Thursday, February 08, 2024
VOZ - Value Over Zero
Everyone has their own VOZ method, the Value over Zero. The zero-point is the point at which that thing has no value. This is most clearly demonstrated with Fantasy Leagues. If you play Fantasy sports games, congratulations, you have a VOZ method. In a world where you have several hundred players, but only a few hundred will get selected, all the unselected players have a value of zero. You are only going to spend money on players who have value above the zero-baseline.
That zero-baseline is different for every position. A below league-average batter at catcher has value, while the same batting line for a 1B has almost no value. This concept is quite clear in Fantasy sports. It's a little murkier with real baseball players, but it's real nonetheless. All we need to do is establish what that zero-baseline is.
On Twitter, I asked what a 200 IP, 11-11 pitcher was equal to in value, and the most popular response was a 100 IP 8-3 pitcher. Now, follow me here, this is the important part. 11 wins and 11 losses has the exact same value, according to the voters, as someone with 8 wins and 3 losses. (In this illustration, the W/L record is a proxy for a pitcher's overall performance.) Again 11-11 = 8-3. If the two pitchers are equal, then the difference between the two pitchers is zero. In other words, this is what the voters are saying:
11-11 = 8-3 + 3-8
This is obvious, right? 8 wins and 3 losses, plus 3 wins and 8 losses is 11 wins and 11 losses. And since 11-11 = 8-3, then implies that 3-8 = 0
In other words, a pitcher who has 3 wins and 8 losses, or a win% of 3/11, or .273, is worth zero. That is the zero-baseline: .273, at least in this illustration.
A fairly high number actually chose 7-4 as being equal to 11-11. This implies the zero-baseline for this group of folks was 4-7, or a .364 win%.
The smallest group chose 9-2 as being equal to 11-11, which implies a .182 win%.
To summarize: 51% implied .273, 34.5% implied .364, and 14.5% implied .182. Collectively that comes out to .291 win%. In other words, the zero-baseline level, the point at which a player has no value, is a win% of .291. This is what is commonly called the replacement level, but my preferred term is the Readily Available Talent level. And so, value over zero, or in this case Wins Over Zero (WOZ) is set so that we subtract .291 wins per game for every player.
An 11-11 pitcher is compared to a .291 pitcher given 22 decisions. And .291 x 22 is 6.4 wins and 15.6 losses. So, subtracting 11 wins by 6.4 wins is +4.6 wins, or 4.6 WOZ.
And that 8-3 pitcher? Well, .291 given 11 decisions is 3.2 wins and 7.8 losses. And 8 wins minus 3.2 wins is 4.8 wins, or 4.8 WOZ. The 7-4 pitcher has 3.8 WOZ. So, somewhere between 8-3 and 7-4, but closer to 8-3, is where you find your pitcher equivalent to 11-11.
That's how WAR works.
I asked a similar question in this poll:
https://twitter.com/tangotiger/status/1755659747435380943
In this illustration, it works out to a .323 win% as the zero-baseline level.
So, one poll suggested .291, and another poll suggested .323. The average of the two is .307.
And that’s how it always works out, no matter what illustrations I come up with, no matter who I ask, or when I ask. The answer always comes back to somewhere around .300 as the zero-point.
And that’s why WAR is set to compare players to the .300 level.