As a note: I number all 140 games based on a simple formula:
- Game start in GMT.
- If two or more games start at the same time in GMT, the game further to the east gets listed first.
I could probably do this by the order (that makes no sense) in which the games are listed on USCHO’s week-by-week results, or I could do it series-by-series. This is the way that I’ve chosen to do it the last three seasons.
- Game 83: Minnesota State 2, Michigan Tech 2 (OT)
- Game 86: Michigan Tech 3, Minnesota State 1
- Game 91: Minnesota State 8, Lake Superior 0
- Game 93: Minnesota State 5, Lake Superior 1
In “Re-thinking the Goal Differential Bonus“, I was responding to a criticism of the wise Tim Braun of Tech Hockey Guide, who was wondering why Mankato’s destruction of Lake State netted them more points than the Huskies picking up three points against the Mavericks. It’s a fair question! Let’s do the math.
As a starting point: the current main constant in BELOW calculations, generally referred to as K, is 40. The multiplier of the goal-differential is 10.
- Game 83 BELOWs: Minnesota State 1698, Michigan Tech 1580.
- Game 83 Expected Values: MSU .664, MTU .336.
- Game 83 Results: MSU .500, MTU .500.
Again from calculating BELOW, we take the difference between the expected result and the actual result and use that to calculate a new BELOW.
For Mankato: BELOW 83,7 = 1698 + (40 + 10*0) * (.500-.664) = 1691.
To deconstruct that:
- We start with Mankato’s BELOW coming into the game.
- We calculate our volatility factor by adding the base constant (40) to the goal multiplier (10) by the goal differential (0).
- We calculate the final factor by comparing the real result to the expected one. A positive value here means that the team outperformed the results.
Multiply and add and you’ll see that Mankato loses 7 BELOW points by tying with Tech. The two teams are indeed pretty far apart in BELOW, but a tie just reverts them to the mean a bit. Is that enough? We’ll consider that below.
Consider the range of possible outcomes for Mankato’s BELOW on Game 83:
- Mankato wins by three or more goals: +24
- Mankato wins by two goals: +20
- Mankato wins in regulation by a goal: +17
- Mankato wins in overtime: +4
- Mankato tie: -7
- Mankato loses in overtime: -21
- Mankato loses by one goal in regulation: -33
- Mankato loses by two goals: -40
- Mankato loses by three or more goals: -46
Because the difference between the two teams is significant, decisive results move the teams closer fairly significantly. A three-goal Huskies win makes the margin 1652 to 1626 — a vastly different affair.
So with that said, the Friday result didn’t change a lot in terms of BELOW, because the expected value of each team is pretty close to the tying result (+/- .164).
What about Saturday?
- Game 85 BELOWs: Minnesota State 1691, Michigan Tech 1587.
- Game 85 Expected Values: MSU .647, MTU .353.
- Game 85 Results: MSU 0.00, MTU 1.000 by two goals.
BELOW 84,8 = 1587 + (40 + 10*2) * (1.000-.350) = 1625.
That means that Tech, on the weekend, gained 45 BELOW points — but Mankato also lost those points. A gap that was 118 points was now just 28.
Now you know what? I just found an error in my spreadsheet, which makes me want to hurl my computer across the room. I had done a sanity check that Tech’s BELOW had gone up with the result, but I hadn’t fully audited the equation. That, Tim, is what addresses your question about the result.
So I guess I get to audit this again! That’s what I get for making the spreadsheet on midnight shifts.
Let’s complete the exercise, though. Now to Mankato-Lake the next weekend, Games 91 and 93:
- Game 91 BELOWs: Minnesota State 1652, Lake Superior 1430.
- Game 91 Expected Values: MSU .739, MTU .261.
- Game 91 Results: MSU 1.000, LSSU 0.000 by eight goals (capped at three).
BELOW 91,7 = 1652 + (40 + 10*3) * (1.000-.739) = 1671.
Even though it was a huge win, Mankato was so much of a lock that it barely moved the needle. Again, compare that result to Game 83: +24 there vs. just +19 here.
- Game 93 BELOWs: Minnesota State 1652, Lake Superior 1430.
- Game 93 Expected Values: MSU .777, MTU .233.
- Game 93 Results: MSU 1.000, LSSU .000 by four goals (capped at three).
BELOW 93,7 = 1671 + (40 + 10*3) * (1.000-.777) = 1686.
That’s also worth noting: because the Friday result said, “Wow, the Mavs are way better than the Lakers,” the marginal improvement on Saturday was smaller.
So on the Mankato @ Tech weekend, the Huskies picked up 45 points; on the Lake @ Mankato weekend, the Mavericks picked up just 34. Improving in BELOW is as much or more of a matter as who you beat as it is by how much, but it’s also a cumulative, relative measure of value.
Mankato’s high BELOW this year is 1744, and they have eight weeks above 1700 (and a ninth at 1698), so bringing that down will take more than just one good weekend for the home side in Houghton.
I hope that this answers some questions. Hopefully this is the only error in my spreadsheet.
Lastly, on the topic of goal differentials: what if I nix the multiplier completely? That weekend goes +36 for the Huskies (remember, there are lots of other games in there), while the Mavericks pick up +19. As to whether a marginal multiplier is “right”, I’d have to do something like error minimization between the actual and expected results. That’s … a lot more math, and I’d have to be diving into Minitab or Matlab to make that work.