Strategy June 20, 2006

# Projecting Wins

By Bob Hoyng

Projecting the number of games a team is going to win during the course of the upcoming year is definitely not to the point that it’s an exact science. We can try to use tools such as the expected lineup’s Runs Created/27 outs or other such methods to project the runs the team will score. We can look at what type of era we expect the team to put up as a whole as well, and apply the Pythagorean Expectation formula to try and estimate the team’s wins. It’s kind of like predicting the weather – it may not be 100% but it’s the best that we’ve got.

My interest in this article is in explaining how we can extend this approach to predicting pitchers. And more importantly to try and project the wins for ALL pitchers – not just starting pitchers. In order to determine the winning percentage for a team from the Pythagorean Expectation formula we need two numbers – runs scored and runs against. In projecting the wins for pitchers we need one extra number – the number of opportunities (decisions) that we expect the pitcher to receive. While there can certainly be progress made from the point that this article will take us, the general approach that I will lay out here is a good start to estimating the number of decisions any pitcher will receive. Before we get into the detailed examination of predicting opportunities though, let’s take a look at the first two numbers – runs scored and runs against.

Runs scored is very simple for the purposes of this article. We’re simply taking the expected runs scored per game for the pitcher’s team. There are many ways to project this… modeling an entire season based on player projections using Diamond Mind Baseball, adding up one ninth of the RC/27 for each hitter in the lineup as well as many other methods. Obviously the better your runs scored projection the better your wins projection will be so it’s definitely worth the time to get a solid projection for each team’s expected offensive output, before you start the process of projecting the wins for a pitcher.

Runs allowed can be determined in a few ways. ERA would be the most obvious approach. If you use ERA then it would make sense to add a modifier to simulate the number of unearned runs given up. I’ve found in looking at past data that 1.1 * ERA usually comes fairly close to the total runs given up. If you’re looking for a more skills based estimation (especially important for MR’s whose ERA’s are often lower than they should be since they allow inherited runners to score but don’t give up their own runs) then I would recommend using a Defense Independent Pitching Statistic like DICE. Just like ERA, I would use 1.1 * DICE to simulate the unearned runs that score (since DICE is supposed to represent ERA).

The number of decisions that we can expect the pitcher to receive is a bit trickier. Before we get into the nuts and bolts though, I think it’s worthwhile to look at the obvious. Every game has two decisions given out – a win and a loss. Every game also averages about 18 innings pitched. Each year I’ve looked at has been different, as extra inning games and home teams only coming to the plate 8 times in a winning game effect the total number of innings pitched in a game, but for the most part it averages out to about 18 innings pitched per game. So when we average that out we see that we can expect about 1 decision every 9 innings pitched. That’s a very important number because it gives us a good benchmark from which to examine our numbers once we begin delving in to the specific types of roles that pitchers perform.

Projection decisions for a starting pitcher is very easy once you consider the important axiom we uncovered above: Every 9 innings pitched will yield 1 decision. It’s so brutally simple that it’s amazing. If a pitcher pitches 36 innings over the course of 4 complete game outings then he is obviously going to end up with 4 decisions – he was the only pitcher in the game. Most starting pitcher’s seem to hover just above 2/3 of their starts ending in decisions. Not surprisingly, most starting pitchers also seem to hover just above 6 innings pitched per start. Most of you have probably already realized our formula for predicting the number of decisions for starting pitchers – IP / 9. However, this is just a theoretically derived formula. How well does it hold up when you apply it to real baseball? The answer is surprisingly well, but not well enough to keep us from revising the formula. Obviously starting pitchers have a slight advantage in receiving a win in that their team just needs to maintain the lead once they’ve left with the lead. This leads to a slight advantage for starting pitchers which is supported by the actual statistics from the 2003-2005 seasons. Instead of 9 innings pitched per decision, starting pitchers averaged 8.435 IP / Decision, meaning that our formula we should use to determine the number of decisions is IP / 8.435. This formula could obviously be refined simply by examining more data. Correlation could be looked for between the number of runs scored, versus the league average by the pitcher’s team, in making it easier to get a decision (ie: if your team scores more runs, does it lower the number of innings it takes on average to receive a decision). But as a projection tool I’d say IP / 8.435 is a great starting point for starting pitchers.

Projecting decisions for middle relievers and closers followed the same mindset going in. The only tricky part, which I don’t plan on covering in detail during the course of this examination, is leverage. Some middle relievers (Scott Shields for instance) are almost always used in high leverage situations. Others are almost never used in high leverage situations. I would venture a guess that the innings pitched by the Scott Shields types are vastly underrepresented in the total number of innings pitched by middle relievers, which would explain the following numbers. Over the course of the 2003-2005 seasons middle relievers averaged 10.099 IP / Decision, while closers averaged 8.787 IP / Decision. This is where it gets tricky though. It looks like closers are very close to SP’s in their ability to get wins while middle relievers lag quite a bit behind. But remember what we just mentioned – a small percentage of MR’s are more like closers in their percentage of high leverage innings. Scott Shields for example pitched 345.1 innings over the 3 years we’re studying and received 42 decisions – a 8.222 IP / Decision ratio which is much better than the average MR. Scott Linebrink on the other hand (a very good setup man in his own right) had 250 innings and 24 decisions for a ratio of 10.417 IP / Decision. Was their something different in the usage patterns of these two that led to this discrepancy? Possibly, but I doubt it. It appears that the highest leverage innings as far as receiving a decision, are the first inning (since a starting pitcher need only have the lead when he leaves, and have his team hold that lead) and the final inning (since many games are decided in the last at bat). Since closers almost always pitch these final innings, all non-closer relief pitchers are going to have a slightly lower chance of recording a decision. From 2003-2005 this is represented by closers being 96.00% as likely as a starter to receive a decision, while middle relievers were only are 83.53% as likely to receive a decision.

So what’s the bottom line? To determine wins, we need to first settle on the expected run support per game. Then we need to determine how many runs our pitcher we’re examining will give up per game (I would recommend 1.1 * DICE). Then apply one of the Pythagorean Expectation formulas – I would use RF ^ 1.82 / (RF ^ 1.82 + RA ^ 1.82). Finally we need to determine our expected number of decisions. For starting pitchers I would recommend IP / 8.435. For closers I would recommend IP / 8.787. For middle relievers you have a decision to make. Do you think this pitcher is closer to a closer in innings leverage, a standard MR, or even slightly worse than a standard MR. As I showed with the Linebrink example above though, even high leverage MR’s can fall closer to the average – the fact that they aren’t finishing games and they’re not the #1 closer on their team can hurt those decision totals. I would definitely not be against the approach of applying IP / 10.099 to ALL middle relievers and would caution against adjusting that number too far for anyone but Shields himself. Once you determine the number of expected decisions you would simply multiply the result from the Pythagorean Expectation formula (which returns an expected winning percentage) by the number of decisions and voila – we have our projected wins.

Let’s do a simple example. Take Scott Shields for instance. Let’s say we expect him to pitch 100 innings this year with a DICE of 2.90. Let’s say we expect the Angels to score about 4.4 runs per game. Finally, let’s be generous and give Shields an IP / Decision ratio of 9.000. The DICE of 2.90 gives us a total number of runs given up per game of 1.1 * 2.90 or 3.19. The result from the Pythagorean Expectation would be 4.4 ^ 1.82 / (4.4 ^ 1.82 + 3.19 ^ 1.82) or a .642 expected winning percentage. We expect 100 / 9 decisions or 11.11 decisions which we’ll round down to 11. Multiplying those 11 wins by our .642 expected winning percentage gives us about 7 wins for a 7-4 record.

As a final aside, I’d like to discuss the significance of these projections. Once you have win projections with which you are comfortable, the obvious next step for those of us in a limited IP roto league would be to find out how many wins per inning pitched each pitcher is giving us. While on the surface a middle reliever looks less likely to provide us with wins due to their higher IP / Decision ratio, that may not always be the case. Because many of the quality middle relievers give up less runs than the starters that you can get at the same point in the draft, they will provide more wins per decision than a lesser starting pitcher. As a simple example we projected Shields to give us 7 wins in 100 innings. A bad starting pitcher that has an inverse winning percentage to Shields (ie a .358 instead of .642) that pitches 202.1 innings would get about 24 decisions to Shields’ 11, but would only get 8 or 9 wins. Even a starting pitcher with a .500 expected winning percentage would only put up 12 wins in this example. While both starting pitchers put up more wins than Shields, we can see that Shields took less innings to contribute each win – 14.29 IP / win for Shields, versus 16.86 IP / win for the .500 pitcher, and 25.29 IP / win for a SP that only contributed 8 wins. Especially in a low max IP league (such as the 1250 IP limit in standard Yahoo leagues) this is an important concern. If you have the roster space for a Scott Shields, or any other MR that projects to at least match if not better the IP / win ratio of a replacement level starting pitcher, then it makes a lot of sense to pick them up. Since their ratios (k/9, era and whip) are usually superior to all but the best starting pitchers, even a slightly worse IP / win makes them a positive play. When the IP / win is in favor of the middle reliever it becomes a no-brainer – a quality middle reliever is usually better for your end of the year bottom line in wins, than a mediocre starting pitcher.

 2003 2003 2003 2004 2004 2004 2005 2005 2005 Total Total Total Dec% IP Dec IP/Dec IP Dec IP/Dec IP Dec IP/Dec IP Dec IP/Dec Starter 17554 2146 8.180 19024 2222 8.562 20908 2447 8.544 57486 6815 8.435 100.00% Middle Reliever 8807 819 10.753 9913 1045 9.486 9334 914 10.212 28054 2778 10.099 83.53% Closer 2964 340 8.718 2637 280 9.418 2588.3 312 8.296 8189.3 932 8.787 96.00% Starter – Any pitcher who did not have a relief appearance Middle Reliever – Any pitcher who did not start a game and had less than 8 saves Closer – Any pitcher with 8 or more saves

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