Thursday, February 23, 2006

Seeds and tiebreakers

UPDATED with CORRECTIONS!

Thanks to ORU Tex for pointing out a serious error. The changes can be found in bold.

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Thanks to tmh8286 on the ORU message board, we are reminded of the tiebreaker rules for any of you who want to make sense of the seeding possibilities in the final week of the conference regular season.

And thanks to Blevins on the same board, I now know I was wrong to state in an earlier article that IUPUI has locked up the #1 seed, because they haven't:

We're NO. 1 if...

We win out and
IUPUI loses out and
SUU wins out and
Valpo loses out and

because...

if SUU wins out, they leap-frog Valpo in the standings, therefore giving us the tiebreaker due to our sweep of Southern. UMKC never factors in because we both swept the Kangaroos.

So it's a bit of a longshot, but very possible considering IUPUI and Valpo both finish on the road.


Hence, I thought it would be a good time (before tomorrow's games) to be a little more diligent in my "reporting".


School W-L Home Away Sweeps Swept By Split
------ --- ---- ---- ------ -------- -----
IUPUI 13-1 8-0 4-2 OU,UMKC,WIU,VU,CC ORU
ORU 11-3 7-0 4-3 CSU,SUU,OU,UMKC WIU,IUPUI
UMKC 9-5 5-2 4-3 CC,CSU,OU IUPUI,ORU SUU
Valpo 8-6 6-2 2-4 CC IUPUI OU,SUU,WIU,CSU
SUU 7-7 5-1 2-6 WIU ORU VU,CSU,CC,UMKC
CSU 6-8 4-2 2-6 CC,WIU ORU,UMKC SUU,VU
OU 5-9 3-5 2-4 WIU IUPUI,ORU,UMKC VU,CC
WIU 3-12 2-5 1-7 CC OU,IUPUI,VU,SUU,CSU ORU
CC 2-13 1-6 1-7 UMKC,VU,WIU,CSU, SUU,OU
IUPUI


IUPUI has games left at SUU and CSU
ORU has a home game left against VU and a game at CC
UMKC has a home game left against VU and a game at WIU
VU has games left at UMKC and ORU
SUU has home games left against IUPUI and OU
CSU has home games left against IUPUI and OU
OU has games left at CSU and SUU
WIU has one home game left against UMKC
CC has one home game left against ORU

Both ORU and IUPUI have clinched at least the #2 seed, so one of them will be #1 and the other #2. UMKC is the only one who can tied with either one of them and they lose the tiebreaker with either one.

If IUPUI loses their last 2, ORU wins their last 2, Valpo loses their last 2, and SUU wins their last 2, the following would be the top-half standings (we'll give UMKC a win over WIU as well, since they don't figure in the tie-breakers)


ORU 13-3 1-1 vs. IUPUI
IUPUI 13-3 1-1 vs. ORU
UMKC 11-5 0-2 vs. IUPUI, 0-2 vs. ORU
SUU 9-7 1-1 vs. IUPUI, 0-2 vs. ORU -------- ORU wins the tiebreaker
VU 8-8
...


Thus ORU would be #1, IUPUI #2 (either way, both would play Saturday night), UMKC would be #3, SUU #4, and VU #5. Even if UMKC loses at WIU, they would still be 10-6 and have the #3 seed in this scenario.

Now, suppose VU wins one of their remaining games. If it is against ORU, then IUPUI has the #1 seed without any tiebreaker, and ORU ends up with the #2 seed. UMKC would be 11-5 or 10-6 with the #3 seed. We could tackle the question of who gets the #4 seed between VU and SUU, but it really doesn't matter. They'd play each other Sunday night on a neutral court either way.

If instead, VU beats UMKC but loses to ORU, then that question DOES become important because we have to figure out which team to use as tiebreaker first. If VU finishes higher than SUU, then IUPUI wins the tiebreaker because they swept VU while ORU split with them.

So in this case, the standings would be:

ORU 13-3
IUPUI 13-3
UMKC 10-6 or 9-7 depending on WIU game
SUU 9-7
VU 9-7
CSU 8-8 or 7-9 depending on OU game
OU 6-10 or 5-11 depending on CSU game
WIU 4-12 or 3-13 depending on UMKC game
CC 2-14

Assuming UMKC beats WIU, VU split with ORU, but SUU was swept by ORU, while VU was swept by IUPUI, but SUU split with them. In this case, we'd a deadlock condition, which means the deadlock has to be broken (see below for analogy to computer science) by swapping out the lower priority tie-breaker (and that would be this VU-SUU tie). In that case, we'd have to look to CSU, and in this scenario, ORU swept CSU while IUPUI split with them, so ORU gets the #1 seed.

If instead UMKC loses to WIU, we'd have the same thing as in the preceding paragraph, except with a 3-way tie, so ORU gets the #1 seed once again.

So the only ways that IUPUI secures the #1 seed is by winning one more game (on the road) OR by Valpo finishing 1 game ahead of SUU.

Phew...

UMKC can lock up the #3 seed by beating VU tomorrow, giving them a 2 game lead with 1 game to go, never mind that they would also own the tiebreaker having swept VU. If they tie with VU, it will have to be in part because VU beats them tomorrow. Valpo would also have to beat ORU or UMKC lose to WIU. If both happen, VU gets the #3 seed, and UMKC would play in the 4-5 game. If VU beats ORU, then both teams would be 10-6. Moreover, having split their 2 games, we'd have to look elsewhere for a tiebreaker. Both were swept by IUPUI, but VU would have swept ORU while UMKC was swpet by ORU, so VU would get the #3 seed in that scenario as well. If instead, UMKC loses to WIU, both teams would be 9-7, but even then, VU would still split with ORU, so either way, VU gets the #3 seed. Of course, if VU loses to ORU and UMKC beats WIU, then UMKC still gets the #3 seed.

Except(!) - If SUU also finishes 9-7 (VU beats UMKC and loses to ORU, UMKC beats WIU, and SUU beats OU and IUPUI), then we have a 3 way tie between UMKC, VU, and SUU. VU's record among the 3 in this case is 2-2, SUU's record is 2-2, and UMKC's record is 2-2, so we look at either IUPUI or ORU. VU and UMKC are 0-2 against IUPUI, but SUU is 1-1, so that would give SUU the #3 seed. That again leaves VU and UMKC playing each other, and who cares which is which? On the other hand, VU is 1-1 against ORU, while UMKC and SUU are both 0-2 against ORU, so that would give the #3 seed to VU, and UMKC and SUU would play each other.

If IUPUI beats CSU, then it would go to SUU.

If, on the other hand, IUPUI goes 0-2 (also losing to CSU) and ORU also beats CC, we have a mess:

ORU 13-3
IUPUI 13-3
UMKC 9-7
VU 9-7
SUU 9-7
CSU 8-8 or 7-9 depending on OU game
OU 5-11 or 6-10 depending on CSU game
WIU 3-13
CC 2-14

We have to break the ORU-IUPUI tie first. Again they split with each other, but who do we look to next to break the tie????? At first glance it looks like an unresolvable circularity (need to break the UMKC-VU-SUU tie to break the IUPUI-ORU tie, but the IUPUI-ORU resolution depends in turn on the UMKC-VU-SUU resolution).

Well, we can look at each one individually and see if we come up with the same result occurs, but I think we know already it won't:

UMKC: Both 2-0
VU: IUPUI 2-0, ORU 1-1
SUU: IUPUI 1-1, ORU 2-0

Unfortunately, both VU and SUU break the tie and each one breaks it the opposite way. We have ourselves a deadlock condition.

All I can do as a software engineer is fall back on my computer science background. The way to resolve a deadlock is through priorities. Obviously, the top-most tiebreaker has the priority, and as describe above, CSU breaks the tie in ORU's favor.

Now we can break the 3-way tie.


VU is 1-1 against ORU while the other 2 are 0-2, so VU gets the #3 seed, and UMKC would play SUU in the 4-5 game.

WOW!!!! .... OK, hangin' in there with me?

VU has clinched at least a #6 seed since they are 3 games ahead of Oakland. Likewise, UMKC has clinched at least the #5 seed, since they are 3 games ahead of CSU. Again if VU ends up in a two-way tie with SUU at 9-7 (we already covered the 3-way tie with UMKC above), then they play each other and who cares which is which? If they end up tied together with CSU at 8-8, then VU's record in the 3-way tie is 2-2, SUU is 2-2, and CSU is 2-2. At this point it matters if SUU's one win is against Oakland or IUPUI. If Oakland, then IUPUI has #1 seed and is first up in any tiebreakers. All 3 were swept by IUPUI so we go to ORU, who swept CSU and SUU but split with VU, hence VU would have the #4 seed, and with SUU splitting with CSU, it would fall next to UMKC to break the tie. SUU split with UMKC, but CSU was 0-2 against them, so SUU would play VU and CSU would get the #6 seed.

If, on the other hand, SUU's one win was against IUPUI, we have another mess. SUU would be 1-1 against IUPUI while VU and CSU are 0-2, but VU would be 1-1 against ORU while SUU and CSU are 0-2 against them. So it depends on who wins the tiebreaker between IUPUI and ORU. In this scenario, IUPUI would definitely be 13-3 because they have to lose to CSU for CSU to be 8-8. If ORU doesn't go 2-0 - i.e., if they lose to CC - then it would be IUPUI and SUU would have the #4 seed. Since VU split with CSU, it would fall to ORU to break the tie, with VU 1-1 and CSU 0-2, so again VU would play SUU and CSU would be #6.

If ORU DOES go 2-0, then we have:

ORU 13-3
IUPUI 13-3
UMKC 11-5 or 10-6 depending on WIU game
VU 8-8
SUU 8-8
CSU 8-8
OU 6-10
WIU 3-13 or 4-12 depending on UMKC game
CC 2-14

We have to break the ORU-IUPUI tie first. Again they split with each other, they both swept UMKC, but who do we look to next to break the tie?????

Here we go again...

VU: IUPUI 2-0, ORU 1-1
SUU: IUPUI 1-1, ORU 2-0
CSU: IUPUI 1-1, ORU 2-0

All 3 teams break the tie this time, but unfortunately they don't all break it the same way! We have our deadlock situation again. Since we've resolved that above, ORU gets the #1 seed.

Now back to breaking this tie: VU wins the tiebreaker based on splitting with ORU, so they get the #3 seed. This leaves a tie between CSU and SUU. SUU split with UMKC while CSU was swept by them, so SUU gets the #5 seed and CSU gets the #6 seed..

Blimey...

SUU, CSU, and OU have all clinched at least a #7 seed. If they end up in a 3 way tie at 7-9, it will mean that IUPUI finishes 14-2 and has the #1 seed.

Head-to-head-to-head: OU would be 3-1, SUU would be 2-2, CSU 1-3, so CSU would end up with the #7 seed.

Head-to-head: OU split with SUU. Both were swept by IUPUI and ORU, both split with UMKC and VU, so CSU would break the tie with OU 2-0 vs. SUU 1-1, giving OU the #5 seed and SUU the #6 seed.

If OU and CSU end up in a 2-way tie at 7-9 or 6-8, OU wins the tiebreaker by having swept CSU and would get the #6 seed.

Western Illinois has simply clinched the #8 seed because they swept CC. So they will open either against ORU or IUPUI.

Let me see if I can summarize all this....

IUPUI: #1 if they to 1-1 or 2-0 OR if ORU goes 1-1 or 0-2 OR if VU finishes ahead of SUU. Otherwise #2.

ORU: #1 if they go 2-0 AND IUPUI goes 0-2 AND SUU goes 2-0 and VU goes either 1-1 or 0-2. Otherwise #2.

UMKC: #3 if they beat VU OR they go 1-1 and VU goes 1-1 OR they go 0-2 and VU goes 1-1 and SUU goes 2-0. Otherwise #4 or #5.

VU: #3 if (VU goes 2-0 AND SUU goes 1-1 or 0-2) OR (VU goes 1-1 and UMKC goes 0-2 and SUU goes 1-1 or 0-2) OR (VU goes 0-2 AND CSU goes 2-0 AND SUU beats IUPUI and loses to OU). Otherwise #4 or #5.

SUU: #3 if UMKC goes 0-2 AND SUU goes 2-0 AND (VU goes 1-1 AND IUPUI beats CSU) OR (VU goes 0-2 AND IUPUI goes 0-2 AND ORU goes 2-0). #6 if they go 0-2 AND CSU goes 1-1 AND OU goes 2-0. Otherwise #4 or #5.

CSU: #4 or #5 if ORU goes 2-0 AND IUPUI goes 0-2 AND VU goes 0-2 AND CSU goes 2-0 AND SUU goes 1-1. #7 if they go 1-1 AND SUU goes 0-2 AND OU goes 2-0. Otherwise #6.

OU: #5 if they go 2-0 AND SUU goes 0-2 AND CSU goes 1-1. #6 if SUU wins at least 1 AND (OU goes 2-0 AND CSU goes 1-1) OR OU goes 1-1 AND CSU goes 0-2). Otherwise #7.

WIU: #8

CC: eliminated from tourney field.

Clear as mud?

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