None of all this rankings gee-gaw is worth it if you don’t try to do something with it, after all. We’re pretty far along in the season, but given the unbalanced schedule of the WCHA, it’s pretty difficult to figure out how things will go.
Except when you let math join the picture. I’ll construct a narrative below, but here are the BELOW-based predictions for the three league series this weekend:
2015-16 BELOW: Week 16 PredictionsHere's the bottom-line for the math this week. Each series starts with the current BELOW, randomly plays the game, and then calculates a BELOW for each team post-Friday's action to do another random play of the Saturday game.
|Series (1000 Trials)||Visitor W+W||Visitor W+T||Split (W+W or T+T)||Home W+T||Home W+W|
|UAH @ FSU||7.9%||5.6%||31.1%||13.9%||41.5%|
|UAF @ NMU||8.6%||6.9%||33.1%||14.2%||37.2%|
|MSU @ MTU||30.9%||13.3%||37.1%||9.0%||9.7%|
How could this week play out?
We all know the drill when trying to figure out how your favorite team is going to do: what results most favor my team? If, like me, you are a UAH fan, you are rooting for Northern Michigan to sweep Alaska while your beloved Chargers, donning the light jerseys on the road for the first time in years, stampede into Big Rapids to pick up the sweep of Ferris State.
Hey, it could happen, right? That combination puts UAH at 5-11-2 (12 points), alongside the Nanooks at 4-12-4 (12 points) and two games in hand. Furthermore, Alaska-Anchorage is idle and would be at 12 points (with two games on UAH and four on UAF, two of which are head-to-head).
But how likely is that to happen, anyway? Jack and Shane note that Ferris has tended to split this season, and the only team that UAH has swept on the road (or at all) is Lake Superior. (That series was pretty much 50-50 from a BELOW perspective, and 50-50 means that each team sweeps about 25% of the time.)
With FSU 5th in BELOW after Week 15 at 1509 — again, a little bit better than a theoretical league average of 1500 — and UAH dead last at 1357, the hopes of UAH’s fans seem faint. In fact, you expect Ferris to win 73.2% of the time.
As you’ll note from above, those hopes are indeed faint: UAH sweeps about 7.9% of the time, while UAF is swept about 37.2% of the time. I don’t have the chain of “how often UAH wins twice while UAF loses twice” into the system just yet — I should by next week — but basic probability multiplies those two numbers and says that UAH’s desired scenario happens 2.9% of the time, which is a lot better than Powerball odds but still not very good. #UnitedWeCharge
A league-wide look at the weekend
Going back to the probabilities above, let’s take the most-likely scenario from the predictions table above and project new standings:
|Team||Wk 16||Rk | W-L-T (Pts)||Week 16 BELOW|
|MSU||1-1-0||1st | 11-3-4 (26)||1693|
|BGSU||Off||2nd | 9-3-4 (22)||1636|
|MTU||1-1-0||3rd | 10-7-1 (21)||1601|
|NMU||2-0-0||4th (tie) | 8-6-4 (20)||1557|
|BSU||Off||6th | 7-8-3 (17)||1548|
|FSU||2-0-0||4th (tie) | 9-7-2 (20)||1537|
|LSSU||Off||7th | 5-5-4 (14)||1471|
|UAA||Off||8th (tie) | 5-7-2 (12)||1442|
|UAF||0-2-0||8th | 4-12-4 (12)||1395|
|UAH||0-2-0||10th | 3-13-2 (8)||1322|
I don’t know about you, but that mostly feels right to me.
The man behind the curtain
I should probably end this by talking about how I’m coming up with these predictions. It’s pretty easy:
- I started with the already-calculated BELOW for each team.
- I defined an Expected Value for each team in each Friday night game based off of those BELOWs.
- I created a set of bands for each of the five results that can happen in a WCHA men’s ice hockey game: win, overtime win, tie, overtime loss, and loss. The band is skewed to favor the better team (more in a later post).
- I use a random number generator that goes 0.000-1.000. This random value is different for every game in the spreadsheet.
- I use the random number and slot it in the bands developed in #3 above.
- I apply that result to each team, re-calculate BELOW, and carry that result to the Saturday game, repeating Steps 1-5.
- I calculate a final BELOW for the weekend for each team.
I do this process — calculate, band, roll dice, slot, calculate, repeat — 1,000 times. So there are 1,000 Friday games based on the history that exists to-date, and then there are 1,000 theoretical Saturday games based on a single, theoretical Friday game. This is a crude Monte Carlo simulation.
I anticipate some questions:
- Why do you have just 1,000 runs? Simply, it’s all my little MacBook Air could handle when I was working on this during my spare time at work. Now that I’m doing this exclusively at home on a much more powerful machine, I can probably do more with it.
- Have you done this for all weeks of the season? Nope, I’ve just done this week. I pretty much finished this an hour ago and started pecking this so I could get it out before drops tonight.
- Will you play out all the scenarios more than 1,000 times and do it for all weeks? That’s the goal. I even want to have it where I can update day by day with game results.
- Will you make this spreadsheet public? Yeah, maybe in another week or two.
- Will you develop this so it can be a tool that I can play around with on the web to run scenarios? Sure, I’m hoping to try that and do that by the end of the season. If not then, it’ll be up for 2016-17.