Engineers build model bridges and automobiles to place them into wind tunnels. Economists create social programs and test them in computer simulations. Mathematicians produce formulaic functions to demonstrate relationships between variables. And Game Theorists construct scenarios, “games,” that mimic conditions in the real world to offer insight. I spent a few hours conceiving a game that mirrors the NPI as it pertains to Men’s Volleyball. It’s analogous for how points flow to its participants based on a player’s choices and actions. I thought describing a simple child’s game might be a starter to dive into what I’ve learned about the real thing. Turned out a little long & a little wrong.
I called it “Noisy Point Incentives.” i.e. The NPI game. It’s not wrong in spirit because it does fairly represent the numerical flow of NPI points for any volleyball team. It’s wrong in context, though. In NPI the game, a player takes a turn by choosing a token with a value on it, but in D3MVB, business partners come together to schedule a match. The token can’t say, “No, don’t choose me” in the game, but in volleyball, one business partner can say, “No, it’s not good business sense for me to play you.” The game makes it a self-centered pursuit by a player to optimize a score incentivized by that motivation alone. However, as seen through the lens of the NPI, the second is nothing like that. An opponent isn’t prey. Both partner’s interests don’t need to be perfectly aligned, nor usually are they. Yet any one’s interest should not completely trump the others without transparency for the arrangement as it relates to NPI, either. And therein lies a problem.
The NPI’s system doesn’t balance risk and reward in a way that cultivates healthy competitive incentives. The risk outweighs the reward by too much in its current form. And to make matters worse, this flaw is most accentuated nearer the bubble, the one place it needs to be at its best because the NPI’s endgame is choosing at-large bid recipients who live there. Let me explain by sharing a story of #10, the consummate bubble team in the land, who not only forecasts the NPI values he’d earn with every win or loss against any of the top 80, but he also knows the probability for his team to have won or lost any of them, too. (Courtesy of the T100 metrics model which has been shown to be pretty decent at that.) Focus on the graph’s shape first, and then just three matches from it indicated by the gold, red, and green points:
This is what it looks like if playing out the string from a purely NPI metric mentality…
What initially was believed to be an “elegant” piece of math, I now discover offends for its lack of risk vs. reward balance. This is a direct result of the win probability rate of change which exists in MVB. Even if the NPI ends up offering reasonable at-large bids to teams which seem to deserve them in the early years, there is little chance its incentive structure will be good for the game in the long run, acting like a journalist who embeds himself in the story only to change its trajectory, or a scientist whose bias taints an experiment.
What cultivates this lack of balance in the NPI? How about I choose a random team from the landscape – The 48th best, for example. (see the graphic below)
Look left to see their NPI metrics getting larger, and look right to see them getting smaller. They often “squish” themselves from the low 70’s down to the high 20’s, left to right, with 50 dead center above the “middle of the pack.” i.e. 64th for MVB. Inversely, you see win probabilities for the team you chose go from 50% approaching 0% by scanning left, and from 50% approaching 100% scanning to its right. Demonstrated earlier, Expected Values (EVs) are found by multiplying these variables.
In math when you multiply an increasing function by one that decreases, you arrive at a new one which often has a maximum value. The simplest version of this is (x)(-x) = -x2, an “n shaped parabola” has a maximum turning point.” In every EV graph for the NPI system the maximum average NPI reward for a match is produced by playing progressively weaker teams, but that isn’t the most egregious trait. This is seen by noticing where the minimums crater to the left. The rate at which win probability reduces doesn’t allow the EV to catch up because of a slow increasing rate of the NPI in that moment. Who wants an incentive structure for teams to prefer playing those significantly weaker than themselves while needing to avoid others ranked just a few spots better because there’s not enough reward for that risk?
The best balance for risk and reward is achieved when incentivizing teams to play others closest to their own rank. When the turning point of an EV graph is right above any team in the landscape, then better balance exists. Funny thing is that its not only better for rating/reward systems but its better for volleyball competition and spectating on the whole, too. Everybody wins with that type of incentive structure!
Another slide to point out the expected NPI value of bubble teams competing against each other can be seen below. The top edge of the red area is #7’s EV curve and the bottom edge is the #17’s EV curve. Take note of which ranked opponent each maximizes its NPI points on average. (Those who want to point out the bubble really is only half that large, I contend there are no less than double that who think they are worthy of a bubble before the season begins.)
Every earlier attempt to study NPI had a “backwards design” focus – Analyzed by first looking at who it would choose for at-large bids, then to study the differences between those it would and those it wouldn’t. That is how I came to know its top 8% ranked is unlikely to be too flawed most years, and why I suggested it may infrequently produce an epic fail once every 5 yrs or so. Backwards design is what I see everybody doing across all D3 sports on the internet as they write about it on their blogs, particularly D3MBB. Theirs is a critical analysis of the output to understand where it diverges from the previous selection system. It is what our committees were asked to do when they back tested the previous 3 years to see how its results would have been different from their decisions, too. All backwards designed.
Listening to a “Freakonomics” podcast recently I was reminded how Steve Levitt, the Economist who co-authored the book by the same name, would always tease the truth by focusing on incentives. It challenged me to create a forward design “thought experiment.” I have never been “an ends justifies the means” kind of guy and I was also interested in seeing a different perspective of this construct called NPI. A Steve Levitt quote was a constant reminder as I forged ahead, “An incentive is a bullet, a key: an often tiny object with astonishing power to change a situation.” It is fundamental to everything I’ve offered in this post. The formulas forecasting rank to NPI and win-probability might not be perfect and their values might have smallish margins of error. However, there is no denying the behavior of these EV graphs, where their valleys and peaks are formed. This model shows what people most interested in the NPI will come to know about it moving forward, though it would take a couple years for them to empirically see it. Others would never have known because they probably don’t even care. It’s okay not to care, but not okay, not to know. When your team is sought out for a match there is lots to consider. Ignoring this one thing is not good for the sport, nor is it good for your team. Though feel free to minimize it to any degree you’d like.
I do have concern it will influence scheduling behavior in negative ways depending on a team’s circumstances. To whatever degree the future NPI discourages matchups stakeholders most want to see played, but aren’t scheduled because of it, there will have been too many. For those that think mechanisms related to qualifying for NCAAs is really not so influential to the scheduling network, consider last year there was a team that went 26-5 when an automatic bid wasn’t available, and is now 7-11 when it is available, and they still are better than a 75% chance to secure it. Last year playing against well less than half the AVCA ranked opponents as they do this year. Oh, and more than 80% of its team’s kills so far have come from the same 5 players both years, too! The 11 who defeated this nearly equivalent squad a year later certainly faced tremendous risk for what will be a far lesser reward than any thought when they built their schedule for 2025. There’s nothing wrong with this approach at all. It makes perfect sense. I mention it only to demonstrate that circumstances do at times drive major scheduling paradigm shifts that have major ripple effects across the landscape.
Michael Douglas played Gordon Gekko in the movie “Wall Street.” Perhaps his most famous quote from that movie was “Greed is Good!” The fact remains he wasn’t referring to the NPI in D3MVB because the math related to its risk and reward has spoken, and it is most definitely saying, “Greed is NOT Good!”
Should any reader have a thirst for more, here are a couple of slides that didn’t make the cut.
Additional Slide #1: The Forging of a Model
The very first graphic I created with EV curves of the #3 thru #17 ranked teams playing the top 60 either Away/Neutral/Home. I learned that the weighting of the NPI points earned after the fact is far less influential on the NPI than the rate of change in probability to win the match is in the first place. Home is still King! For some teams more than others, I know!
Additional Slide #2: A Case Study of #15’s Sweet Spot
I got to thinking about #15’s Sweet Spot being opponents in the mid-30’s. Coincidently right where the win-bonuses begin to evaporate. What if it played 7 non-conference opponents ranked between #32 & #38? And then, what if its conference had a top 5 team in the country and 3 others ranked between 39th & 50th, sticking them in “no-man’s land.” If it had gone 20-3 having lost all 3 times to the conference champion and never defeated any team better than 32nd along the way, then would their NPI be at-large worthy? Click to find out!
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