Demarini, Easton and TPX Baseball Bats
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— Where BTF's Members Investigate the Grand Old Game
Tuesday, March 08, 2005
The Snow Index Project, Part 1
The development of a new statistic.
Project Snow Index – Step 1: What do we have?
Readers of Snowbaseball.com and my friends and colleagues, both within and outside of baseball, are most certainly aware of the existence of, if not the inner workings of, the Snow Index, the statistical formula I developed to measure hitter efficiency. I created it with the intent of replacing OPS (on base plus slugging), Runs Created and others as the single most accurate statistic showing the full offensive value of a player, expressed as an average result per at bat.
Several people, after hearing my ideas, have asked why I would try to replace OPS, and what it is within the system, which is largely accepted, that makes it a flawed system in terms of effectively rating hitter efficiency. Here’s the argument, in its shortest possible form:
The small problem: OPS includes some things which I don’t feel a player should be rewarded for, most notably the ability to get hit by pitches. Without a doubt, some players have made a career of taking one for the team, and Don Baylor, Fernando Vina and others inevitably come to mind when having this conversation. However, if you had a young hitter, and you were trying to teach him to get on base more, you would not, under any circumstances, tell him to stay in the box and stare down a fastball. Simply put, getting hit by pitches is usually, and I say usually because of Vina and Baylor, not a tremendously notable skill or something you would want to reward a hitter for. In fact, in some places, including here at Baseball Think Factory, I’ve seen it listed as a cause of concern when young players like Rickie Weeks show too much of a tendency to “take one for the team.”
The large problem: OPS uses values for events which seem to be quite skewed from what they should be. If you expand the formula out, here’s what you have:
To simplify the issue, if you had a hitter who did the following things every time he came up, here’s what his OPS would be:
HBP: 1.000 (.500)
BB: 1.000 (.500)
Single: 2.000 (1.000)
Double: 3.000 (1.500)
Triple: 4.000 (2.000)
Home Run: 5.000 (2.500)
I find it makes things easier to bring everything down to the point where a single is worth one base, so the numbers in parentheses are the values cut in half, to make things simpler. Also, note that stolen bases are not noted at all, so a hitter who walks, steals second, then steals third every time up has exactly the same OPS as a plodder who walks and gets doubled off every trip to the plate.
In Moneyball, Paul Depodesta told Billy Beane that OBP was worth three times as much as slugging. I’d argue that it’s not that much. But I think the above numbers have some serious problems, mainly the improper valuing of walks and home runs.
Let’s take a look at the value of home runs first. A home run is the only single event in baseball that absolutely guarantees a run. It’s not reliant upon runners being on base when it happens, and it’s not reliant on the next hitter getting on base, it’s lineup independent. As such, it seems logical, in an intuitive sort of way, to assign home runs a value at least equivalent to 4 singles, and perhaps more.
Next, what is a walk truly worth? If you believe that OBP is the logical alternative to batting average, perhaps you would argue that a walk is worth the same thing as a single. A more purist argument would be that a walk doesn’t advance a runner as far as a single would, if at all, and so the actual value is closer to the .5 singles used in OPS. Here’s my argument:
With the bases empty, a walk and a single have the same value. It makes perfect sense when you think about it. If no one is on base, it doesn’t matter how you get to first, as long as you don’t get hurt doing it. In 2004, 57.4% of all major league plate appearances fell into this category.
With runners on base, a hitter has three tasks to fulfill (get on base, don’t produce an out, advance the runner). Therefore, by singling, they fulfill all three requirements and get 1 single. However, if they walk, they only fill two of the three tasks, as the runner probably will not advance as far as they could or would have on a single. Therefore, in these situations, a walk is worth two thirds of a single. The remaining 42.6% of 2004 plate appearances fell into this category.
1(.574)+2/3(.426) = .864 Given these conditions, then, and accepting this value for a walk in the given situations, .864 is the value of a walk in the average of all situations. So here is, then, the first adjustment of my Snow Index formula:
It is also worth noting that while .864 was calculated based on 2004 statistics, it doesn’t greatly change when other seasons are substituted in. For example, the 1984 co-efficient turns out to be .8676. Unless you’re Barry Bonds, the difference is minor.
But this formula still lacks one important factor, the stolen base. Barry Bonds stole 6 bases in 2004, and one certainly would not argue that those 6 stolen bases were his most highly valued attribute. However, there are players, both recent and historic; who’s valued was raised greatly by the ability to gain an extra base or two by stealing it. Just taking a raw stolen base figure will not do, though, because that fails to take into account how many times a runner cost his team the opportunity to score by getting caught attempting to steal.
Thankfully, many baseball experts, most recently John Sickels of Minorleagueball.com, provide an easy ideal stolen base percentage. If a runner can steal successfully two thirds of the time, the gains from stealing and the losses from getting caught balance out exactly. Anything above that is a gain, anything below is a loss. Mathematically, SB – 2(CS) gives you a number, either positive or negative, showing the actual impact of a base stealer, in terms of bases gained or lost.
So finally, here is the Snow Index formula, as I’ve been using it recently. It gives an average achievement, in terms of bases gained, per trip to the plate, with an adjusted figure for stolen bases and walks:
Over the course of their careers, this raises the values of Rickey Henderson, Tim Raines and Lou Brock by 56, 49, and 29 points, respectively. Interestingly enough, it lowers Pete Rose by 7 points.
Going back to my point from above, here are the individual event values with the current Snow Index:
Home Run: 4.000
Stolen Base (for gain): 1.000 (added to total)
Step 2: The Problem
I think these values make considerably more sense than those used within OPS., both intuitively and after some thought. However, when put into practice, the system proved to be a similar method of predicting offensive success to the existing systems. To put it flatly, the system I had worked so hard to create showed no more effectiveness than the system I was trying to replace. As data, I used the team Snow Indexes of all 30 major league teams by season, from 1999-present, and compared them to their actual runs scored, looking for a correlation. Team OPS showed a .912 correlation, out of 1. The Snow Index showed a .881 correlation, just slightly worse. So, simply, more work is needed. More factors need to be considered, perhaps some factors need to be devalued, perhaps others need to have their values raised, but regardless, something needs to be changed. To find potential options, I looked to other baseball statistics and statistical studies. Here are my findings.
I feel that I gained the most through Voros McCracken’s “DIPS” concept. McCracken’s basic concepts focus on pitchers, and operate on a basic assumption. “There is little if any difference among major-league pitchers in their ability to prevent hits on balls hit in the field of play,” McCracken said in this article. And the farther you look into the statistics, the more you realize he’s right. But then the question becomes, if it’s that simple for pitchers, why isn’t it that simple for hitters?
McCracken’s system uses the three things a pitcher can do that are completely outside the control of his defense: strikeouts, walks, and home runs. All other balls put in play had their fortune decided by luck, or the strength of the defense, or a combination of the two. So while luck plays some part, and in many cases a rather large part, in the end result a pitcher faces, the only statistics providing an actual measure of a pitcher’s ability are the numbers a pitcher generates independent of any other forces.
So why is it any different for hitters? The short answer just may be that it’s not. Walks and strikeouts are exactly the same, just reversed. And furthermore, to a point you can identify a hitter’s ability to get on base, both by walks and by hits, by these numbers. Especially recently, heavy emphasis has been placed on plate discipline, taking pitches, wearing out opposing pitchers, waiting for the right opportunity to swing. Vladimir Guerrero may be the only hitter among baseball’s present elite who doesn’t have notable plate discipline. Almost to a man, more plate discipline equals more effective hitting.
And what of power hitting, the ability to connect for extra bases? It’s possible that’s covered here, too. Consider, for a second, this proposal. All doubles and triples fall into one of two categories:
1) Ground balls down the line/fly balls in the gap. Both of these are functions of luck. An extra base may be gained by speed, but if a ground ball is hit down the first base line and would be a triple, it is at best only a few feet away from being a routine out on the left side, or a foul ball on the right. The positioning of that ball is largely good fortune.
2) Balls hit with power, the same kind of power which produces home runs. A long fly ball off the wall is generally only a few feet, tiny fractions of an inch on the bat away from being a home run, and is generally hit by someone who has the ability to hit that ball over the fence, too.
Here’s the statistical portion of that argument. 44 of the top 100 single-season
doubles totals have been achieved since 1986. Right now, a total of 48 doubles in a season would earn you a tie for 100th place on the All-time list. Of the 44 hitters who have made that list in my lifetime, here are two lists:
First, the high end:
Now, the low end:
Note that no one appears in the first table more than once, in fact, among players on that list, only Craig Biggio ever hit 48 doubles again. The second list is populated entirely by known power hitters. The remaining 30 of the 44 hitters all ended up with ratios relatively close to the league’s 2B/HR ratio, 1.64. So, therefore, even baseball’s greatest doubles hitters, or at least most of them, do not vary from the norm so much that their ability to hit for extra bases could not be feasibly derived from their home run totals.
It can be taken one step farther, however. 103 hitters in big league history have reached base 308 times or more in a season. If you measure the percentage of times on base gained via extra base hits, you get this high end/low end differential:
Around 80 of the others fall somewhere between 16% and 30%, which seems like a wide margin of extra base hits, but of those, around 70 fall above 20% but still below 30%. Also, note that changes in era dominate both the low and high ends. At the top, only Stan Musial breaks the trend, all other hitters are from either the Ruth era or the Bonds era. It’s also worth noting that none of the players on the low end ever reached base 300 times in a season again.
Conclusion: A hitter’s ability to hit doubles is largely predictable by his ability to hit home runs. Furthermore, hitters who get on base frequently tend to hit a predictable number of extra base hits, largely based on their power.
Certainly, the data is available, whether it comes from Pete Palmer, or the few who have recreated his study since, to determine what a walk is worth in any of the myriad of situations that occur in a game. The problem, however, lies largely in converting what I would find in said data into something I could actually use. Take, for example, a situation with a runner on first and no one out. If a hitter walks, the run expectation jumps a fair amount as the situation changes. However, if the hitter singles and advances the runner to third, the run expectation jumps farther, as the runner moves closer to home. In that situation the result is quantifiable. I am not in a position to go situation by situation and adjust that data to determine an average situation. In fact, in the current absence of ability to do that, I am happier to keep my current, simpler method, where a walk with a runner on base is worth two thirds of a single and a walk with no one on is worth the same as a single.
Conclusion: Run expectations could provide some insight towards the value of a single versus the value of a walk, but one would have to do so on a situation-by-situation basis which would be difficult to translate back to an average situation, which would need to be done for my purposes.
In Baseball’s All Time Best Hitters, Michael J. Schell provides an interesting problem, but shows some incredibly flawed logic in solving it. However, before I go any farther, I should point out that Schell’s tools are designed to be used to compare hitters across eras, a task which I feel I am not yet ready to undertake, as I have yet to prove the Snow Index is good enough to judge hitters from one era against each other, much less different eras.
With that being said, here are my critiques of the way Schell goes about his project. First of all, he uses batting average to rate players, effectively changing the question involved in his book from “who is the best hitter of all time?” to “who is the best contact hitter of all time?” I’m considerably less interested in the second question. Judging hitters purely by batting average with no regard for power is like comparing pitchers by their fastball speed with no regard for their control. A hitter’s power and ability to make contact go hand-in-hand when determining a hitter’s value. One simply cannot judge a hitter based purely on one of the two factors.
Beyond that, however, I would argue one of the claims Schell makes about why eras in baseball are different. He makes a case for a standard deviation score for the average talent level of the league, claiming that changes over time based on outside factors. However, consider this brief timeline:
My point is this: The talent pool is always being lowered by one factor and raised by another, and while it may be true that the talent level varies slightly with a change in the climate of baseball, it is my opinion that it always remains near the same level, and therefore an adjustment for talent level within eras is unnecessary. Schell also makes an argument for park factors, which I agree with to a point, on a season-to-season basis, but I deem them unnecessary for determining the lifetime value of most current players, who will very rarely, if ever, play their entire career in one park.
The biggest points I accept for comparing hitters across eras are late career decline adjustments and mean adjusted Snow Indexes. Schell makes the point that when you compare a great player’s career percentages to those of a somewhat less talented player, the great player’s numbers will be weighted down because their career will in all likelihood be longer, and their additional at bats will drag down their percentages. Schell suggests using only the first 8,000 AB to determine their peak value, and I accept that, with a few corrections:
1) The number has to be adjusted to plate appearances. On average, major league hitters walk about once in every six plate appearances, meaning 8000 AB would adjust to roughly 9333 plate appearances. This means it will not take a hitter who walks frequently as long to reach the milestone, all hitters will reach it at an equal pace.
2) The set starting point needs to be eliminated. If a hitter does better in the 500 plate appearances after he reaches 9333 than he did in his first 500 PA, then the better numbers should be used, to get a better feel for how good the hitter actually was at his peak. For example, Barry Bonds already has over 11,000 PA in his career, but his most recent 4 seasons, in which he picked up over 2300 PA, were considerably more successful than his first 4 big league seasons. If one stopped rating Bonds at 9333 PA, they would not get an accurate assessment on Bonds’ prowess as a hitter.
Furthermore, while changes in era do not necessarily get reflected in the talent
pool, they do frequently show in rule changes and strategy changes, which will affect the average Snow Indexes of players in that era. Therefore, I accept Schell’s proposal of mean adjustment, which is essentially a system of comparing hitters to others of their era, before comparing them across eras. For example, Frank Chance hit .293 in 1907, which seems low until one realizes only 6 players in the NL were better. In comparing players across eras, Chance would be given a handicap of sorts to make up for the fact that hits simply weren’t falling as frequently when he played.
Conclusion: Translating data across eras is possible, with some adjustments being necessary and others being overvalued, but the entire subject is moot until I produce a Snow Index which can accurately rate players against others within their own era.
Step 3: The Next Move
Obviously, a lot of work needs to be done to continue on in my search for the ultimate baseball statistic. Here are my short term goals.
Determine what factors, if any, need to be added to the Snow Index. Take, for example, the case of home runs. As the only play in baseball which produces a run independent of all other factors, home runs are critically important to the run scoring chances of most teams. It is possible that, even at 4 bases instead of OPS’ 2.5, home runs are still undervalued. And while intuitively that argument makes sense, it is also possible that a recent trend of increased power hitting has resulted in an era where the correct number is somewhere in between. Similarly, strikeouts need to be considered, as the absence of all possibility of a base gained. It is possible an extra penalty, if you will, may be added to the Snow Index to show how often a hitter completely removes the opportunity to succeed by failing to make contact.
Determine how much variation in run scoring is caused purely by luck. By taking the number of runs a team scores by all methods other than home runs, and dividing that by the number of runners a team gets on base (minus their home runs), you can get an average number of runners on base per run scored. From that, one could determine how often a team is getting fortunate in their scoring of runs, and how much that may be affecting their total production.
Adjust any potential inaccuracies in the values of existing variables. For example, a walk may produce more or less than .864 singles value in terms of actual runs produced. Run expectations, if I am able to find a way to work them into my system, may give me a better insight on the matter.
These are the steps that lay ahead of me. I look forward to confronting them as I carry on.
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