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The Challenge Rating System

Today's post was written by Solanus, with a little editing by me. I asked him to write up a description of his Challenge Rating system, which he developed as a way to measure strength of schedule. He e-mailed it to me last night, so I'm posting it for him this morning. Thanks, Solanus, for writing this up; the floor is now yours.

We've heard everybody complain that such-and-such team has bloated its record by piling up wins against easy opponents, or that all of our team's opponents get hot just in time to face us. These statements are usually backed up by cherry-picked examples or partially remembered anecdotes. Wanting to get a clearer picture of what was actually happening (and trying to kill significant dead-time at work without resorting to HR-alert-worthy options), I came up with a system to determine the strength of schedule for every team in the majors.

The Challenge Rating (CR) is a weighted combination of two factors: 1) the opponent's overall winning percentage, and 2) the opponent's winning percentage in games played immediately before and after their series against your team. The first factor measures the opponent's overall skill, and the second estimates the level at which the opponent is playing at the time your team happens to run into them. Teams go through hot and cold spells; they endure injuries and make roster moves which can alter their "degree of difficulty" at various points in the season. Just consider the 2006 Cardinals: They had the second-best record in the NL for most of the year, which would make them seem a difficult foe, but if your team caught them in August --- when they were playing without Eckstein and Edmonds, and with the injured Isringhausen still at closer --- they were not too hard to knock off.

An average CR is 1000; CRs higher than 1000 denote difficult opponents, while those lower than 1000 denote easy ones. An opponent with a CR of 1200 might be a .600 team that's playing at its normal level, or it could be a .500 team that's in the midst of a hot streak; even a .450 team can have a CR of 1200 if it's playing well enough. A CR of 800 would be just the opposite --- a lousy team playing at its usual level, an average team that's playing poorly, or a good team that's hit the skids.

I won't bore everyone with all the math here; for those of you who care, the formula is at the bottom of this post.

Over the course of a season, the average CR of a team's opponents will tend to even out quite a bit --- but not entirely. Some teams will get unlucky and run into more hot opponents than cold ones; others will catch a break and tend to run into teams when they're playing at their worst. This can be pretty revealing. When I first described this system at VEB last season, the Cardinals were 15 games over .500, but the Challenge Rating system showed that the Cardinals' schedule in the first two months of the season had been (as I termed it) "criminally easy." That suggested to me that the team's overall record was partly an illusion: "Collectively they're just a .500 team waiting for Albert to do something spectacular to save the day or for Carp to pitch a gem." That turned out to be a pretty accurate description of the 2006 Cardinals.

What does the CR system say this year? Through their first 41 games, the Cardinals had faced opponents with an average Challenge Rating of 1025, making theirs the 7th most difficult schedule among the 16 NL teams --- slightly tougher than average. The toughest belongs to the Nationals, at 1104. By contrast, the Astros have had the easiest road so far at 868. (The best/worst in the AL: Cleveland at 885, Kansas City at 1142.) Looking deeper into the Cardinals' record, it is fairly apparent that we aren't necessarily as terrible as our record suggests, but we're not any good either:

  • Against bad opponents (CR of 850 or less), the Cards are 4-4. Could be better, but ... meh.
  • Against average opponents (CR between 850 and 1150), the Cards are 11-12. OK, we're an average team playing .500 against other average teams ... meh again.
  • Against good opponents (CR of 1150 or higher), the Cards are 1-9. Yeah, you read that right --- one and FRICKIN' nine. That 1-9 came against the Mets in the opening series (0-3), the two sets against the Brewers (1-4), and the two-game sweep against the Giants.
That's right, the Giants, a 21-22 team overall, were among the Cardinals' toughest challenges this year. That's because they were smoking hot at the time the Cards hit them --- they came into the series on a mild hot streak (won 3 out of 5) and then went 5-0 after the Cardinals left town. Because they were 8-2 before/after they played the Cardinals, the Giants had a high CR of 1270 for that series --- they were an average team that happened to be playing very well when they came up on the Cards' schedule.

By contrast, when the Astros played them last week, the Giants didn't pose nearly as difficult a challenge; San Fran went 2-3 coming into the series and has gone 1-2 since, so Houston caught them at a good time: The Giants' CR for that series was only 855. The Astros took 2 out of 3.

Here's a complete look at the NL Central to date. The "weak" column covers games against opponents with a CR of 850 or lower; "average" applies to opponents between 850 and 1150; and "hard" covers foes at 1150 or higher:

W-L vs weak vs avg vs hard
Brewers 915 27-17 15-8 9-6 3-3
Astros 868 21-22 10-13 7-4 4-5
Cubs 1016 20-22 9-8 4-6 7-8
Pirates 1028 19-24 2-7 15-10 2-7
Cardinals 1025 16-25 4-4 11-12 1-9
Reds 1020 17-27 2-4 11-15 4-8

The Cards have played only 8 games against easy opponents all year, while the Brewers and Astros have played 23 apiece. The Cards have an easy series this week; the Pirates carry a CR of 796 into the series, the third-lowest CR the Cardinals have run into this season. But the Cardinals' own CR is even worse than Pirates' --- an abysmally low 390 --- thanks to the five-game losing streak we're riding. We're a bad team playing badly; there is no easier challenge. I really hate to say it, but right now the Cardinals are as a big a slump-buster as I've seen in a while. A win against us right now doesn't mean squat. We're playing like crap, so the opposition should expect to win.

The Math:

  1. Calculate the team's winning percentage in the 5 games before and 5 games after the series in question.
  2. Add 0.5.
  3. Multiply the sum by the team's overall winning percentage times 2.
  4. Multiply by 1000 to get a nice round number.
To use an example, let's calculate the CR for the Cards' last opponent, the Tigers:
  1. Calculate the team's winning percentage in the 5 games before and 5 games after the series in question. The Tigers went 1-4 in the five games before this series, and are 0-0 in the five games after; their winning percentage is .200, or 0.2. (After the Tigers play their next five games, the Challenge Rating score may change.)
  2. Add 0.5. 0.2 plus 0.5 = 0.7.
  3. Multiply the sum by the team's overall winning percentage times 2.The Tigers' overall winning percentage is .628, so the equation is 0.7 x (.628 x 2), or 0.7 x 1.256 = .8792.
  4. Multiply by 1000 to get a nice round number. .8792 x 1000 = 879.2, or 879. That was the Tigers' CR for that series.