Why (and how) I use scoring margin in xHPI.
The use of scoring margin in ranking systems is somewhat controversial. One of the criticisms of early versions of the BCS formula was that the computer systems encouraged teams to “run up the score” in an effort to earn higher ratings by systems that included margin of victory. Consequently, the BCS no longer allows any of its computer rankings to include margin of victory as a factor affecting rankings of teams.
For most people, however, margin of victory is intuitively an important factor in judging the outcome of games. Most people treat, in some way, the scoring margin in a game as an indicator of the relative quality of the two teams. We expect highly ranked teams to blow out weaker opponents, and generally consider them to have had a bad game if they fail to do so. We tend to view betting lines the same way. The point spread set by oddsmakers is viewed by most people as the difference in quality between the two teams. That intuition is supported by experience–while there are plenty of upsets, close games that shouldn’t be close, and blowouts that shouldn’t be blowouts, most people would agree that generally, the scoring margin of most games generally is a pretty close reflection of the difference in quality between those two teams.
As I’ve developed xHPI over the past few years, I’ve thought it’s important to retain that intuitive idea that we share. My rankings treat each game as information about the teams involved, and scoring margin in the game is an important element of that information.
Despite what I feel is a pretty compelling reason to incorporate scoring margin, it’s important to address some of the reasons that people object to its use in rankings. Those who raise these objections have some valid points.
Running up the score – This is the primary reason that the BCS has not allowed computer rankings that incorporate scoring margin to be part of the BCS selection process since the 2004 season. Commentators were convinced that some coaches were running up the score in blowouts in an effort to look better on some of the computer rankings, with the hope that those improved rankings would help them land in a berth in a BCS bowl game, or even the BCS championship game. While no college football coach is even aware of xHPI (and they wouldn’t really care about xHPI if they did), I still think it’s important to deal with this objection. The flip side of this argument may actually be more important for relatively unknown computer rankings like xHPI: teams’ efforts to avoid running up the score have the effect of depressing their ranking, because their true ability is not demonstrated.
xHPI addresses these related problems by using a measure of “game dominance” rather than final score. The final score margin is an important part of this measure; in fact, it makes up half of the dominance measure*. The other half of the measure is a weighted average of the score at the end of each quarter. The weighting process essentially reduces the effect of any one quarter in isolation, so that if a dominant team does run up the score, its late scores are discounted. I won’t explain the weighting process here. It will be addressed in the “Technical Note” section of this blog.
*Throughout this paragraph I use “score,” but technically, I don’t mean the actual score. I substitute a “share of the total score” measure for score, as will be explained below.
The game that got away – A similar objection to scoring margin as a measure of the relative strength of any two teams is based on the fact that weird things sometimes happen (and happen systematically) in the late minutes of relatively games. In such games, the team that is behind often finds that it has to gamble to have a chance to win. Sometimes these gambles pay off, but often they do not, leading to easy scoring chances for the team that is in the lead. Such games often end up with much wide scoring margins that do not match the closeness of the majority of the game.
The same adjustment that contributes minimizes the effect of running up the score also addresses this objection. The winning team gets credit for winning and partial credit for the scoring margin, but a significant component of the “dominance” measure reflects the closeness of the game.
Pace – The innovations in college football offense in recent years suggests a third (and to me, the most significant) problem with using scoring margin. High-powered offenses such as the spread offenses that many teams use have contributed to an significant increase in the average total of points scored in games. Generally, offenses are able to score much more quickly, which also means that defenses are more susceptible to giving up quick scores. That affects what a given scoring margin truly signifies. When scores are high (particularly for both times), I believe that the actual scoring margin does not reflect the same degree of closeness of a game as when scores are relative low. For example, a 56-28 victory indicates a solid victory for a team, but I would argue that it does not reflect the same degree of dominance that a 28-0 victory demonstrates. In the latter case, the winning team demonstrated an ability to score, while being defensively dominant. In both cases, the scoring margin was the same, but I believe that the winning team was much more dominant in the lower scoring game.
xHPI addresses this issue by substituting the adjusted percentage of total points scored for the actual scoring margin. This adjustment is applied both to the final score (which accounts for half of the dominance measure) and each quarterly score (whose weighted averages account for the other half). The adjustment, which is explained in the Technical Note, is made to remove the effect of a score of zero for a team. Without the adjustment, a 7-0 victory would look as dominant as a 28-0 victory, for example, which runs counter to most fans’ beliefs. However, the adjustment still preserves some reward for a shutout, because it would still give more credit for a 7-0 victory than a 42-35 victory.