Historic Win Shares Per PA

Through 2003, Barry Bonds now has 36.10 win shares per 648 plate appearances, which is 5th on the list behind Ruth, Mantle, Williams, and Wagner, although virtually even with Wagner, and within striking distance of Williams and Mantle.

Players who played in lower run scoring environments, such as Wagner and to some degree Mantle, have an advantage on this measure, because for the League there will be fewer plate appearances per game, but the same number of win shares available per game.

Good point, Steve.  I think the best way to average Win Shares is per out, which can be applied to batters, pitchers and fielders and is consistent over the history of baseball (at least, most of it that I know of).

It seems to me that win shares per out is not the best kind of rate statistic to use for win shares. For batters, of course outs made will factor into both the calculation of runs created and also the process of removing sub-marginal runs (background runs as Bill James also calles it) to determine a batter’s marginal runs created. But if on top of that you then compute a rate statistic by taking win shares per out, it seems to me you may be biasing the result in favor of hitters whose win shares were heavily based on on base percentage as opposed to other factors.

In the New Historical Baseball Abstract, James used the concept of win shares per 162 games for position players, and that works pretty well, except for players who often play only partial games. I think an alternative, particularly for offensive win shares, would be to use plate appearances, but to make an adjustment based on the player’s team’s number of plate appearances per game.

To illustrate the issue, in 2003, if we were just comparing offensive win shares between Bonds and Pujols, Pujols had 38.92 offensive win shares in 685 plate appearances. I am not sure how Morong derived 648 plate appearances to represent a full season for a player, but using that figure, Pujols had 36.82 offensive win shares per 648 plate appearances.  Bonds had 36.06 offensive win shares in 550 plate appearances, or 42.49 offensive win shares per 648 plate appearances.

But to a modest degree, I think that comparison unfairly discriminates against
Pujols. The Cardinals in 2003 averaged 39.91 plate appearances per game, compared to only 38.53 for the Giants. Thus 648 plate appearances for the Giants represents a greater percentage of the team’s offensive games than 648 plate appearances for the Cards. Since the Cardinals’ had a 2.9% greater number of plate appearances per game than the Giants, it seems to me that for 2003, Pujols offensive win shares per 666.8 plate appearances would be a more appropriate comparison to Bonds’ offensive win shares per 648 plate appearances. This would boost Pujols’ result from 36.82 to 37.89, closer to but still quite a bit less than Bonds’ 42.49 offensive win shares per 648 plate appearances. It is a batter’s plate appearances in comparison to his team’s plate appearances that gives him the opportunity to accumulate win shares.

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For fielding win shares, the analagous rate statistic I think would be win shares per inning played. I know that innings played defensively is not available thoughout the historical data base, although as I recall James had a methodology for estimating defensive innings for the historical data base.

Pitching also raises some interesting issues.  As I recall, in the New Historical Baseball Abstract, James used win shares per start, and he treated 2 relief appearances as equivalent to a start. If you want to use outs recorded by the pitcher, that of course translates into innings pitched, which could be OK, although I think you would still need to make some distinction between starters and relievers. Clearly under the win shares system, relief aces have the expectation of generating more win shares per inning pitched than starters.

What I’m looking for is a standard upon which to base Win Shares Above Average.  The approach I worked out in previous articles is just too complicated for anyone to understand.  Win Shares is already complicated enough.

I would like to calculate a league-wide Win Shares “per something” for fielders, batters and pitchers.  I feel comfortable using innings played for fielders (luckily, I’m only using current data).

For pitchers, you could use “leveraged innings” which are already computed to determine relievers’ Win Shares.  I think this would make comparisons between starters and relievers equitable.

Good thoughts on plate appearances and outs for batters.  I have to look at that.  I still think it may be appropriate to base WSAA on outs, because they are used to measure marginal runs in the first place (as you say).  By basing WSAA on outs made, you’re maintaining continuity between the method for creating marginal runs and the WSAA “baseline”, if you will.

I think that makes sense.  I’ll play with the data to see what comes out.  Thanks for your comments, Steve (and keep them coming!).

Steve, if you’re still around, I’ve been playing with this.  When looking at WS per plate appearance, I don’t believe you need to adjust for a team within the same season.  Said differently, you don’t need to adjust for the fact that the Cardinals had a greater number of PA per game than the Giants.

The reason is that a team with more plate appearances will also have more batting Win Shares.  So there’s no artificial constraint on the number of batting Win Shares available—as there is when comparing across seasons with different run environments.

Does that make sense?

studes,

Let’s concsider two scenarios. In the first one, let’s assume that Team A and Team B are equally good offensively—in that they both have the same number of offensive win shares. But let’s assume that Team A plays it homes games in an extreme hitters park, and Team B plays its home games in an extreme pitchers park. Team A is not any better offensively than Team B,  but Team A will score quite a few more runs than Team B, and thus is likely to have more plate appearances.  Thus Team A will have fewer win shares per plate appearance than Team B, even though the two teams are equally as good offensively and end up with the same number of offensive win shares.

Let’s take another simplified scenario where Team A and Team B both play in neutral parks in the same League but Team A is much better offensively than Team B, and thus scores a lot more runs and has more plate appearances. One of the principles of win shares is that the number of win shares that a given player accumulates is not dependent on the quality of his teammates. So let’s take two players who are equally as good, one on Team A and one on Team B. The two players accumulate the same number of win shares. But the player on team A is a much smaller percentage of his team’s offense, and thus a much smaller percentage of his team’s offensive win shares. Since Team A will have more plate appearances, and assuming the two players are playing the same number of games, the player on Team A will have fewer win shares per plate appearance, other things being equal, despite the fact that they are equally good.

Offensive win shares per game played by a position player is generally a good measure of his rate of performance. Where this breaks down is differences between players in the extent to which they are playing full or partial games. Also, if two players are playing the same number of games, but one is batting high up in the order and the other lower, the one batting lower in the order will have fewer plate appearances, and therefore less of an opportunity to accumulate win shares. So offensive win shares per plate appearance seems to make sense to address those issues when looking at rate of performacne. However, it seems to me if you do that you still have to adjust for issues of context such as I discussed in the earlier post. That is what as I was trying to get at.

With the kind of adjustment I was talking about, the number of plate appearances, taken in the context of the team’s total number of plate appearances, becomes, in effect, a measure of the percentage of a team’s offensive games that a player has played, in a similar way that the number of innings played defensively can be used to measure the percentage of a team’s defensive games that a player has played at a position.

Ah, okay.  I forgot about the park adjustment aspect.  That’s a great example.

However, I don’t get the Team A and Team B example.  Let’s say two players on Team A and Team B are “equivalent”, if you will.  To me, that means that they create the same number of runs per out, because the relationship between marginal runs and batting Win Shares is key.

If they get the same number of plate appearances, or opportunities, they will get the same number of marginal runs and Win Shares.  But if Player A gets more plate appearances cause his teammates are good, then he will create more marginal runs and receive more batting Win Shares.

That’s why dividing by plate appearances helps, because it corrects for this sort of thing.  It will bring Player A in line with Player B.

Adjusting for run environment, whether induced by league or park, makes a lot of sense to me.  I don’t mean to be difficult, but I don’t see the teammate adjustment.

Okay, I’ve worked out what you’re saying Steve.  Thank goodness I’m so obsessive-compulsive.

To restate the argument, win shares per out are the best metric to use in general, because outs are the basic “clock” of baseball, and they can substitute for player-specific “games played.”

However, using outs to create a rate stat for batting Win Shares can create problems, because it overemphasizes high-OBP batters (I know there’s a strong logic here, but I’m not very good at articulating it).

So we use Plate Appearances instead of Outs to create a rate stat for batting Win Shares.  The goal is still the same: to determine some sort of equivalent “games played” for each batter, but teams differ in the number of plate appearances they accrue per game.  So plate appearances for each player need to be adjusted to a league-average level, based on his team’s PA/Game vs. the league PA/Game.

Hope I got it right.  That’s the approach I plan to use for expected Win Shares.