The Stat That Will Revolutionize Baseball: Introducing UVI

Nathaniel StoltzSenior Analyst IApril 16, 2008

It was August of 2006.

I was in Vermont, visiting my uncle. He and my cousin were having a fight over something, so I was told to just sit in my room and wait it out. There wasn't a TV or computer or really much around me that could keep me occupied.

There was, however, a stack of paper over in one corner.

Being an avid fan of Baseball Prospectus and an amateur post-Moneyball stathead, I had recently been pondering how no one stat really gets to the heart of how good a player is.

Really, name any stat, and I can name plenty of things that it leaves out in its ultimate conclusion. 

So with nothing better to do, I sat down in front of this stack of paper with a pen and said to myself "Let's change the world."

(I did seriously say that, I'm not saying it for some dramatic effect.)

It's been nearly two years since that day where I initially started playing with the numbers, and I finally think I've gotten somewhere.

And without further ado, ladies and gentlemen, I give you Ultimate Value Index.

Ultimate Value Index, or UVI, as I'll refer to it from here on out, is a measure of a player's "ultimate value." This might sound like a nebulous concept, but it isn't.

What UVI essentially measures is this: Without outside help, how many bases does a hitter get every plate apperance? How many does a pitcher allow?


The formulas for UVI work on different variables, so we'll examine hitting first. UVI for hitters works a lot like slugging percentage, but there are a few differences.

1.) Slugging percentage is based on at-bats; UVI is based on plate appearances.

One of the reasons why OPS is a bad stat that skews toward sluggers is that OBP and SLG are based differently; one on ABs and the other on PAs.

2.) UVI includes baserunning.

That's right, Juan Pierre fans; this gives your boy credit for all those steals and bunts, and penalizes sluggers for all their GIDPs. The fact that UVI combines both offense and baserunning is, in my opinion, a big point in its favor.

First-order hitting UVI 

There are three UVIs: first, second, and third-order.

First is simply what the raw data tells us, second is park-adjusted, and third is park and level-adjusted. Since I've briefly explained the concepts above, here is the first-order UVI formula, for all the world to know:

(Total Bases + Walks + HBPs + SB - CS + .25(Bunts + Sac Flies) - GIDP - .1K)/PA

I figured that situational hitting does matter some. If a manager wants a player to bunt, and he does so succesfully, that at least means that a runner advanced on the out. The same goes for sac flies.

I thought since no one can advance on a strikeout, the penalty of .1 bases/K was reasonable. You can agree or disagree on that, but the formula is obviously subject to change if that's wrong. Since a second out is guaranteed on a GIDP, that's -1 extra base. (If any of this doesn't make sense to you, just comment at the bottom and I'll explain).

Second-order hitting UVI 

Second-order UVI adjusts for the batter's home park.

To get it, first you divide 1000 by the park factor (NOT THE PARK FACTOR BY 1000!!!). Take that number (let's call it x) and multiply it by the batter's singles, doubles, triples, and homers. Thus:

Second-order singles: (First-order singles)*x

Second-order doubles: (First-order doubles)*x...etc. for triples and HR.

Then just plug the new numbers into the first-order formula.

Third-order hitting UVI 

Third-order UVI adjusts for the batter's level and home park. For MLB players, second and third-order UVI are the same.

Essentially, third-order UVI is the result of changing the following attributes: singles, doubles, triples, homers, walks, strikeouts, stolen base percentage, HBPs, and GIDPs. Yeah, that's right, I let them keep their bunts and sac flies.

Minor league translations are very much an inexact science.

I guarantee none predicted Hanley Ramirez to be so good so fast. Same with Ryan Braun. Therefore, I'm not going to give the exact numbers I use for this, because your guess is as good as mine, but I'll basically tell you how it works.

Each one of those attributes has a coefficient assigned to it. Then, to get the third-order stat, you do something like this:

Third-order singles = Coefficient^(levels away from majors)*Second-order singles

Therefore, if you use a coefficient of .9, that means an AAA hitter gets .9 of their singles, an AA hitter gets .81, a High-A hitter .729, and so on. Therefore, this tells you how many singles they would have gotten had they played in a neutral park in the majors.

Like I said, it's tough to really nail down good coefficients because of all the weird career paths in the minors, so there's no sense in telling you the exact ones I use, because they're just educated guesses. Still, a lot of the numbers, when I run them, look pretty accurate, so I'm confident that there aren't any destructive flaws in what I'm doing.

So yeah, that's hitting UVI.


Pitching UVI works quite a bit differently. Some major differences between hitting and pitching UVI are:

1.) Hitting UVI tells you what a player has done; pitching UVI tells you what a pitcher should have done.

It draws on Voros McCracken's DIPS theory to take the elements of luck out of pitching.

2.) Pitching UVI doesn't include baserunning against.

The main reason for this is simply because I don't have baserunning against data. Also, this is really a function of the catcher more than the pitcher, so it would skew things.

It took me the better part of two years to figure pitching UVI out to a level that satisfied me, whereas hitting wasn't too hard. It's pretty complicated, so here's how it works:

All you need to know to calculate a pitcher's UVI is the following: IP, H, HR, BB, K, HBP, and GB%. In return, my system spits out the following: Expected IP, Expected Hits, Expected WHIP, Expected ERA, Expected BABIP, Expected BAA, Expected OBPA, Expected SLGA, Expected OPSA, and Expected UVI.

Several years ago, Voros McCracken proposed DIPS theory, which states that a pitcher has no control over balls in play and that the only things a pitcher can control are walks, strikeouts, and home runs allowed. 

Not quite.

It has since been found that a pitcher can also control their groundball rate, and that groundballs have a different BABIP than flies.

So first, from the variables above, we need to figure out how many plate appearances there were against the pitcher. Simply add 3*IP to the hits, walks, and HBP for that.

Then, we can break down the plate appearances into definite-outcome PA's and indefinite-outcome PAs. To do this, just subtract Ks, BBs, HRs and HBP.

For reference, we'll use Erik Bedard's 2007 line. Bedard faced 749 batters last year; he K'd 221, walked 57, gave up 19 HR, and hit 5. Therefore, Bedard had 302 plate appearances that he controlled the outcome of, and 447 that he did not.

Next, take the indefine-outcome plate appearances and multiply them by the pitcher's groundball percentage. Now, you have split it into grounders and non-grounders.

To continue with the Bedard example, his 49.8 GB% gives him 232 grounders and 235 non-grounders.

A grounder has a BABIP of .251 (Trust me, I researched this to death) and about eight percent of grounders go for extra bases. When you factor in triples to the equation, you get something along the lines of 1.095 bases per groundball hit. Multiply that by the BABIP of .251 and it comes out to .275 bases per grounder.

Thus, Bedard should have allowed .275*232, or 64, bases on grounders last year. This would come on .251*232 = 58 hits. The other 174 hits should have gone for outs.

Flies are much trickier, and caused me a ton of trouble, mainly due to the fact that all are not created equal. Liners, high flies, and popups are all dramatically different. However, I'll spare you the story of my trials and tribulations with flies and simply tell you how to get to the UVI.

First, batters hit .3606 on flies, including homers. So take .3606*the flies to see how many flyball hits the pitcher should allow.

In Bedard's case, .3606*235 = 84 hits. Then, subtract the homers allowed, and multiply the remaining number by 1.394, which, according to my calculations (that is the only time in my life I will ever be able to say "according to my calculations"), is the average number of bases on inside-the-park non-groundball hits.

In Bedard's case, he allows 65 non-homer hits on flies, so 65*1.394 = 91 bases on flies.

Got all that?

Thank God I made a spreadsheet to do all this.

OK, now we can finally get somewhere. Add walks, HBP, and 4*HR to the expected groundball and flyball bases (the 64 and 91 in the Bedard example), and you have your expected total bases allowed. Divide that by the plate appearances, and you have UVI!

Bedard's comes out to .391.

To get expected hits allowed: Just add together the groundball hits and flyball hits (the 58 and 84 in the Bedard example).

To get expected IP: (PA's - BB - HBP - H)/3

Expected WHIP: The formula is in the name, guys.

Expected ERA: I just figured four bases to an earned run, and it works surprisingly well. 

Getting the AVG, OBP, SLG, and OPS from here is easy enough that I won't explain it. If you need help just ask.

Second and Third-order Pitching UVI 

The only thing a park really affects that a pitcher can really control is the homers, so just divide 1000 by the park factor and multiply by the homer total. Then just rerun the stats again.

Third-order stuff is the same as with hitters; just mess with coefficients for BB, K, HR, and GB% in similar way, although this time the coefficients will be greater than 1.


What's a good UVI and a bad UVI?

One of the reasons I like the pitching UVI so much is that the system can spit out the other numbers along with it. Not only do you have the UVI itself, but you have more familiar things to compare it to, like ERA and WHIP. Generally, if the other stats all look good, the UVI will be good as well.

For hitters, it obviously depends on the position. I've run enough UVIs that I would guess "average" is somewhere around .460 or .470. In general, below .400 is very bad and above .500 is very good. Also note that pitchers and hitters have inverse UVI's; that is, the higher the UVI, the better for a hitter, but the lower the better for a pitcher.

Does this have predictive value?

Yes and no. While I don't currently have a formula in place, predicting UVI increases until age 27, stability through 30, and decline from there is easy to see. The tough thing is getting all the other data as well to line up. It's my next big project, but no, there is currently no set system in place.

This sounds pretty interesting, but there's no way in hell I have as much time on my hands to do this as you do. Can I have the UVI spreadsheet?

Sure, just email me at stoltznh@jmu.edu. You need to have a basic knowledge of how to work Excel.

What is (player x)'s UVI?

Feel free to ask me this, but be aware that I can't get to everyone. You can always just run it yourself. If you have any ideas for a study I can do on something, or a question that you think this can solve, I might write up an article on it (just comment here or post on my board).

Where does one find HBP and GIDP and all that stuff to put into the formula?

I'd recommend The Baseball Cube for that, since they have minor league stuff through '07. Baseball Reference is good for the '08 major league data. '08 minor league data on GIDP, HBP, bunts, and sac flies can be a pain to find; check the team's website and hope you get lucky.

Why UVI Tells Us More Than We Already Knew

UVI is the only stat that exists that combines baserunning and situational hitting with pure offense to determine a batter's overall value. It also has a fair amount of in-game tactical value. If the pitcher on the mound has a .4 UVI, and the batter has a .5 UVI, we can estimate that the batter will create an average of .45 bases per plate appearance against that pitcher.

It's the only stat that really transcends the differences between hitting and pitching, so it's a useful comparable for hitters and pitchers. It also works better than VORP because it isn't a counting stat, so it's not about how much you play, but instead, simply how you play

I hope you've found this both informative and interesting.  If you have any questions about this, just comment here, post a note on my profile, or send me an email. Feel free to use UVI wherever you want—I'll even help you out if you want to do a study involving it—but give me credit for my idea.


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