning percentage rather than total wins for analysis of top 5 games, and relegating schedule strength to tie-breaker status makes them at least non-stupid.

The thing about using the hockey PWR is that people just say "that's a hockey system" and ask why we're trying to use our criteria to judge their sport. Plus if we wanted to just imposr our favorite criteria on lacrosse, I'd say take the top N teams in the KRACH and be done with it. No fuss, no muss.

By using the pairwise comparison method and taking the lacrosse criteria as a starting point, we can illustrate how an objective method could be applied using the criteria that are deemed important by the lacrosse PTBs.

I'm thinking in retrospect that perhaps the criterion should be modified when one of the teams is undefeated, to look first at wins minus losses, then at winning percentage. So in Perl terms

if (($a->pa = 0 and $a->pf > 0) or ($b->pa = 0 and $b->pf > 0) {
    ($b->pf - $b->pa) <=> ($a->pf - $b->pa)
        or $b->pct <=> $a->pct;
} else {
    ($b->pf * $a->pa) <=> ($a->pf * $b->pa)
        or $b->pf <=> $a->pf
        or $a->pa <=> $b->pa;
}

That means that 3-0 > 4-1 > 2-0 > 3-1 > 4-2 > 1-0 > 2-1 > 3-2 > 3-3 > 2-2 > 1-1 > 2-3 > 2-4 > 1-2 > 1-3 > 1-4 > 0-0 > 0-1 > 0-2 > 0-3.

I think the problem with this is that there are some pathalogical examples like
2-1 > 5-3 (winning percentage)
5-3 > 1-0 (wins minus losses)
1-0 > 2-1 (winning percentage)
that make it no longer an ordering relation.

John T. Whelan '91 wrote:

The thing about using the hockey PWR is that people just say "that's a hockey system" and ask why we're trying to use our criteria to judge their sport.

You'd think so. But actually, many of the more thoughtful posters on laxpower are starting to buy into the PWR after I've explained it 3 or 4 times.

Many fans recognized that the current criteria are broken, while many more are at least willing to listen if you actually engage them in a rational discussion of the logic behind the system.

Still, your point remains valid, the lax PTB are never gonna switch to the PWR given that it "wasn't invented here." That having been said, if enough fans bitch loud enough about the quality win horseshit, maybe the committee will actually make some changes that at least move in the right direction.

If we can show people that an impartial, consistant method of selecting a field is a good thing and that such a system exists and is actually being used in college athletics, can that be a bad thing?

JTW,

I don't know if you are aware of this, but the

[www.e-lacrosse.com]

page has a link to the RPI....and it is to your page!

This may have been answered elsewhere, but, given the AQ's, how would the results using your hockey PWR formula have differed from what actually happened (seedings aside)?

Seedings via PWR

1. JHU v. (8. Princeton / 9. Fairfield)
2. Syracuse v. (7. Cornell / 10. Stony Brook)
3. Georgetown v. (6. UMass / 11. Manhattan)
4. UVa v. (5. Hofstra / 12. Hobart)

Actual seeding

1. Hopkins v. (8.UMass / 9. Fairfield)
2. Syracuse v. (7. Duke / 10. Hobart)
3. Virginia v. (6. Cornell / 11. Stony Brook)
4. Princeton v. (5. Georgetown / 12. Manhattan)

Heh, what I like about it is that Cornell is (rightfully) highlighted; visitors are probably scratching their heads trying to figure out what the significance of that is.

Congradulations John. Does this mean you've made the big time ?

No, the mention he gets on the Swami's site is what means he's made the big time! )