What's a Chris Singleton Worth?

I'm currently working on a program that will allow me to replace a player in a team's lineup with one or more players, or even to build theoretical lineups and player rotations from scratch. This will have some fun applications--who would win if all-conference teams could play each other?--but more importantly it'll make it possible to assess exactly what kind of impact an injury or suspension of a key player is likely to have on a team. It's not ready yet, but hopefully I'll have the bugs worked out in time for the NCAA Tournament.

Until then, though, we can use PAPER to make some quick calculations about what kind of impact a key player's absence might have. Here's how, using Florida State's Chris Singleton, out for at least a month with a broken foot, as the test case:

PAPER tells us that Singleton is an ordinary offensive player (worth 0.1 points per 100 possessions less than an average BCS-league power forward) and an outstanding defensive one (5.2 points per 100 possessions better than an average BCS power forward). For every 40 minutes that Singleton spends on the floor, his team is going to be about 3⅓ points better than they would be if they had an ordinary player.

Of course, Florida State won't be replacing Singleton with one ordinary player; they'll be filling his 30 minutes per game by increasing the minutes played by Okaro White and Bernard James and the return from injury of Xavier Gibson and Terrance Shannon. So we'll have to make some guesses about how Leonard Hamilton will distribute playing time, and four our purposes I'm going to give 10 minutes each to White and James and 5 minutes each to Gibson and Shannon. According to PAPER, the rates for the five players in question are thus:

Player	Offense	Defense
Chris Singleton	-0.10	-5.21
Okaro White	-0.55	-1.11
Bernard James	-0.23	-3.34
Xavier Gibson	-4.16	+0.26
Terrance Shannon	-4.27	+0.85

The value of the four-headed monster replacing Singleton can be determined by simply multiplying each individual's value by the share of Singleton's minutes he'll be filling, so on offense it's:

[(-0.55 x 10) + (-0.23 x 10) + (-4.16 x 5) + (-4.27 x 5)] / 30

Which yields -1.67 points per 100 possessions. Since Singleton himself is worth -0.1 points per 100 possessions, the difference between Singleton and his replacements on offense is -1.57 points per 100 possessions. Performing the same calculation for the defensive side of the ball, we get a value for the four-headed replacement of -1.3 points per 100 possessions, or 3.91 points per 100 possessions more than Singleton would allow.

All this is still pretty abstract, so it's time to put those numbers into context. To do that, let's apply them to Florida State's TAPE ratings. To do that, we just multiply each difference by the proportion of FSU's minutes played by Singleton (because the 25% of the game during which Singleton was on the bench before will for our purposes be unaffected by his absence), and then add that number to FSU's offensive and defensive effectiveness.

On offense, a Singleton-free Florida State team would score 0.9459 points per possession against an average BCS team, which drops the Seminoles from #157 to #190 nationally. On defense, they would allow 0.9434 points per possession, which amazingly still keeps them at #2 in the nation. What's important here is to note that the offensive number is still higher than the defensive one. Florida State's TAPE rating without Singleton would be .50484. Since TAPE is scaled to BCS-average, that means that even without Singleton, the Seminoles would be an NCAA Tournament bubble team.

Bottom line: In terms of points on the scoreboard, over the course of a 40-minute, 69-possession conference game, Florida State will score 0.8 fewer points and give up 2 more points without Singleton than they would with him. Over the final five games of the season, his absence is going to cost the Seminoles about four-tenths of a win. It shouldn't keep Florida State out of the NCAA Tournament, but if Singleton's still not ready to go by mid-March, it probably should cost Florida State a couple seed-lines on the S-curve.