Win Shares and Loss Shares

A different look

By Tangotiger

I suggest you read my previous synopsis on Bill James' Win Shares, first. And if you have a few extra minutes, look at the more detailed look at Win Shares.

The flaw - negative loss shares

How much is Pedro's 2000 season worth? I'll estimate, that given average run support and average defense, he would be 20-4. You guys can come up with your own estimate, but it's reasonable to say that we'll all be close. A .500 pitcher therefore would have gone 12-12. If we are going to debate this last point, let's stop now. So, Pedro is worth about +8 wins over a .500 pitcher. Or +24 win shares over a .500 pitcher.

How many win shares does a .500 pitcher have, given about 24 decisions? Well, if you've got 81x3 win shares to distribute, and the pitchers get 35% of that, then all pitchers should get about 85 win shares. Therefore, if you split that up by innings (or decisions, or whatever reasonable thing you want to use), it's fair to say that a .500 pitcher should have about 12 or 13 win shares. This means that Pedro must have 12+24 = 36 win shares.

This .500 pitcher should also have 12 or 13 loss shares. Pedro therefore would have 12-24 = -12 loss shares.

Remember: Wins over .500 = (W - L) / 2

3 win shares per win

Negative loss shares? What's that? It's the result of an impossibility. Therefore, we are forced to conclude that either the methdology or (some of) the assumptions of the methodologies are wrong. Why give out 3 win shares per win? James just gives it out as if it's an inconsequential thing. But it is in fact pivotal.

And in the case of Win Shares, a pivotal mistake.

Mills Brothers and Win Expectancy

Many of you are probably familiar with Run Expectancy. More important a concept that follows that is Win Expectancy. For example, if you come up with a man on 1B, 2 outs, and down by 1 run in the bottom of the 9th, what is the likelihood of you winning? Let's estimate this as .249. (That is, you have about a 25% chance of winning.) What if you get a walk, and now you have runners on 1B and 2B: what is the new likelihood of you winning? Let's estimate .413. That difference of .164 wins can be attributed to that plate appearance. Specifically, the batter, the runner, the pitcher, and the fielder. They all get a "share" in that change in Win Expectancy (WE). The runner actually didn't do anything, as getting to 2B was in the hands of the batter. The fielders also didn't do anything, as giving up the walk was the pitcher's fault. So, there was a change in WE of +.16 for the offense, and of course, -.16 for the defense. We attribute the "win shares" of .16 to the hitter, and a "loss share" of .16 to the pitcher. After every PA, the win shares and loss shares will balance out.

In essence, this is what the Mills Brothers did. For every change in WE, an accounting of this was given out to the offense and defense, so that it all balanced out. By the end of the year, you'd have someone with +10.6 win shares and +3.4 loss shares. The Mills Brothers counted this as "points" instead, and you'd see this example as 10,600 win points and 3,400 loss points, and then they expressed this as a percentage: 10.6/(10.6+3.4) = 75.7%. An average player would of course be 50.0%.

All of this was very hard to do, and really not beneficial because of the huge possible swings in WE. At least, that's what most of the stat-heads think. The stat-heads say that looking at the change in Run Expectancy (RE) from year 1 to the WE of year 2 had a higher correlation than the WE of year 1 to the WE of year 2. Normally, what correlates the best is its own stat. However, all of this means is that RE is a better PREDICTOR of WE. However, this does not take away from the fact what WE measures, and that is the actual change in Wins at any moment.

Now what?

As you can see, the closer the game, and the more leads that change, then the more WE changes there are. This means more win shares and loss shares given out. For games where Pedro pitches, the change in WE will be very small from PA to PA. It will (usually) go in one direction, and so you won't get all of these swings. Therefore, you do NOT want to make it a rule that all games have 3 win shares and 3 loss shares. In fact, you might find that the average game will have 1.5 win shares and 1 loss shares for the winning team, and 1 win share and 1.5 loss shares for the losing team. The total on both sides is 2.5 win shares and 2.5 loss shares. However, in games pitched by Pedro and Randy Johnson, you might have 0.9 win shares and 0.4 loss shares on the winning team, and 0.4 win shares and 0.9 loss shares on the losing team. And, Pedro will probably make up most of that 0.9 win shares. In fact, the winning pitcher will probably make up 0.5 win shares in either game.

This however is very complicated. Who wants to do all that? I agree. But this is what you should do. If you don't want to do all this, then you have to create a model that will estimate what really happens in baseball. And Bill James' Win Shares does not do that. What you should do is start off where the Mills Brothers left off. This is essentially what Pete Palmer's Hidden Game of Baseball did. All you have to do is just follow a similar but different track from Palmer.

Take the Tango Track

Let's take for granted that every sporting contest follows the general theme of wins and losses, namely

Everyone starts off at 0, meaning 0 wins and 0 losses. After every play, whether a batted ball, a shot on goal, a serve, etc, the outcome of the game has changed slightly. And it has changed equally for each side. Suppose that a goal is scored at 5 minutes in hockey. What is the likelihood of the team scoring winning the game? Perhaps the estimate is that it advances you 20% towards your goal of winning. On the flip side, it advances the opponent who gave up the goal 20% towards the loss.

Every event causes a shift, either slightly (taking a called strike pitch on a 3-0 count in the 1st inning) or massively (down by 3 runs in bottom of the 9th, bases loaded, 2 outs, 0-2 count, HR). And of course, the direction can change as well. You can find yourself 20% towards a Loss after 3 innings, and then find yourself 30% towards a Win after scoring 4 runs in the 4th.

Win and Loss Advancements

What you can do is to count each of these movements within a game. You can put the "good" events into one ledger "Win Advancement" and the "bad" events into another ledger "Loss advancement". At the end of the game, you add up all these ledger entries. You will find that the total of your Win Advancement minus Loss Advancement will equal to exactly 1 for the winning team. Loss Advancement minus Win Advancement will also equal exactly 1 for the losing team.

The other important point is that it doesn't matter (too much) if you play on a .400 team or a .600 team. The win advancement potential of a single will be close in either case. However, being on a very good or very bad team will start to skew things. Your potential to maximize your Win advancement is to play in as many close games as possible. The more blowouts you play in (on either side), the less win (or loss) impact you will have. We are not trying to measure what a .300 hitter would do on an average team, but what a .300 hitter did do on his actual team. The closer the games, the more impact this player will have, and the more value he will generate.

You will "probably" find that over the course of a season, that the winning team will have 1.50 Win Advancements, and 0.50 Loss Advancements for each game (and the reverse for the losing team). So, a team that wins 100 and loses 62 will end up with 181 Win Advancements and 143 Loss Advancements. That difference is exactly 38, which is the difference between the wins (100) and the losses (62). Not coincidentally, Wins + 81 equals Win Advancement (same for losses). You can add up the totals for all the players, and you'll end up with a player's Win Advancement total and Loss Advancement total.

Even better is that everything remains in balance after every pitch. There is no need to adjust or rebalance anything.


One track that you can follow is that positive events (hits, HR, walks) lead to a change in Win Advancement, while negative events (like outs) lead to a change in Loss Advancement. I believe that you can determine, with a little effort, how to estimate the Win Advancement and Loss Advancement points. And it will have a direct relationship to Palmer's Linear Weights.



Note 1: I have not read the Mills book, and my example here is taken from my memory of 15 years ago from what was written in the Hidden Game of Baseball. Whether Mills did exactly this or not is not important. I just want to attribute the idea to them.

Note 2: the chart I show regarding the WE is an estimate based on my simulator. In fact, you'd have to have separate WE tables for every park. This WE chart gets even more complicated, as you'd have to account for fielding. But that's the topic of another article.