The April 30, 2005 New York Times had an article by Alan Schwarz called "A Walk May Not Be as Good as a Hit." It outlined a concept by David Neft for re-calculating on-base percentage (OBP) and therefore OPS (OBP + slugging percentage (SLG)). Neft argues that a walk to a player with a high SLG has less value than a walk to a guy with a low SLG since you lose more total bases if the high SLG batter gets walked. So he gives each walk the value of 1 minus the hitter's SLG. That is then used to calculate an alternate to OBP called "on-base advantage" or OBA. OBA plus SLG is called OAPS. I examine OAPS to see if it explains team scoring better than OPS and how switching from OPS to OAPS will affect a hitter's predicted run value if he were added to an average team.

Before I get into the analysis, here is an example. Suppose a player had 500 ABs, 150 hits, a .300 AVG, 100 BBs and an SLG of .600. His OBP would be (150 + 100)/(500 + 100) = .417. Then his OPS would be 1.017. But his "on-base advantage" or OBA would have to first de-value the walks. Each walk would be worth 1 - .6 or .4. So his walk total goes from 100 to 40. His OBA would be 190/540 = .352, leaving an OAPS of .952.

But does this new stat, OAPS, predict runs better than OPS? I looked at all AL teams from 2002-2005 (so 56 observations). The relationship between team OPS and runs per game from a linear regression was:

(1) R/G = 12.81*OPS - 4.95

the r-squared was .921, meaning that 92.1% of the variation in team runs per game is explained by the equation. The standard error over 162 games was 23.14. Then I did the same thing with OAPS and got

(2) R/G = 14.09*OAPS - 5.53

The r-squared was .912 and the standard error over 162 games was 24.55. So OPS actually predicts a little better, but not by much. I also ran the regression with runs per plate appearance (PA) as the dependent variable as well as regressions with OPS broken down into OBP and SLG separately and OAPS broken down into OBA and SLG separately. The accuracy is always just about the same for the two stats, OPS and OAPS.

So we don't have any better idea of how many runs a team will score if we use OAPS instead of OPS. It seems like a reasonable idea that walks to some players are not as damaging as they are to others and that if you accounted for this, you could better predicted scoring. For some reason, that is not what I found.

But how individual hitters are rated could still be affected by this new method. So I then looked all AL hitters in this period who had at least 400 PAs in a season. The correlation between their OPS and OAPS was .994. The chart below shows the relationship. Each player's OAPS is on the vertical axis and his OPS is on the horizontal axis.

So, if we know a player's OPS, we will have very good idea of what his OAPS will be. This might seem to indicate that OAPS or OBA add nothing new. But I still want to look at how we would rate hitters. The big question is how many runs will a player add to a team. So I used the relationship between team runs and the two stats to estimate how many more or few runs a team would scored if a new player replaced one of their current players (assuming each player was identical).

To look at this, I assumed that a given player would take up one-ninth of an average team's PAs and about one-ninth of the at-bats (it varies for some players-see technical notes). Then that average team's OPS or OAPS would either go up or down. Then that new value for OPS or OAPS was plugged into either equation (1) or equation (2). That gives a predicted runs per game which gets multiplied times 162 to get the value for a whole. Then I found how that differed from the number of runs either equation (1) or equation (2) predicted for an average team.

In this time, the average team had and OBP of .337 and an SLG of .429 (I used at-bats, hits, walks and HBP to calculate OBP). That means the average team had an OPS of .766. The average team had an OBA of .308 so the average team OAPS was .737. Equation (1) predicts that an average team would score 4.863 runs per game and equation (2) also predicts 4.856.

Ichirio Suzuki in 2004 had an OBP of .416 (just using hits, walks and HBP) and an SLG of .455 for an OPS of .871. His OBA was .397 and his OAPS was .852. If he were added to an average team and he made up one-ninth of the PAs (not realistic since he normally bats leadoff) and about one-ninth of the ABs, the team's OPS would become .778. Such a team would score 5.013 runs per game. For an entire season, they would score 24.39 more runs than an average team.

If Suzuki replaced a hitter on an average team, their OAPS would be .751. They would score 5.049 runs per game. That is 31.22 more runs per game than equation (2) predicts.

I did this for all players with 400+ PAs. Below are the top 25 seasons in runs added using equation (1) and OPS in the AL from 2002-05:

So if Jim Thome of 2002 were added to an average team, they would score 75.88 more runs.

Now the top 25 in runs added according to equation (2) and OAPS

The next table shows the top 25 players in terms of the difference between the additional runs a player would add from OPS and what he would add from OAPS. Garret Anderson in 2003 would add 29.43 runs using OPS but OAPS predicts he would add 37.28. So OAPS predicts 7.85 more runs added for him. That was the highest differential.

Now the lowest 25. OPS predicts that Giambi of 2005 would add 44.69 runs but OAPS says 36.96. That leaves a negative differential of 7.72.

There were 427 players in this study and 383 of them were within plus or minus 5 runs for each method. That is, the difference in the runs added prediction for the two different methods (OPS and OAPS) was less than 5 runs for 383 players. 280 were with 3 runs. So we don't get too many huge differences in the two methods. If we look at the two extremes, Giambi 2005 (-7.72) and Anderson 2002 (+7.85), the gap is 15.57. That means that Anderson gains 15.57 runs relative to Giambi if we use OAPS instead of OPS. A big gain, but all the other relative changes will be smaller.

We can say that some players will be judged differently if we use OAPS instead of OPS to see how many runs they add to an average team if they replaced one of the players on that team. The differences may not be that great, though. Using OAPS to predict team runs is reasonably accurate, but certainly no better than using OPS. So, although the idea of OAPS is reasonable, it is not clear that we should rate hitters using it even though it does change their predicted value somewhat.

Technical notes: The reason why I did not assume a player's SLG would get a one-ninth weighting in determining the new team SLG is that some player walk alot more than average so they get fewer at-bats (ABs). That means they will have less than one-ninth of the team's ABs, so in calculating the new team SLG their SLG was adjusted to account for whatever percentage of team ABs they would get. There are also other ways to estimate how many more or fewer runs an average team will score when a given player replaces another. I also looked at the relationship between OPS & OAPS had with runs per plate appearance. In that case, not only did I find how a team's runs per PA would change, I also took into account any more or fewer PAs per game a team would get when a given player was added (if team OBP goes up, the team will have more PAs and more chances to score). The results were not too different than what I present here. But the meaning of plate appearances can be different using OAPS. Since each walk only has a fraction of its value, it means that each player's PAs is lower than the official total because a walk is a PA. That then changes runs per PAs. When I ran the numbers taking this into account, the differences grew. For example, Anderson in 2003 would add about 11 more runs using OAPS vs. OPS, as opposed to the 7.85 shown in Table 3. Giambi 2005 would be about -11. To calculate a team's OBA, I found the adjusted number of walks for each player on the team with 25 or more PAs. By that I mean I multiplied their walks (including HBP) times (1-SLG). Then hits plus these adjusted walks were added to get the total number of times on base for each player. Then each player's total was added together to get the team total of times on base (call it X). Then each player's ABs were added to the adjusted walk total to get an adjusted total for PAs (call it Y). Then X was divided by Y to get the team OBA. That got added to team SLG to get team OAPS.