One of my favorite parts of sports trivia is remembering a guy you have absolutely no business remembering.
Not a Hall of Famer.
Not somebody whose jersey is hanging in an arena.
A guy who was weirdly useful in fantasy football for three weeks in 2014.
A backup offensive lineman from an Eagles team I watched too closely.
Someone who bounced around the league for a few years, disappeared, and then suddenly comes back into your brain 15 years later.
Oh man. That guy.
That feeling is a big part of why I made Roster Relay.
It is also why I needed something called a Rarity score.
And figuring out how to calculate that turned out to be much less obvious than it sounds.
The part of Immaculate Grid I liked most
I love Immaculate Grid.
Obviously there is satisfaction in completing the grid.
But the part that always got me was seeing how few other people had picked the same player.
You could choose a completely obvious answer and safely fill the square.
Or you could remember somebody like Stefen Wisniewski and get that little payoff when the game tells you almost nobody else thought of him.
That second feeling is more fun to me.
My friends and I already had our own less organized version of this.
We have a text chain that can go silent for months, and then somebody will suddenly drop the name of some random athlete we haven't thought about in 15 years.
Then everybody starts going again.
There is no point.
That's the point.
Roster Relay was partly an attempt to turn that “remember some guys” feeling into an actual game with rules a computer could verify.
Instead of merely naming somebody obscure, you have to use that player to connect two athletes through real shared rosters.
If you remember Knile Davis, great.
Now make him useful.
But how do you tell a computer that Knile Davis is obscure?
This is where things get annoying.
Humans are pretty good at having an intuitive sense of fame.
Put LeBron James next to a journeyman who played 42 games in the NBA and almost everyone will agree which one is more famous.
A computer needs numbers.
And ideally those numbers should come from data I can actually access and verify.
I can't just create a spreadsheet where I personally assign every athlete a score based on:
Yeah, I definitely remember this guy.
That would take forever.
It would also be an extremely Ben-specific measure of fame.
So the game needed a proxy.
Something imperfect, but useful.
My first answer was basically: how long did you play?
Career length is an attractive shortcut.
If somebody played a lot of games over a long career, there's a decent chance more people know who they are.
If somebody appeared briefly and disappeared, there's a decent chance they're more obscure.
Reasonable.
Except it breaks pretty quickly.
There are players who hung around professional sports for a long time without ever becoming particularly famous.
And there are superstars whose careers were shorter, interrupted, or otherwise didn't simply rack up the most games played.
So the original approach could do something pretty dumb:
It could decide that a long-career journeyman was more of a Household Name than a player everybody actually knew.
The code now basically describes the old problem as exactly that: longevity was getting mistaken for fame.
Once you see that happening, the formula has failed the smell test.
You don't need a complicated statistical argument.
You can just look at the names and say:
Nope.
Fame isn't one statistic
The problem is that there isn't really a universal “fame” column in sports data.
So Roster Relay now uses different signals depending on the league.
For MLB, things like All-Star selections are useful.
For the NFL, the available data includes things like Pro Bowls, All-Pro recognition, Hall of Fame status and career value.
For the NBA, the current system uses career production across major counting statistics as a practical fame signal because the same clean accolade source isn't available in the dataset I'm using.
Career length can still help.
It just shouldn't be the whole answer.
The important change was basically this:
Being notable should dominate simply having been around for a long time.
That feels much closer to what Rarity is supposed to mean.
I am not claiming to have mathematically solved fame
I want to be very clear about this.
Roster Relay does not contain the world's definitive ranking of how famous every professional athlete is.
That would be ridiculous.
Fame changes by generation.
It changes by team.
It changes by geography.
Fantasy football can make you remember someone your neighbor has never heard of.
A Phillies fan and a Mariners fan may have completely different ideas about whether a certain middle reliever is obscure.
There are also limits to the data I can practically use.
So sometimes I look at a player's Rarity score and think:
Huh. I probably would have had him a little higher.
Or lower.
That's okay.
The goal is not to create a universal scientific measurement of celebrity.
The goal is for the ranking to work directionally well enough inside each sport that picking an actual deep cut feels different from picking an obvious star.
If LeBron and some 12th man end up in roughly the same Rarity tier, something is wrong.
If two fairly obscure players are in slightly different order than I would personally rank them, I can live with that.
Rarity is really there to reward the fun answer
Imagine Roster Relay gives you two endpoints and there are multiple valid ways to connect them.
One route goes through a superstar.
Safe.
Obvious.
Efficient.
Another route goes through a player you remember because he had a strange one-year stint with your team and somehow lodged permanently in your brain.
Both routes are valid.
But the second one tells you something more interesting about how you got there.
That's what Rarity is trying to recognize.
Not player quality.
Not how valuable someone was to their team.
Not whether they “deserved” more attention.
Just:
How surprising is it that you remembered this person?
That is a much more fun thing to score.
Different sports make this weird in different ways
The three leagues also behave differently.
MLB careers can be very long.
NFL careers are often shorter, and different positions accumulate completely different kinds of statistics.
NBA rosters are smaller, so even relatively obscure players may be more familiar to fans.
Accolades mean different things too.
An MLB All-Star selection, NFL Pro Bowl, and NBA statistical profile aren't interchangeable concepts.
So I don't think it would make sense to pretend Rarity 72 in baseball is some exact universal equivalent of Rarity 72 in football.
The useful comparison is mostly within the game you're currently playing.
Who were the obvious players?
Who were the deep cuts?
Did you reach into the weird part of your sports memory?
That's enough.
Then the scoring system created another problem
Once you start rewarding obscure players, people have an obvious incentive:
Add more obscure players.
And that is actually fun.
Suppose you somehow get onto the 2007 Phillies roster and you remember everybody.
Relievers.
Bench guys.
September call-ups.
People whose Baseball-Reference pages probably get six visits a month, three of them from you.
I want Roster Relay to let you enter those guys.
If you remember them, type them in.
See the headshot.
See the Rarity score.
Have your little:
Oh my God, I forgot about him.
moment.
The problem was that the original scoring could also reward you for simply staying on essentially the same roster and piling up player after player.
Then you're no longer building a more interesting connection between the endpoints.
You're just farming rarity.
That eventually led to another scoring change, which probably deserves its own article.
The short version is that the game now tries to preserve the fun of entering those players without letting repeated use of the same team-season inflate the scored route.
You still get to remember the guy.
You just don't get infinite points for remembering his entire bench.
The community data may eventually make this better
The most natural rarity measure is probably the one Immaculate Grid already uses:
How many people actually picked this player?
Roster Relay already collects anonymous aggregate information about the players people use in their finished routes, including solved and give-up attempts.
As the player base grows, that creates some interesting possibilities.
Maybe the game can eventually learn that a player I assumed was obscure is actually selected constantly.
Maybe somebody the formula considers fairly recognizable almost never gets picked.
That would be useful information.
Right now, though, the game isn't large enough for me to treat community selection percentage as a stable universal score.
If only a small number of people have played a puzzle, one person remembering a random backup shouldn't completely redefine the player's fame.
So the data-driven Rarity system acts as the baseline.
The community stats are another lens.
Sometimes the formula is wrong and that's useful
This is one thing I have gotten much more comfortable with while building these games.
A scoring system doesn't have to be perfect to be useful.
It does have to fail in ways you can notice.
The first Rarity system failed in a very visible way.
It told me:
This guy played for a long time, therefore everybody knows him.
And I could look at the player and say:
Absolutely not.
Good.
That meant I knew what needed fixing.
The newer system isn't perfect either.
But when I look across the player pool now, the broad ordering feels much more like the game I was actually trying to build.
Stars generally look like stars.
Deep cuts generally look like deep cuts.
And the guys in the middle are messy.
Which seems appropriate, because human memory is messy too.
The best Roster Relay answer is the one you enjoy remembering
You can play Roster Relay in different ways.
Maybe you want the shortest possible chain.
Maybe you want the highest Rarity.
Maybe you want to find a route involving players from your favorite team.
Maybe you just remembered Matt Asiata for the first time in a decade and now you're determined to make him part of today's answer.
I don't really care which one you choose.
These aren't professional competitions.
Nobody is currently receiving a million-dollar prize for being the world's best Roster Relay player.
If that changes because someone gives me a television show, I will revisit the scoring rules.
For now, Rarity exists mostly to give that obscure-player part of the game a little extra reward.
You remember the name.
You type it in.
The connection works.
The face pops up.
And for a second you get to think:
Oh yeah. That guy.
That's the score I actually care about.